· the parma polyhedra library conﬁgured java language interface user’s manual (version 1.2)...

The Parma Polyhedra LibraryConfigured Java Language Interface

User’s Manual∗

(version 1.2)

Roberto Bagnara†

Patricia M. Hill‡Enea Zaffanella§

Abramo Bagnara¶

February 11, 2016

∗This work has been partly supported by: University of Parma’s FIL scientific research project (ex 60%) “Pure and Applied Math-ematics”; MURST project “Automatic Program Certification by Abstract Interpretation”; MURST project “Abstract Interpretation,Type Systems and Control-Flow Analysis”; MURST project “Automatic Aggregate- and Number-Reasoning for Computing: fromDecision Algorithms to Constraint Programming with Multisets, Sets, and Maps”; MURST project “Constraint Based Verificationof Reactive Systems”; MURST project “Abstract Interpretation: Design and Applications”; EPSRC project “Numerical Domains forSoftware Analysis”; EPSRC project “Geometric Abstractions for Scalable Program Analyzers”.†[email protected], Department of Mathematics, University of Parma, Italy, and BUGSENG srl.‡[email protected], BUGSENG srl.§[email protected], Department of Mathematics, University of Parma, Italy, and BUGSENG srl.¶[email protected], BUGSENG srl.

Copyright © 2001–2010 Roberto Bagnara ([email protected])Copyright © 2010–2016 BUGSENG srl (http://bugseng.com)

This document describes the Parma Polyhedra Library (PPL).Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free

Documentation License, Version 1.2 or any later version published by the Free Software Foundation; withno Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is includedin the section entitled “GNU Free Documentation License”.

The PPL is free software; you can redistribute it and/or modify it under the terms of the GNU GeneralPublic License as published by the Free Software Foundation; either version 3 of the License, or (at youroption) any later version. A copy of the license is included in the section entitled “GNU GENERALPUBLIC LICENSE”.

The PPL is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; withouteven the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Seethe GNU General Public License for more details.

If you have not received a copy of one or both the above mentioned licenses along with the PPL, writeto the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.

For the most up-to-date information see the Parma Polyhedra Library site:

http://bugseng.com/products/ppl/

3

http://www.fsf.org

http://www.fsf.org

http://bugseng.com/products/ppl/

Contents1 Main Page 1

2 GNU General Public License 2

3 GNU Free Documentation License 11

4 Module Index 154.1 Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Namespace Index 155.1 Namespace List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6 Hierarchical Index 166.1 Class Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Class Index 217.1 Class List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

8 Module Documentation 318.1 Java Language Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

9 Namespace Documentation 339.1 Package parma polyhedra library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

10 Class Documentation 4110.1 parma polyhedra library.Artificial Parameter Class Reference . . . . . . . . . . . . . . 4110.2 parma polyhedra library.Artificial Parameter Sequence Class Reference . . . . . . . . 4210.3 parma polyhedra library.BD Shape double Class Reference . . . . . . . . . . . . . . . 4210.4 parma polyhedra library.BD Shape float Class Reference . . . . . . . . . . . . . . . . 4610.5 parma polyhedra library.BD Shape int16 t Class Reference . . . . . . . . . . . . . . . 5010.6 parma polyhedra library.BD Shape int32 t Class Reference . . . . . . . . . . . . . . . 5310.7 parma polyhedra library.BD Shape int64 t Class Reference . . . . . . . . . . . . . . . 5710.8 parma polyhedra library.BD Shape int8 t Class Reference . . . . . . . . . . . . . . . . 6110.9 parma polyhedra library.BD Shape long double Class Reference . . . . . . . . . . . . 6510.10 parma polyhedra library.BD Shape mpq class Class Reference . . . . . . . . . . . . . 6810.11 parma polyhedra library.BD Shape mpz class Class Reference . . . . . . . . . . . . . 7210.12 parma polyhedra library.Bounded Integer Type Overflow Enum Reference . . . . . . . 7610.13 parma polyhedra library.Bounded Integer Type Representation Enum Reference . . . . 7610.14 parma polyhedra library.Bounded Integer Type Width Enum Reference . . . . . . . . 7710.15 parma polyhedra library.By Reference< T > Class Template Reference . . . . . . . . 7710.16 parma polyhedra library.C Polyhedron Class Reference . . . . . . . . . . . . . . . . . 7810.17 parma polyhedra library.Coefficient Class Reference . . . . . . . . . . . . . . . . . . . 8010.18 parma polyhedra library.Complexity Class Enum Reference . . . . . . . . . . . . . . . 8110.19 parma polyhedra library.Congruence Class Reference . . . . . . . . . . . . . . . . . . 8110.20 parma polyhedra library.Congruence System Class Reference . . . . . . . . . . . . . . 8210.21 parma polyhedra library.Constraint Class Reference . . . . . . . . . . . . . . . . . . . 8210.22 parma polyhedra library.Constraint System Class Reference . . . . . . . . . . . . . . . 8310.23 parma polyhedra library.Constraints Product C Polyhedron Grid Class Reference . . . 8310.24 parma polyhedra library.Constraints Product Grid C Polyhedron Class Reference . . . 8710.25 parma polyhedra library.Constraints Product Grid NNC Polyhedron Class Reference . 9010.26 parma polyhedra library.Constraints Product NNC Polyhedron Grid Class Reference . 9410.27 parma polyhedra library.Control Parameter Name Enum Reference . . . . . . . . . . . 9810.28 parma polyhedra library.Control Parameter Value Enum Reference . . . . . . . . . . . 98

The PPL Configured Java Language Interface User’s Manual (version 1.2). See http://bugseng.com for more information.

http://bugseng.com

10.29 parma polyhedra library.Degenerate Element Enum Reference . . . . . . . . . . . . . 9810.30 parma polyhedra library.Domain Error Exception Class Reference . . . . . . . . . . . 9910.31 parma polyhedra library.Double Box Class Reference . . . . . . . . . . . . . . . . . . 9910.32 parma polyhedra library.Float Box Class Reference . . . . . . . . . . . . . . . . . . . 10310.33 parma polyhedra library.Generator Class Reference . . . . . . . . . . . . . . . . . . . 10610.34 parma polyhedra library.Generator System Class Reference . . . . . . . . . . . . . . . 10810.35 parma polyhedra library.Generator Type Enum Reference . . . . . . . . . . . . . . . . 10810.36 parma polyhedra library.Grid Class Reference . . . . . . . . . . . . . . . . . . . . . . 10910.37 parma polyhedra library.Grid Generator Class Reference . . . . . . . . . . . . . . . . 11310.38 parma polyhedra library.Grid Generator System Class Reference . . . . . . . . . . . . 11410.39 parma polyhedra library.Grid Generator Type Enum Reference . . . . . . . . . . . . . 11410.40 parma polyhedra library.Int16 Box Class Reference . . . . . . . . . . . . . . . . . . . 11510.41 parma polyhedra library.Int32 Box Class Reference . . . . . . . . . . . . . . . . . . . 11910.42 parma polyhedra library.Int64 Box Class Reference . . . . . . . . . . . . . . . . . . . 12210.43 parma polyhedra library.Int8 Box Class Reference . . . . . . . . . . . . . . . . . . . . 12610.44 parma polyhedra library.Invalid Argument Exception Class Reference . . . . . . . . . 13010.45 parma polyhedra library.IO Class Reference . . . . . . . . . . . . . . . . . . . . . . . 13010.46 parma polyhedra library.Length Error Exception Class Reference . . . . . . . . . . . . 13110.47 parma polyhedra library.Linear Expression Class Reference . . . . . . . . . . . . . . . 13110.48 parma polyhedra library.Linear Expression Coefficient Class Reference . . . . . . . . 13210.49 parma polyhedra library.Linear Expression Difference Class Reference . . . . . . . . . 13310.50 parma polyhedra library.Linear Expression Sum Class Reference . . . . . . . . . . . . 13410.51 parma polyhedra library.Linear Expression Times Class Reference . . . . . . . . . . . 13510.52 parma polyhedra library.Linear Expression Unary Minus Class Reference . . . . . . . 13610.53 parma polyhedra library.Linear Expression Variable Class Reference . . . . . . . . . . 13710.54 parma polyhedra library.Logic Error Exception Class Reference . . . . . . . . . . . . 13710.55 parma polyhedra library.Long Double Box Class Reference . . . . . . . . . . . . . . . 13810.56 parma polyhedra library.MIP Problem Class Reference . . . . . . . . . . . . . . . . . 14110.57 parma polyhedra library.MIP Problem Status Enum Reference . . . . . . . . . . . . . 14710.58 parma polyhedra library.NNC Polyhedron Class Reference . . . . . . . . . . . . . . . 14710.59 parma polyhedra library.Octagonal Shape double Class Reference . . . . . . . . . . . 15010.60 parma polyhedra library.Octagonal Shape float Class Reference . . . . . . . . . . . . . 15310.61 parma polyhedra library.Octagonal Shape int16 t Class Reference . . . . . . . . . . . 15710.62 parma polyhedra library.Octagonal Shape int32 t Class Reference . . . . . . . . . . . 16110.63 parma polyhedra library.Octagonal Shape int64 t Class Reference . . . . . . . . . . . 16510.64 parma polyhedra library.Octagonal Shape int8 t Class Reference . . . . . . . . . . . . 16810.65 parma polyhedra library.Octagonal Shape long double Class Reference . . . . . . . . . 17210.66 parma polyhedra library.Octagonal Shape mpq class Class Reference . . . . . . . . . . 17610.67 parma polyhedra library.Octagonal Shape mpz class Class Reference . . . . . . . . . . 17910.68 parma polyhedra library.Optimization Mode Enum Reference . . . . . . . . . . . . . . 18310.69 parma polyhedra library.Overflow Error Exception Class Reference . . . . . . . . . . . 18410.70 parma polyhedra library.Pair< K, V > Class Template Reference . . . . . . . . . . . . 18410.71 parma polyhedra library.Parma Polyhedra Library Class Reference . . . . . . . . . . . 18410.72 parma polyhedra library.Partial Function Class Reference . . . . . . . . . . . . . . . . 18710.73 parma polyhedra library.PIP Decision Node Class Reference . . . . . . . . . . . . . . 18810.74 parma polyhedra library.PIP Problem Class Reference . . . . . . . . . . . . . . . . . . 18810.75 parma polyhedra library.PIP Problem Control Parameter Name Enum Reference . . . 19210.76 parma polyhedra library.PIP Problem Control Parameter Value Enum Reference . . . . 19210.77 parma polyhedra library.PIP Problem Status Enum Reference . . . . . . . . . . . . . . 19310.78 parma polyhedra library.PIP Solution Node Class Reference . . . . . . . . . . . . . . 19310.79 parma polyhedra library.PIP Tree Node Class Reference . . . . . . . . . . . . . . . . . 19410.80 parma polyhedra library.Pointset Powerset BD Shape double Class Reference . . . . . 19510.81 parma polyhedra library.Pointset Powerset BD Shape double Iterator Class Reference 19710.82 parma polyhedra library.Pointset Powerset BD Shape float Class Reference . . . . . . 198

ii

10.83 parma polyhedra library.Pointset Powerset BD Shape float Iterator Class Reference . . 20010.84 parma polyhedra library.Pointset Powerset BD Shape int16 t Class Reference . . . . . 20110.85 parma polyhedra library.Pointset Powerset BD Shape int16 t Iterator Class Reference . 20310.86 parma polyhedra library.Pointset Powerset BD Shape int32 t Class Reference . . . . . 20410.87 parma polyhedra library.Pointset Powerset BD Shape int32 t Iterator Class Reference . 20610.88 parma polyhedra library.Pointset Powerset BD Shape int64 t Class Reference . . . . . 20610.89 parma polyhedra library.Pointset Powerset BD Shape int64 t Iterator Class Reference . 20910.90 parma polyhedra library.Pointset Powerset BD Shape int8 t Class Reference . . . . . . 20910.91 parma polyhedra library.Pointset Powerset BD Shape int8 t Iterator Class Reference . 21210.92 parma polyhedra library.Pointset Powerset BD Shape long double Class Reference . . 21210.93 parma polyhedra library.Pointset Powerset BD Shape long double Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410.94 parma polyhedra library.Pointset Powerset BD Shape mpq class Class Reference . . . 21510.95 parma polyhedra library.Pointset Powerset BD Shape mpq class Iterator Class Refer-

ence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21710.96 parma polyhedra library.Pointset Powerset BD Shape mpz class Class Reference . . . 21810.97 parma polyhedra library.Pointset Powerset BD Shape mpz class Iterator Class Refer-

ence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22010.98 parma polyhedra library.Pointset Powerset C Polyhedron Class Reference . . . . . . . 22110.99 parma polyhedra library.Pointset Powerset C Polyhedron Iterator Class Reference . . . 22310.100 parma polyhedra library.Pointset Powerset Double Box Class Reference . . . . . . . . 22310.101 parma polyhedra library.Pointset Powerset Double Box Iterator Class Reference . . . . 22610.102 parma polyhedra library.Pointset Powerset Float Box Class Reference . . . . . . . . . 22610.103 parma polyhedra library.Pointset Powerset Float Box Iterator Class Reference . . . . . 22810.104 parma polyhedra library.Pointset Powerset Grid Class Reference . . . . . . . . . . . . 22910.105 parma polyhedra library.Pointset Powerset Grid Iterator Class Reference . . . . . . . . 23110.106 parma polyhedra library.Pointset Powerset Int16 Box Class Reference . . . . . . . . . 23210.107 parma polyhedra library.Pointset Powerset Int16 Box Iterator Class Reference . . . . . 23410.108 parma polyhedra library.Pointset Powerset Int32 Box Class Reference . . . . . . . . . 23410.109 parma polyhedra library.Pointset Powerset Int32 Box Iterator Class Reference . . . . . 23710.110 parma polyhedra library.Pointset Powerset Int64 Box Class Reference . . . . . . . . . 23710.111 parma polyhedra library.Pointset Powerset Int64 Box Iterator Class Reference . . . . . 23910.112 parma polyhedra library.Pointset Powerset Int8 Box Class Reference . . . . . . . . . . 24010.113 parma polyhedra library.Pointset Powerset Int8 Box Iterator Class Reference . . . . . 24210.114 parma polyhedra library.Pointset Powerset Long Double Box Class Reference . . . . . 24310.115 parma polyhedra library.Pointset Powerset Long Double Box Iterator Class Reference 24510.116 parma polyhedra library.Pointset Powerset NNC Polyhedron Class Reference . . . . . 24510.117 parma polyhedra library.Pointset Powerset NNC Polyhedron Iterator Class Reference . 24810.118 parma polyhedra library.Pointset Powerset Octagonal Shape double Class Reference . 24810.119 parma polyhedra library.Pointset Powerset Octagonal Shape double Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25010.120 parma polyhedra library.Pointset Powerset Octagonal Shape float Class Reference . . . 25110.121 parma polyhedra library.Pointset Powerset Octagonal Shape float Iterator Class Refer-

ence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25310.122 parma polyhedra library.Pointset Powerset Octagonal Shape int16 t Class Reference . 25410.123 parma polyhedra library.Pointset Powerset Octagonal Shape int16 t Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25610.124 parma polyhedra library.Pointset Powerset Octagonal Shape int32 t Class Reference . 25710.125 parma polyhedra library.Pointset Powerset Octagonal Shape int32 t Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25910.126 parma polyhedra library.Pointset Powerset Octagonal Shape int64 t Class Reference . 26010.127 parma polyhedra library.Pointset Powerset Octagonal Shape int64 t Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26210.128 parma polyhedra library.Pointset Powerset Octagonal Shape int8 t Class Reference . . 262

iii

10.129 parma polyhedra library.Pointset Powerset Octagonal Shape int8 t Iterator Class Ref-erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

10.130 parma polyhedra library.Pointset Powerset Octagonal Shape long double Class Refer-ence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

10.131 parma polyhedra library.Pointset Powerset Octagonal Shape long double Iterator ClassReference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

10.132 parma polyhedra library.Pointset Powerset Octagonal Shape mpq class Class Reference 26810.133 parma polyhedra library.Pointset Powerset Octagonal Shape mpq class Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27110.134 parma polyhedra library.Pointset Powerset Octagonal Shape mpz class Class Reference 27110.135 parma polyhedra library.Pointset Powerset Octagonal Shape mpz class Iterator Class Ref-

erence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27310.136 parma polyhedra library.Pointset Powerset Rational Box Class Reference . . . . . . . 27410.137 parma polyhedra library.Pointset Powerset Rational Box Iterator Class Reference . . . 27610.138 parma polyhedra library.Pointset Powerset Uint16 Box Class Reference . . . . . . . . 27710.139 parma polyhedra library.Pointset Powerset Uint16 Box Iterator Class Reference . . . . 27910.140 parma polyhedra library.Pointset Powerset Uint32 Box Class Reference . . . . . . . . 27910.141 parma polyhedra library.Pointset Powerset Uint32 Box Iterator Class Reference . . . . 28210.142 parma polyhedra library.Pointset Powerset Uint64 Box Class Reference . . . . . . . . 28210.143 parma polyhedra library.Pointset Powerset Uint64 Box Iterator Class Reference . . . . 28410.144 parma polyhedra library.Pointset Powerset Uint8 Box Class Reference . . . . . . . . . 28510.145 parma polyhedra library.Pointset Powerset Uint8 Box Iterator Class Reference . . . . 28710.146 parma polyhedra library.Pointset Powerset Z Box Class Reference . . . . . . . . . . . 28810.147 parma polyhedra library.Pointset Powerset Z Box Iterator Class Reference . . . . . . . 29010.148 parma polyhedra library.Poly Con Relation Class Reference . . . . . . . . . . . . . . . 29010.149 parma polyhedra library.Poly Gen Relation Class Reference . . . . . . . . . . . . . . . 29110.150 parma polyhedra library.Polyhedron Class Reference . . . . . . . . . . . . . . . . . . . 29210.151 parma polyhedra library.Rational Box Class Reference . . . . . . . . . . . . . . . . . 29410.152 parma polyhedra library.Relation Symbol Enum Reference . . . . . . . . . . . . . . . 29810.153 parma polyhedra library.Timeout Exception Class Reference . . . . . . . . . . . . . . 29810.154 parma polyhedra library.Uint16 Box Class Reference . . . . . . . . . . . . . . . . . . 29910.155 parma polyhedra library.Uint32 Box Class Reference . . . . . . . . . . . . . . . . . . 30210.156 parma polyhedra library.Uint64 Box Class Reference . . . . . . . . . . . . . . . . . . 30610.157 parma polyhedra library.Uint8 Box Class Reference . . . . . . . . . . . . . . . . . . . 31010.158 parma polyhedra library.Variable Class Reference . . . . . . . . . . . . . . . . . . . . 31410.159 parma polyhedra library.Variable Stringifier Interface Reference . . . . . . . . . . . . . 31410.160 parma polyhedra library.Variables Set Class Reference . . . . . . . . . . . . . . . . . . 31510.161 parma polyhedra library.Z Box Class Reference . . . . . . . . . . . . . . . . . . . . . 315

Index 321

iv

1 Main PageThe Parma Polyhedra Library comes equipped with an interface for the Java language. The Java interfaceprovides access to the numerical abstractions (convex polyhedra, BD shapes, octagonal shapes, etc.) im-plemented by the PPL library. A general introduction to the numerical abstractions, their representationin the PPL and the operations provided by the PPL is given in the main PPL user manual. Here we justdescribe those aspects that are specific to the Java interface. In the sequel, prefix is the path prefix underwhich the library has been installed (typically /usr or /usr/local).

Overview

Here is a list of notes with general information and advice on the use of the Java interface.

• When the Parma Polyhedra Library is configured, it will automatically test for the existence of theJava system (unless configuration options are passed to disable the build of the Java interface; seeconfiguration option --enable-interfaces). If Java is correctly installed in a standard loca-tion, things will be arranged so that the Java interface is built and installed (see configuration option--with-java if you need to specify a non-standard location for the Java system).

• The Java interface files are all installed in the directory prefix/lib/ppl. Since this includesshared and dynamically loaded libraries, you must make your dynamic linker/loader aware of thisfact. If you use a GNU/Linux system, try the commands man ld.so and man ldconfig formore information.

• Any application using the PPL should:

– Load the PPL interface library by calling System.load and passing the full path of thedynamic shared object;

– Make sure that only the intended version(s) of the library has been loaded, e.g., by calling staticmethod version() in class parma polyhedra library.Parma Polyhedra Library;

– Starting from version 0.11, initialize the interface by calling static method initialize ←↩

library(); when all library work is done, finalize the interface by calling finalize ←↩

library().

• The numerical abstract domains available to the Java user as Java classes consist of the simple do-mains, powersets of a simple domain and products of simple domains. Note that the default con-figuration will only enable a subset of these domains (if you need a different set of domains, seeconfiguration option --enable-instantiations).

– The simple domains are:

* convex polyhedra, which consist of C Polyhedron and NNC Polyhedron;

* weakly relational, which consist of BD Shape N and Octagonal Shape N where N is oneof the numeric types signed char, short, int, long, long long, mpz class, mpq class;

* boxes which consist of Int8 Box, Int16 Box, Int32 Box, Int64 Box, Uint8 Box, Uint16 ←↩

Box, Uint32 Box, Uint64 Box, Float Box, Double Box, Long Double Box, Z Box, Rational←↩

Box; and

* the Grid domain.

– The powerset domains are Pointset Powerset S where S is a simple domain.

– The product domains consist of Direct Product S T, Smash Product S T and Constraints ←↩

Product S T where S and T are simple domains.

1

• In the following, any of the above numerical abstract domains is called a PPL domain and anyelement of a PPL domain is called a PPL object.

• A Java program can create a new object for a PPL domain by using the constructors for the classcorresponding to the domain.

• For a PPL object with space dimension k, the identifiers used for the PPL variables must lie between0 and k− 1 and correspond to the indices of the associated Cartesian axes. For example, when usingmethods that combine PPL polyhedra or add constraints or generators to a representation of a PPLpolyhedron, the polyhedra referenced and any constraints or generators in the call should follow allthe (space) dimension-compatibility rules stated in Section Representations of Convex Polyhedra ofthe main PPL user manual.

• As explained above, a polyhedron has a fixed topology C or NNC, that is determined at the timeof its initialization. All subsequent operations on the polyhedron must respect all the topologicalcompatibility rules stated in Section Representations of Convex Polyhedra of the main PPL usermanual.

• A system of constraints (i.e., an instance of class parma polyhedra library.Constraint←↩

System) is implemented by extending class java.util.ArrayList (note: java.util.←↩

Vectorwas used up to version 1.0.) As a consequence, it is possible to iterate over the constraints inthe system by using corresponding inherited methods. Similarly, it is possible to modify a system ofconstraints by using methods such as add; be warned, however, that the constraint system obtainedfrom a PPL object is a copy of the (C++) data structure used in the object itself: any modificationwill not directly affect the original PPL object; clearly, the modified constraint system can be usedwith appropriate methods to, e.g., build a new PPL object or modify an existing one. The sameobservations apply to systems of congruences and systems of (grid) generators.

2 GNU General Public LicenseVersion 3, 29 June 2007

Copyright (C) 2007 Free Software Foundation, Inc. http://fsf.org/Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it

is not allowed.

PreambleThe GNU General Public License is a free, copyleft license for software and other kinds of works.

The licenses for most software and other practical works are designed to take away your freedom toshare and change the works. By contrast, the GNU General Public License is intended to guarantee yourfreedom to share and change all versions of a program–to make sure it remains free software for all itsusers. We, the Free Software Foundation, use the GNU General Public License for most of our software; itapplies also to any other work released this way by its authors. You can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our General Public Licensesare designed to make sure that you have the freedom to distribute copies of free software (and charge forthem if you wish), that you receive source code or can get it if you want it, that you can change the softwareor use pieces of it in new free programs, and that you know you can do these things.

To protect your rights, we need to prevent others from denying you these rights or asking you to sur-render the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or ifyou modify it: responsibilities to respect the freedom of others.

For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass onto the recipients the same freedoms that you received. You must make sure that they, too, receive or canget the source code. And you must show them these terms so they know their rights.

Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on thesoftware, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it.

2

http://fsf.org/

For the developers' and authors' protection, the GPL clearly explains that there is no warranty for thisfree software. For both users' and authors' sake, the GPL requires that modified versions be marked aschanged, so that their problems will not be attributed erroneously to authors of previous versions.

Some devices are designed to deny users access to install or run modified versions of the software insidethem, although the manufacturer can do so. This is fundamentally incompatible with the aim of protectingusers' freedom to change the software. The systematic pattern of such abuse occurs in the area of productsfor individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed thisversion of the GPL to prohibit the practice for those products. If such problems arise substantially in otherdomains, we stand ready to extend this provision to those domains in future versions of the GPL, as neededto protect the freedom of users.

Finally, every program is threatened constantly by software patents. States should not allow patents torestrict development and use of software on general-purpose computers, but in those that do, we wish toavoid the special danger that patents applied to a free program could make it effectively proprietary. Toprevent this, the GPL assures that patents cannot be used to render the program non-free.

The precise terms and conditions for copying, distribution and modification follow.

TERMS AND CONDITIONS

0. Definitions.

“This License” refers to version 3 of the GNU General Public License.“Copyright” also means copyright-like laws that apply to other kinds of works, such as semiconductor

masks.“The Program” refers to any copyrightable work licensed under this License. Each licensee is addressed

as “you”. “Licensees” and “recipients” may be individuals or organizations.To “modify” a work means to copy from or adapt all or part of the work in a fashion requiring copyright

permission, other than the making of an exact copy. The resulting work is called a “modified version” ofthe earlier work or a work “based on” the earlier work.

A “covered work” means either the unmodified Program or a work based on the Program.To “propagate” a work means to do anything with it that, without permission, would make you directly

or secondarily liable for infringement under applicable copyright law, except executing it on a computeror modifying a private copy. Propagation includes copying, distribution (with or without modification),making available to the public, and in some countries other activities as well.

To “convey” a work means any kind of propagation that enables other parties to make or receive copies.Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying.

An interactive user interface displays “Appropriate Legal Notices” to the extent that it includes a con-venient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells theuser that there is no warranty for the work (except to the extent that warranties are provided), that licenseesmay convey the work under this License, and how to view a copy of this License. If the interface presentsa list of user commands or options, such as a menu, a prominent item in the list meets this criterion.

1. Source Code.

The “source code” for a work means the preferred form of the work for making modifications to it. “Objectcode” means any non-source form of a work.

A “Standard Interface” means an interface that either is an official standard defined by a recognizedstandards body, or, in the case of interfaces specified for a particular programming language, one that iswidely used among developers working in that language.

The “System Libraries” of an executable work include anything, other than the work as a whole, that(a) is included in the normal form of packaging a Major Component, but which is not part of that MajorComponent, and (b) serves only to enable use of the work with that Major Component, or to implement aStandard Interface for which an implementation is available to the public in source code form. A “MajorComponent”, in this context, means a major essential component (kernel, window system, and so on) of

3

the specific operating system (if any) on which the executable work runs, or a compiler used to produce thework, or an object code interpreter used to run it.

The “Corresponding Source” for a work in object code form means all the source code needed togenerate, install, and (for an executable work) run the object code and to modify the work, includingscripts to control those activities. However, it does not include the work's System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activitiesbut which are not part of the work. For example, Corresponding Source includes interface definition filesassociated with source files for the work, and the source code for shared libraries and dynamically linkedsubprograms that the work is specifically designed to require, such as by intimate data communication orcontrol flow between those subprograms and other parts of the work.

The Corresponding Source need not include anything that users can regenerate automatically from otherparts of the Corresponding Source.

The Corresponding Source for a work in source code form is that same work.

2. Basic Permissions.

All rights granted under this License are granted for the term of copyright on the Program, and are irrevo-cable provided the stated conditions are met. This License explicitly affirms your unlimited permission torun the unmodified Program. The output from running a covered work is covered by this License only ifthe output, given its content, constitutes a covered work. This License acknowledges your rights of fair useor other equivalent, as provided by copyright law.

You may make, run and propagate covered works that you do not convey, without conditions so longas your license otherwise remains in force. You may convey covered works to others for the sole purposeof having them make modifications exclusively for you, or provide you with facilities for running thoseworks, provided that you comply with the terms of this License in conveying all material for which you donot control copyright. Those thus making or running the covered works for you must do so exclusively onyour behalf, under your direction and control, on terms that prohibit them from making any copies of yourcopyrighted material outside their relationship with you.

Conveying under any other circumstances is permitted solely under the conditions stated below. Subli-censing is not allowed; section 10 makes it unnecessary.

3. Protecting Users' Legal Rights From Anti-Circumvention Law.

No covered work shall be deemed part of an effective technological measure under any applicable lawfulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, orsimilar laws prohibiting or restricting circumvention of such measures.

When you convey a covered work, you waive any legal power to forbid circumvention of technologicalmeasures to the extent such circumvention is effected by exercising rights under this License with respectto the covered work, and you disclaim any intention to limit operation or modification of the work as ameans of enforcing, against the work's users, your or third parties' legal rights to forbid circumvention oftechnological measures.

4. Conveying Verbatim Copies.

You may convey verbatim copies of the Program's source code as you receive it, in any medium, providedthat you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intactall notices stating that this License and any non-permissive terms added in accord with section 7 applyto the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of thisLicense along with the Program.

You may charge any price or no price for each copy that you convey, and you may offer support orwarranty protection for a fee.

4

5. Conveying Modified Source Versions.

You may convey a work based on the Program, or the modifications to produce it from the Program, in theform of source code under the terms of section 4, provided that you also meet all of these conditions:

• a) The work must carry prominent notices stating that you modified it, and giving a relevant date.

• b) The work must carry prominent notices stating that it is released under this License and anyconditions added under section 7. This requirement modifies the requirement in section 4 to “keepintact all notices”.

• c) You must license the entire work, as a whole, under this License to anyone who comes into pos-session of a copy. This License will therefore apply, along with any applicable section 7 additionalterms, to the whole of the work, and all its parts, regardless of how they are packaged. This Licensegives no permission to license the work in any other way, but it does not invalidate such permissionif you have separately received it.

• d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; however,if the Program has interactive interfaces that do not display Appropriate Legal Notices, your workneed not make them do so.

A compilation of a covered work with other separate and independent works, which are not by theirnature extensions of the covered work, and which are not combined with it such as to form a larger program,in or on a volume of a storage or distribution medium, is called an “aggregate” if the compilation and itsresulting copyright are not used to limit the access or legal rights of the compilation's users beyond whatthe individual works permit. Inclusion of a covered work in an aggregate does not cause this License toapply to the other parts of the aggregate.

6. Conveying Non-Source Forms.

You may convey a covered work in object code form under the terms of sections 4 and 5, provided that youalso convey the machine-readable Corresponding Source under the terms of this License, in one of theseways:

• a) Convey the object code in, or embodied in, a physical product (including a physical distributionmedium), accompanied by the Corresponding Source fixed on a durable physical medium customar-ily used for software interchange.

• b) Convey the object code in, or embodied in, a physical product (including a physical distributionmedium), accompanied by a written offer, valid for at least three years and valid for as long as youoffer spare parts or customer support for that product model, to give anyone who possesses the objectcode either (1) a copy of the Corresponding Source for all the software in the product that is coveredby this License, on a durable physical medium customarily used for software interchange, for a priceno more than your reasonable cost of physically performing this conveying of source, or (2) accessto copy the Corresponding Source from a network server at no charge.

• c) Convey individual copies of the object code with a copy of the written offer to provide the Cor-responding Source. This alternative is allowed only occasionally and noncommercially, and only ifyou received the object code with such an offer, in accord with subsection 6b.

• d) Convey the object code by offering access from a designated place (gratis or for a charge), andoffer equivalent access to the Corresponding Source in the same way through the same place at nofurther charge. You need not require recipients to copy the Corresponding Source along with theobject code. If the place to copy the object code is a network server, the Corresponding Source maybe on a different server (operated by you or a third party) that supports equivalent copying facilities,provided you maintain clear directions next to the object code saying where to find the CorrespondingSource. Regardless of what server hosts the Corresponding Source, you remain obligated to ensurethat it is available for as long as needed to satisfy these requirements.

5

• e) Convey the object code using peer-to-peer transmission, provided you inform other peers wherethe object code and Corresponding Source of the work are being offered to the general public at nocharge under subsection 6d.

A separable portion of the object code, whose source code is excluded from the Corresponding Sourceas a System Library, need not be included in conveying the object code work.

A “User Product” is either (1) a “consumer product”, which means any tangible personal propertywhich is normally used for personal, family, or household purposes, or (2) anything designed or sold forincorporation into a dwelling. In determining whether a product is a consumer product, doubtful casesshall be resolved in favor of coverage. For a particular product received by a particular user, “normallyused” refers to a typical or common use of that class of product, regardless of the status of the particularuser or of the way in which the particular user actually uses, or expects or is expected to use, the product.A product is a consumer product regardless of whether the product has substantial commercial, industrialor non-consumer uses, unless such uses represent the only significant mode of use of the product.

“Installation Information” for a User Product means any methods, procedures, authorization keys, orother information required to install and execute modified versions of a covered work in that User Productfrom a modified version of its Corresponding Source. The information must suffice to ensure that thecontinued functioning of the modified object code is in no case prevented or interfered with solely becausemodification has been made.

If you convey an object code work under this section in, or with, or specifically for use in, a UserProduct, and the conveying occurs as part of a transaction in which the right of possession and use ofthe User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how thetransaction is characterized), the Corresponding Source conveyed under this section must be accompaniedby the Installation Information. But this requirement does not apply if neither you nor any third partyretains the ability to install modified object code on the User Product (for example, the work has beeninstalled in ROM).

The requirement to provide Installation Information does not include a requirement to continue toprovide support service, warranty, or updates for a work that has been modified or installed by the recipient,or for the User Product in which it has been modified or installed. Access to a network may be denied whenthe modification itself materially and adversely affects the operation of the network or violates the rulesand protocols for communication across the network.

Corresponding Source conveyed, and Installation Information provided, in accord with this sectionmust be in a format that is publicly documented (and with an implementation available to the public insource code form), and must require no special password or key for unpacking, reading or copying.

7. Additional Terms.

“Additional permissions” are terms that supplement the terms of this License by making exceptions fromone or more of its conditions. Additional permissions that are applicable to the entire Program shall betreated as though they were included in this License, to the extent that they are valid under applicable law.If additional permissions apply only to part of the Program, that part may be used separately under thosepermissions, but the entire Program remains governed by this License without regard to the additionalpermissions.

When you convey a copy of a covered work, you may at your option remove any additional permissionsfrom that copy, or from any part of it. (Additional permissions may be written to require their own removalin certain cases when you modify the work.) You may place additional permissions on material, added byyou to a covered work, for which you have or can give appropriate copyright permission.

Notwithstanding any other provision of this License, for material you add to a covered work, you may(if authorized by the copyright holders of that material) supplement the terms of this License with terms:

• a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of thisLicense; or

• b) Requiring preservation of specified reasonable legal notices or author attributions in that materialor in the Appropriate Legal Notices displayed by works containing it; or

6

• c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions ofsuch material be marked in reasonable ways as different from the original version; or

• d) Limiting the use for publicity purposes of names of licensors or authors of the material; or

• e) Declining to grant rights under trademark law for use of some trade names, trademarks, or servicemarks; or

• f) Requiring indemnification of licensors and authors of that material by anyone who conveys thematerial (or modified versions of it) with contractual assumptions of liability to the recipient, for anyliability that these contractual assumptions directly impose on those licensors and authors.

All other non-permissive additional terms are considered “further restrictions” within the meaning ofsection 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed bythis License along with a term that is a further restriction, you may remove that term. If a license documentcontains a further restriction but permits relicensing or conveying under this License, you may add to acovered work material governed by the terms of that license document, provided that the further restrictiondoes not survive such relicensing or conveying.

If you add terms to a covered work in accord with this section, you must place, in the relevant sourcefiles, a statement of the additional terms that apply to those files, or a notice indicating where to find theapplicable terms.

Additional terms, permissive or non-permissive, may be stated in the form of a separately writtenlicense, or stated as exceptions; the above requirements apply either way.

8. Termination.

You may not propagate or modify a covered work except as expressly provided under this License. Anyattempt otherwise to propagate or modify it is void, and will automatically terminate your rights under thisLicense (including any patent licenses granted under the third paragraph of section 11).

However, if you cease all violation of this License, then your license from a particular copyright holderis reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates yourlicense, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonablemeans prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is reinstated permanently if the copyrightholder notifies you of the violation by some reasonable means, this is the first time you have receivednotice of violation of this License (for any work) from that copyright holder, and you cure the violationprior to 30 days after your receipt of the notice.

Termination of your rights under this section does not terminate the licenses of parties who have re-ceived copies or rights from you under this License. If your rights have been terminated and not perma-nently reinstated, you do not qualify to receive new licenses for the same material under section 10.

9. Acceptance Not Required for Having Copies.

You are not required to accept this License in order to receive or run a copy of the Program. Ancillarypropagation of a covered work occurring solely as a consequence of using peer-to-peer transmission toreceive a copy likewise does not require acceptance. However, nothing other than this License grants youpermission to propagate or modify any covered work. These actions infringe copyright if you do not acceptthis License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of thisLicense to do so.

10. Automatic Licensing of Downstream Recipients.

Each time you convey a covered work, the recipient automatically receives a license from the originallicensors, to run, modify and propagate that work, subject to this License. You are not responsible forenforcing compliance by third parties with this License.

7

An “entity transaction” is a transaction transferring control of an organization, or substantially all assetsof one, or subdividing an organization, or merging organizations. If propagation of a covered work resultsfrom an entity transaction, each party to that transaction who receives a copy of the work also receiveswhatever licenses to the work the party's predecessor in interest had or could give under the previousparagraph, plus a right to possession of the Corresponding Source of the work from the predecessor ininterest, if the predecessor has it or can get it with reasonable efforts.

You may not impose any further restrictions on the exercise of the rights granted or affirmed under thisLicense. For example, you may not impose a license fee, royalty, or other charge for exercise of rightsgranted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in alawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importingthe Program or any portion of it.

11. Patents.

A “contributor” is a copyright holder who authorizes use under this License of the Program or a work onwhich the Program is based. The work thus licensed is called the contributor's “contributor version”.

A contributor's “essential patent claims” are all patent claims owned or controlled by the contributor,whether already acquired or hereafter acquired, that would be infringed by some manner, permitted bythis License, of making, using, or selling its contributor version, but do not include claims that wouldbe infringed only as a consequence of further modification of the contributor version. For purposes ofthis definition, “control” includes the right to grant patent sublicenses in a manner consistent with therequirements of this License.

Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the con-tributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify andpropagate the contents of its contributor version.

In the following three paragraphs, a “patent license” is any express agreement or commitment, howeverdenominated, not to enforce a patent (such as an express permission to practice a patent or covenant not tosue for patent infringement). To “grant” such a patent license to a party means to make such an agreementor commitment not to enforce a patent against the party.

If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source ofthe work is not available for anyone to copy, free of charge and under the terms of this License, througha publicly available network server or other readily accessible means, then you must either (1) cause theCorresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent li-cense for this particular work, or (3) arrange, in a manner consistent with the requirements of this License,to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowl-edge that, but for the patent license, your conveying the covered work in a country, or your recipient's useof the covered work in a country, would infringe one or more identifiable patents in that country that youhave reason to believe are valid.

If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate byprocuring conveyance of, a covered work, and grant a patent license to some of the parties receiving thecovered work authorizing them to use, propagate, modify or convey a specific copy of the covered work,then the patent license you grant is automatically extended to all recipients of the covered work and worksbased on it.

A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits theexercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically grantedunder this License. You may not convey a covered work if you are a party to an arrangement with a thirdparty that is in the business of distributing software, under which you make payment to the third party basedon the extent of your activity of conveying the work, and under which the third party grants, to any of theparties who would receive the covered work from you, a discriminatory patent license (a) in connectionwith copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily forand in connection with specific products or compilations that contain the covered work, unless you enteredinto that arrangement, or that patent license was granted, prior to 28 March 2007.

Nothing in this License shall be construed as excluding or limiting any implied license or other defensesto infringement that may otherwise be available to you under applicable patent law.

8

12. No Surrender of Others' Freedom.

If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict theconditions of this License, they do not excuse you from the conditions of this License. If you cannotconvey a covered work so as to satisfy simultaneously your obligations under this License and any otherpertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to termsthat obligate you to collect a royalty for further conveying from those to whom you convey the Program, theonly way you could satisfy both those terms and this License would be to refrain entirely from conveyingthe Program.

13. Use with the GNU Affero General Public License.

Notwithstanding any other provision of this License, you have permission to link or combine any coveredwork with a work licensed under version 3 of the GNU Affero General Public License into a single com-bined work, and to convey the resulting work. The terms of this License will continue to apply to the partwhich is the covered work, but the special requirements of the GNU Affero General Public License, section13, concerning interaction through a network will apply to the combination as such.

14. Revised Versions of this License.

The Free Software Foundation may publish revised and/or new versions of the GNU General Public Licensefrom time to time. Such new versions will be similar in spirit to the present version, but may differ in detailto address new problems or concerns.

Each version is given a distinguishing version number. If the Program specifies that a certain numberedversion of the GNU General Public License “or any later version” applies to it, you have the option offollowing the terms and conditions either of that numbered version or of any later version published by theFree Software Foundation. If the Program does not specify a version number of the GNU General PublicLicense, you may choose any version ever published by the Free Software Foundation.

If the Program specifies that a proxy can decide which future versions of the GNU General PublicLicense can be used, that proxy's public statement of acceptance of a version permanently authorizes youto choose that version for the Program.

Later license versions may give you additional or different permissions. However, no additional obli-gations are imposed on any author or copyright holder as a result of your choosing to follow a later version.

15. Disclaimer of Warranty.

THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLIC←↩

ABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERSAND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANYKIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIE←↩

D WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THEENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARYSERVICING, REPAIR OR CORRECTION.

16. Limitation of Liability.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILLANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THEPROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANYGENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THEUSE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF D←↩

ATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRDPARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),

9

EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OFSUCH DAMAGES.

17. Interpretation of Sections 15 and 16.

If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effectaccording to their terms, reviewing courts shall apply local law that most closely approximates an absolutewaiver of all civil liability in connection with the Program, unless a warranty or assumption of liabilityaccompanies a copy of the Program in return for a fee.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best wayto achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each sourcefile to most effectively state the exclusion of warranty; and each file should have at least the “copyright”line and a pointer to where the full notice is found.

one line to give the program’s name and a brief idea of what it does.Copyright (C) year name of author

This program is free software: you can redistribute it and/or modifyit under the terms of the GNU General Public License as published bythe Free Software Foundation, either version 3 of the License, or(at your option) any later version.

This program is distributed in the hope that it will be useful,but WITHOUT ANY WARRANTY; without even the implied warranty ofMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See theGNU General Public License for more details.

You should have received a copy of the GNU General Public Licensealong with this program. If not, see http://www.gnu.org/licenses/.

Also add information on how to contact you by electronic and paper mail.If the program does terminal interaction, make it output a short notice like this when it starts in an

interactive mode:

program Copyright (C) year name of authorThis program comes with ABSOLUTELY NO WARRANTY; for details type ‘show w’.This is free software, and you are welcome to redistribute itunder certain conditions; type ‘show c’ for details.

The hypothetical commands ‘show w' and ‘show c' should show the appropriate parts of the GeneralPublic License. Of course, your program's commands might be different; for a GUI interface, you woulduse an “about box”.

You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyrightdisclaimer” for the program, if necessary. For more information on this, and how to apply and follow theGNU GPL, see http://www.gnu.org/licenses/.

The GNU General Public License does not permit incorporating your program into proprietary pro-grams. If your program is a subroutine library, you may consider it more useful to permit linking proprietaryapplications with the library. If this is what you want to do, use the GNU Lesser General Public License in-stead of this License. But first, please read http://www.gnu.org/philosophy/why-not-lgpl.←↩

html.

10

http://www.gnu.org/licenses/

http://www.gnu.org/licenses/

http://www.gnu.org/philosophy/why-not-lgpl.html

http://www.gnu.org/philosophy/why-not-lgpl.html

3 GNU Free Documentation LicenseVersion 1.2, November 2002

Copyright (C) 2000,2001,2002 Free Software Foundation, Inc.51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.Everyone is permitted to copy and distribute verbatim copiesof this license document, but changing it is not allowed.

0. PREAMBLEThe purpose of this License is to make a manual, textbook, or other functional and useful document

”free” in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, withor without modifying it, either commercially or noncommercially. Secondarily, this License preserves forthe author and publisher a way to get credit for their work, while not being considered responsible formodifications made by others.

This License is a kind of ”copyleft”, which means that derivative works of the document must them-selves be free in the same sense. It complements the GNU General Public License, which is a copyleftlicense designed for free software.

We have designed this License in order to use it for manuals for free software, because free softwareneeds free documentation: a free program should come with manuals providing the same freedoms thatthe software does. But this License is not limited to software manuals; it can be used for any textual work,regardless of subject matter or whether it is published as a printed book. We recommend this Licenseprincipally for works whose purpose is instruction or reference.

1. APPLICABILITY AND DEFINITIONSThis License applies to any manual or other work, in any medium, that contains a notice placed by

the copyright holder saying it can be distributed under the terms of this License. Such a notice grants aworld-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein.The ”Document”, below, refers to any such manual or work. Any member of the public is a licensee, andis addressed as ”you”. You accept the license if you copy, modify or distribute the work in a way requiringpermission under copyright law.

A ”Modified Version” of the Document means any work containing the Document or a portion of it,either copied verbatim, or with modifications and/or translated into another language.

A ”Secondary Section” is a named appendix or a front-matter section of the Document that dealsexclusively with the relationship of the publishers or authors of the Document to the Document's overallsubject (or to related matters) and contains nothing that could fall directly within that overall subject.(Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain anymathematics.) The relationship could be a matter of historical connection with the subject or with relatedmatters, or of legal, commercial, philosophical, ethical or political position regarding them.

The ”Invariant Sections” are certain Secondary Sections whose titles are designated, as being those ofInvariant Sections, in the notice that says that the Document is released under this License. If a section doesnot fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Documentmay contain zero Invariant Sections. If the Document does not identify any Invariant Sections then thereare none.

The ”Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-CoverTexts, in the notice that says that the Document is released under this License. A Front-Cover Text may beat most 5 words, and a Back-Cover Text may be at most 25 words.

A ”Transparent” copy of the Document means a machine-readable copy, represented in a format whosespecification is available to the general public, that is suitable for revising the document straightforwardlywith generic text editors or (for images composed of pixels) generic paint programs or (for drawings) somewidely available drawing editor, and that is suitable for input to text formatters or for automatic translationto a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparentfile format whose markup, or absence of markup, has been arranged to thwart or discourage subsequentmodification by readers is not Transparent. An image format is not Transparent if used for any substantialamount of text. A copy that is not ”Transparent” is called ”Opaque”.

11

Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo in-put format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conformingsimple HTML, PostScript or PDF designed for human modification. Examples of transparent image for-mats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and editedonly by proprietary word processors, SGML or XML for which the DTD and/or processing tools are notgenerally available, and the machine-generated HTML, PostScript or PDF produced by some word proces-sors for output purposes only.

The ”Title Page” means, for a printed book, the title page itself, plus such following pages as are neededto hold, legibly, the material this License requires to appear in the title page. For works in formats whichdo not have any title page as such, ”Title Page” means the text near the most prominent appearance of thework's title, preceding the beginning of the body of the text.

A section ”Entitled XYZ” means a named subunit of the Document whose title either is precisely X←↩

YZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZstands for a specific section name mentioned below, such as ”Acknowledgements”, ”Dedications”, ”←↩

Endorsements”, or ”History”.) To ”Preserve the Title” of such a section when you modify the Documentmeans that it remains a section ”Entitled XYZ” according to this definition.

The Document may include Warranty Disclaimers next to the notice which states that this Licenseapplies to the Document. These Warranty Disclaimers are considered to be included by reference in thisLicense, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimersmay have is void and has no effect on the meaning of this License.

2. VERBATIM COPYINGYou may copy and distribute the Document in any medium, either commercially or noncommercially,

provided that this License, the copyright notices, and the license notice saying this License applies to theDocument are reproduced in all copies, and that you add no other conditions whatsoever to those of thisLicense. You may not use technical measures to obstruct or control the reading or further copying of thecopies you make or distribute. However, you may accept compensation in exchange for copies. If youdistribute a large enough number of copies you must also follow the conditions in section 3.

You may also lend copies, under the same conditions stated above, and you may publicly display copies.3. COPYING IN QUANTITYIf you publish printed copies (or copies in media that commonly have printed covers) of the Document,

numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose thecopies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover,and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as thepublisher of these copies. The front cover must present the full title with all words of the title equallyprominent and visible. You may add other material on the covers in addition. Copying with changeslimited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can betreated as verbatim copying in other respects.

If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed(as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

If you publish or distribute Opaque copies of the Document numbering more than 100, you must eitherinclude a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaquecopy a computer-network location from which the general network-using public has access to downloadusing public-standard network protocols a complete Transparent copy of the Document, free of addedmaterial. If you use the latter option, you must take reasonably prudent steps, when you begin distributionof Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the statedlocation until at least one year after the last time you distribute an Opaque copy (directly or through youragents or retailers) of that edition to the public.

It is requested, but not required, that you contact the authors of the Document well before redistributingany large number of copies, to give them a chance to provide you with an updated version of the Document.

4. MODIFICATIONSYou may copy and distribute a Modified Version of the Document under the conditions of sections 2

and 3 above, provided that you release the Modified Version under precisely this License, with the Modi-fied Version filling the role of the Document, thus licensing distribution and modification of the ModifiedVersion to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

12

• A. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, andfrom those of previous versions (which should, if there were any, be listed in the History section ofthe Document). You may use the same title as a previous version if the original publisher of thatversion gives permission.

• B. List on the Title Page, as authors, one or more persons or entities responsible for authorship ofthe modifications in the Modified Version, together with at least five of the principal authors of theDocument (all of its principal authors, if it has fewer than five), unless they release you from thisrequirement.

• C. State on the Title page the name of the publisher of the Modified Version, as the publisher.

• D. Preserve all the copyright notices of the Document.

• E. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.

• F. Include, immediately after the copyright notices, a license notice giving the public permission touse the Modified Version under the terms of this License, in the form shown in the Addendum below.

• G. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts givenin the Document's license notice.

• H. Include an unaltered copy of this License.

• I. Preserve the section Entitled ”History”, Preserve its Title, and add to it an item stating at leastthe title, year, new authors, and publisher of the Modified Version as given on the Title Page. Ifthere is no section Entitled ”History” in the Document, create one stating the title, year, authors,and publisher of the Document as given on its Title Page, then add an item describing the ModifiedVersion as stated in the previous sentence.

• J. Preserve the network location, if any, given in the Document for public access to a Transpar-ent copy of the Document, and likewise the network locations given in the Document for previousversions it was based on. These may be placed in the ”History” section. You may omit a networklocation for a work that was published at least four years before the Document itself, or if the originalpublisher of the version it refers to gives permission.

• K. For any section Entitled ”Acknowledgements” or ”Dedications”, Preserve the Title of the section,and preserve in the section all the substance and tone of each of the contributor acknowledgementsand/or dedications given therein.

• L. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles.Section numbers or the equivalent are not considered part of the section titles.

• M. Delete any section Entitled ”Endorsements”. Such a section may not be included in the ModifiedVersion.

• N. Do not retitle any existing section to be Entitled ”Endorsements” or to conflict in title with anyInvariant Section.

• O. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or appendices that qualify as SecondarySections and contain no material copied from the Document, you may at your option designate some or allof these sections as invariant. To do this, add their titles to the list of Invariant Sections in the ModifiedVersion's license notice. These titles must be distinct from any other section titles.

You may add a section Entitled ”Endorsements”, provided it contains nothing but endorsements ofyour Modified Version by various parties–for example, statements of peer review or that the text has beenapproved by an organization as the authoritative definition of a standard.

13

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 wordsas a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage ofFront-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) anyone entity. If the Document already includes a cover text for the same cover, previously added by you or byarrangement made by the same entity you are acting on behalf of, you may not add another; but you mayreplace the old one, on explicit permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License give permission to use theirnames for publicity for or to assert or imply endorsement of any Modified Version.

5. COMBINING DOCUMENTSYou may combine the Document with other documents released under this License, under the terms

defined in section 4 above for modified versions, provided that you include in the combination all of theInvariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections ofyour combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sec-tions may be replaced with a single copy. If there are multiple Invariant Sections with the same name butdifferent contents, make the title of each such section unique by adding at the end of it, in parentheses, thename of the original author or publisher of that section if known, or else a unique number. Make the sameadjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled ”History” in the various original docu-ments, forming one section Entitled ”History”; likewise combine any sections Entitled ”Acknowledgements”,and any sections Entitled ”Dedications”. You must delete all sections Entitled ”Endorsements.”

6. COLLECTIONS OF DOCUMENTSYou may make a collection consisting of the Document and other documents released under this Li-

cense, and replace the individual copies of this License in the various documents with a single copy that isincluded in the collection, provided that you follow the rules of this License for verbatim copying of eachof the documents in all other respects.

You may extract a single document from such a collection, and distribute it individually under thisLicense, provided you insert a copy of this License into the extracted document, and follow this License inall other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKSA compilation of the Document or its derivatives with other separate and independent documents or

works, in or on a volume of a storage or distribution medium, is called an ”aggregate” if the copyrightresulting from the compilation is not used to limit the legal rights of the compilation's users beyond whatthe individual works permit. When the Document is included in an aggregate, this License does not applyto the other works in the aggregate which are not themselves derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if theDocument is less than one half of the entire aggregate, the Document's Cover Texts may be placed on coversthat bracket the Document within the aggregate, or the electronic equivalent of covers if the Document isin electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATIONTranslation is considered a kind of modification, so you may distribute translations of the Document

under the terms of section 4. Replacing Invariant Sections with translations requires special permissionfrom their copyright holders, but you may include translations of some or all Invariant Sections in additionto the original versions of these Invariant Sections. You may include a translation of this License, and allthe license notices in the Document, and any Warranty Disclaimers, provided that you also include theoriginal English version of this License and the original versions of those notices and disclaimers. In caseof a disagreement between the translation and the original version of this License or a notice or disclaimer,the original version will prevail.

If a section in the Document is Entitled ”Acknowledgements”, ”Dedications”, or ”History”, the re-quirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

9. TERMINATIONYou may not copy, modify, sublicense, or distribute the Document except as expressly provided for

under this License. Any other attempt to copy, modify, sublicense or distribute the Document is void, andwill automatically terminate your rights under this License. However, parties who have received copies, or

14

rights, from you under this License will not have their licenses terminated so long as such parties remainin full compliance.

10. FUTURE REVISIONS OF THIS LICENSEThe Free Software Foundation may publish new, revised versions of the GNU Free Documentation

License from time to time. Such new versions will be similar in spirit to the present version, but may differin detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number. If the Document specifies thata particular numbered version of this License ”or any later version” applies to it, you have the option offollowing the terms and conditions either of that specified version or of any later version that has beenpublished (not as a draft) by the Free Software Foundation. If the Document does not specify a versionnumber of this License, you may choose any version ever published (not as a draft) by the Free SoftwareFoundation.

How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and putthe following copyright and license notices just after the title page:

Copyright (c) YEAR YOUR NAME.Permission is granted to copy, distribute and/or modify this documentunder the terms of the GNU Free Documentation License, Version 1.2or any later version published by the Free Software Foundation;with no Invariant Sections, no Front-Cover Texts, and no Back-CoverTexts. A copy of the license is included in the section entitled"GNU Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the ”with...Texts.”line with this:

with the Invariant Sections being LIST THEIR TITLES, with theFront-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other combination of the three, mergethose two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these exam-ples in parallel under your choice of free software license, such as the GNU General Public License, topermit their use in free software.

4 Module Index

4.1 ModulesHere is a list of all modules:

Java Language Interface 31

5 Namespace Index

5.1 Namespace ListHere is a list of all documented namespaces with brief descriptions:

parma polyhedra libraryThe PPL Java interface package 33

15

http://www.gnu.org/copyleft/

6 Hierarchical Index

6.1 Class Hierarchy

This inheritance list is sorted roughly, but not completely, alphabetically:

parma polyhedra library.Artificial Parameter 41

parma polyhedra library.Artificial Parameter Sequence 42

parma polyhedra library.BD Shape double 42

parma polyhedra library.BD Shape float 46

parma polyhedra library.BD Shape int16 t 50




parma polyhedra library.BD Shape long double 65

parma polyhedra library.BD Shape mpq class 68

parma polyhedra library.BD Shape mpz class 72

parma polyhedra library.Bounded Integer Type Overflow 76

parma polyhedra library.Bounded Integer Type Representation 76

parma polyhedra library.Bounded Integer Type Width 77

parma polyhedra library.By Reference< T > 77

parma polyhedra library.Coefficient 80

parma polyhedra library.Complexity Class 81

parma polyhedra library.Congruence 81

parma polyhedra library.Congruence System 82

parma polyhedra library.Constraint 82

parma polyhedra library.Constraint System 83

parma polyhedra library.Constraints Product C Polyhedron Grid 83

parma polyhedra library.Constraints Product Grid C Polyhedron 87

parma polyhedra library.Constraints Product Grid NNC Polyhedron 90

parma polyhedra library.Constraints Product NNC Polyhedron Grid 94

parma polyhedra library.Control Parameter Name 98

16

parma polyhedra library.Control Parameter Value 98

parma polyhedra library.Degenerate Element 98

parma polyhedra library.Domain Error Exception 99

parma polyhedra library.Double Box 99

parma polyhedra library.Float Box 103

parma polyhedra library.Generator 106

parma polyhedra library.Generator System 108

parma polyhedra library.Generator Type 108

parma polyhedra library.Grid 109

parma polyhedra library.Grid Generator 113

parma polyhedra library.Grid Generator System 114

parma polyhedra library.Grid Generator Type 114

parma polyhedra library.Int16 Box 115




parma polyhedra library.Invalid Argument Exception 130

parma polyhedra library.IO 130

parma polyhedra library.Length Error Exception 131

parma polyhedra library.Linear Expression 131

parma polyhedra library.Linear Expression Coefficient 132

parma polyhedra library.Linear Expression Difference 133

parma polyhedra library.Linear Expression Sum 134

parma polyhedra library.Linear Expression Times 135

parma polyhedra library.Linear Expression Unary Minus 136

parma polyhedra library.Linear Expression Variable 137

parma polyhedra library.Logic Error Exception 137

parma polyhedra library.Long Double Box 138

parma polyhedra library.MIP Problem 141

17

parma polyhedra library.MIP Problem Status 147

parma polyhedra library.Octagonal Shape double 150

parma polyhedra library.Octagonal Shape float 153

parma polyhedra library.Octagonal Shape int16 t 157




parma polyhedra library.Octagonal Shape long double 172

parma polyhedra library.Octagonal Shape mpq class 176

parma polyhedra library.Octagonal Shape mpz class 179

parma polyhedra library.Optimization Mode 183

parma polyhedra library.Overflow Error Exception 184

parma polyhedra library.Pair< K, V > 184

parma polyhedra library.Parma Polyhedra Library 184

parma polyhedra library.Partial Function 187

parma polyhedra library.PIP Problem 188

parma polyhedra library.PIP Problem Control Parameter Name 192

parma polyhedra library.PIP Problem Control Parameter Value 192

parma polyhedra library.PIP Problem Status 193

parma polyhedra library.PIP Tree Node 194

parma polyhedra library.PIP Decision Node 188

parma polyhedra library.PIP Solution Node 193

parma polyhedra library.Pointset Powerset BD Shape double 195

parma polyhedra library.Pointset Powerset BD Shape double Iterator 197

parma polyhedra library.Pointset Powerset BD Shape float 198

parma polyhedra library.Pointset Powerset BD Shape float Iterator 200

parma polyhedra library.Pointset Powerset BD Shape int16 t 201

parma polyhedra library.Pointset Powerset BD Shape int16 t Iterator 203


18






parma polyhedra library.Pointset Powerset BD Shape long double 212

parma polyhedra library.Pointset Powerset BD Shape long double Iterator 214

parma polyhedra library.Pointset Powerset BD Shape mpq class 215

parma polyhedra library.Pointset Powerset BD Shape mpq class Iterator 217

parma polyhedra library.Pointset Powerset BD Shape mpz class 218

parma polyhedra library.Pointset Powerset BD Shape mpz class Iterator 220

parma polyhedra library.Pointset Powerset C Polyhedron 221

parma polyhedra library.Pointset Powerset C Polyhedron Iterator 223

parma polyhedra library.Pointset Powerset Double Box 223

parma polyhedra library.Pointset Powerset Double Box Iterator 226

parma polyhedra library.Pointset Powerset Float Box 226

parma polyhedra library.Pointset Powerset Float Box Iterator 228

parma polyhedra library.Pointset Powerset Grid 229

parma polyhedra library.Pointset Powerset Grid Iterator 231

parma polyhedra library.Pointset Powerset Int16 Box 232

parma polyhedra library.Pointset Powerset Int16 Box Iterator 234







parma polyhedra library.Pointset Powerset Long Double Box 243

parma polyhedra library.Pointset Powerset Long Double Box Iterator 245

19

parma polyhedra library.Pointset Powerset NNC Polyhedron 245

parma polyhedra library.Pointset Powerset NNC Polyhedron Iterator 248

parma polyhedra library.Pointset Powerset Octagonal Shape double 248

parma polyhedra library.Pointset Powerset Octagonal Shape double Iterator 250

parma polyhedra library.Pointset Powerset Octagonal Shape float 251

parma polyhedra library.Pointset Powerset Octagonal Shape float Iterator 253

parma polyhedra library.Pointset Powerset Octagonal Shape int16 t 254

parma polyhedra library.Pointset Powerset Octagonal Shape int16 t Iterator 256







parma polyhedra library.Pointset Powerset Octagonal Shape long double 265

parma polyhedra library.Pointset Powerset Octagonal Shape long double Iterator 268

parma polyhedra library.Pointset Powerset Octagonal Shape mpq class 268

parma polyhedra library.Pointset Powerset Octagonal Shape mpq class Iterator 271

parma polyhedra library.Pointset Powerset Octagonal Shape mpz class 271

parma polyhedra library.Pointset Powerset Octagonal Shape mpz class Iterator 273

parma polyhedra library.Pointset Powerset Rational Box 274

parma polyhedra library.Pointset Powerset Rational Box Iterator 276

parma polyhedra library.Pointset Powerset Uint16 Box 277

parma polyhedra library.Pointset Powerset Uint16 Box Iterator 279






20


parma polyhedra library.Pointset Powerset Z Box 288

parma polyhedra library.Pointset Powerset Z Box Iterator 290

parma polyhedra library.Poly Con Relation 290

parma polyhedra library.Poly Gen Relation 291

parma polyhedra library.Polyhedron 292

parma polyhedra library.C Polyhedron 78

parma polyhedra library.NNC Polyhedron 147

parma polyhedra library.Rational Box 294

parma polyhedra library.Relation Symbol 298

parma polyhedra library.Timeout Exception 298

parma polyhedra library.Uint16 Box 299




parma polyhedra library.Variable 314

parma polyhedra library.Variable Stringifier 314

parma polyhedra library.Variables Set 315

parma polyhedra library.Z Box 315

7 Class Index

7.1 Class ListHere are the classes, structs, unions and interfaces with brief descriptions:

parma polyhedra library.Artificial Parameter 41

parma polyhedra library.Artificial Parameter SequenceA sequence of artificial parameters 42

parma polyhedra library.BD Shape doubleJava class interfacing C++ Parma Polyhedra Library::BD Shape<double> 42

parma polyhedra library.BD Shape floatJava class interfacing C++ Parma Polyhedra Library::BD Shape<float> 46

parma polyhedra library.BD Shape int16 tJava class interfacing C++ Parma Polyhedra Library::BD Shape<int16 t> 50

21




parma polyhedra library.BD Shape long doubleJava class interfacing C++ Parma Polyhedra Library::BD Shape<long double> 65

parma polyhedra library.BD Shape mpq classJava class interfacing C++ Parma Polyhedra Library::BD Shape<mpq class> 68

parma polyhedra library.BD Shape mpz classJava class interfacing C++ Parma Polyhedra Library::BD Shape<mpz class> 72

parma polyhedra library.Bounded Integer Type OverflowOverflow behavior of bounded integer types 76

parma polyhedra library.Bounded Integer Type RepresentationRepresentation of bounded integer types 76

parma polyhedra library.Bounded Integer Type WidthWidths of bounded integer types 77

parma polyhedra library.By Reference< T >An utility class implementing mutable and non-mutable call-by-reference 77

parma polyhedra library.C PolyhedronJava class interfacing C++ Parma Polyhedra Library::C Polyhedron 78

parma polyhedra library.CoefficientA PPL coefficient 80

parma polyhedra library.Complexity ClassPossible Complexities 81

parma polyhedra library.CongruenceA linear congruence 81

parma polyhedra library.Congruence SystemA system of congruences 82

parma polyhedra library.ConstraintA linear equality or inequality 82

parma polyhedra library.Constraint SystemA system of constraints 83

parma polyhedra library.Constraints Product C Polyhedron GridJava class interfacing C++ Parma Polyhedra Library::Constraints Product<C Polyhedron,←↩

Grid> 83

22

parma polyhedra library.Constraints Product Grid C PolyhedronJava class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,C←↩

Polyhedron> 87

parma polyhedra library.Constraints Product Grid NNC PolyhedronJava class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,N←↩

NC Polyhedron> 90

parma polyhedra library.Constraints Product NNC Polyhedron GridJava class interfacing C++ Parma Polyhedra Library::Constraints Product<NNC ←↩

Polyhedron,Grid> 94

parma polyhedra library.Control Parameter NameNames of MIP problems' control parameters 98

parma polyhedra library.Control Parameter ValuePossible values for MIP problem's control parameters 98

parma polyhedra library.Degenerate ElementKinds of degenerate abstract elements 98

parma polyhedra library.Domain Error ExceptionExceptions caused by domain errors 99

parma polyhedra library.Double BoxJava class interfacing C++ Parma Polyhedra Library::Double Box 99

parma polyhedra library.Float BoxJava class interfacing C++ Parma Polyhedra Library::Float Box 103

parma polyhedra library.GeneratorA line, ray, point or closure point 106

parma polyhedra library.Generator SystemA system of generators 108

parma polyhedra library.Generator TypeThe generator type 108

parma polyhedra library.GridJava class interfacing C++ Parma Polyhedra Library::Grid 109

parma polyhedra library.Grid GeneratorA grid line, parameter or grid point 113

parma polyhedra library.Grid Generator SystemA system of grid generators 114

parma polyhedra library.Grid Generator TypeThe grid generator type 114

parma polyhedra library.Int16 BoxJava class interfacing C++ Parma Polyhedra Library::Int16 Box 115


23



parma polyhedra library.Invalid Argument ExceptionExceptions caused by invalid arguments 130

parma polyhedra library.IOA class collecting I/O functions 130

parma polyhedra library.Length Error ExceptionExceptions caused by too big length/size values 131

parma polyhedra library.Linear ExpressionA linear expression 131

parma polyhedra library.Linear Expression CoefficientA linear expression built from a coefficient 132

parma polyhedra library.Linear Expression DifferenceThe difference of two linear expressions 133

parma polyhedra library.Linear Expression SumThe sum of two linear expressions 134

parma polyhedra library.Linear Expression TimesThe product of a linear expression and a coefficient 135

parma polyhedra library.Linear Expression Unary MinusThe negation of a linear expression 136

parma polyhedra library.Linear Expression VariableA linear expression built from a variable 137

parma polyhedra library.Logic Error ExceptionExceptions due to errors in low-level routines 137

parma polyhedra library.Long Double BoxJava class interfacing C++ Parma Polyhedra Library::Long Double Box 138

parma polyhedra library.MIP ProblemA Mixed Integer (linear) Programming problem 141

parma polyhedra library.MIP Problem StatusPossible outcomes of the MIP Problem solver 147

parma polyhedra library.NNC PolyhedronJava class interfacing C++ Parma Polyhedra Library::NNC Polyhedron 147

parma polyhedra library.Octagonal Shape doubleJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<double> 150

parma polyhedra library.Octagonal Shape floatJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<float> 153

24

parma polyhedra library.Octagonal Shape int16 tJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<int16 t> 157




parma polyhedra library.Octagonal Shape long doubleJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<long double>172

parma polyhedra library.Octagonal Shape mpq classJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpq class> 176

parma polyhedra library.Octagonal Shape mpz classJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpz class> 179

parma polyhedra library.Optimization ModePossible optimization modes 183

parma polyhedra library.Overflow Error ExceptionExceptions due to overflow errors 184

parma polyhedra library.Pair< K, V >A pair of values of type K and V 184

parma polyhedra library.Parma Polyhedra LibraryA class collecting library-level functions 184

parma polyhedra library.Partial FunctionA partial function on space dimension indices 187

parma polyhedra library.PIP Decision NodeAn internal node of the PIP solution tree 188

parma polyhedra library.PIP ProblemA Parametric Integer Programming problem 188

parma polyhedra library.PIP Problem Control Parameter NameNames of PIP problems' control parameters 192

parma polyhedra library.PIP Problem Control Parameter ValuePossible values for PIP problems' control parameters 192

parma polyhedra library.PIP Problem StatusPossible outcomes of the PIP Problem solver 193

parma polyhedra library.PIP Solution NodeA leaf node of the PIP solution tree 193

25

parma polyhedra library.PIP Tree NodeA node of the PIP solution tree 194

parma polyhedra library.Pointset Powerset BD Shape doubleJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double>> 195

parma polyhedra library.Pointset Powerset BD Shape double IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double>>:: iterator 197

parma polyhedra library.Pointset Powerset BD Shape floatJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float>> 198

parma polyhedra library.Pointset Powerset BD Shape float IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float>>:: iterator 200

parma polyhedra library.Pointset Powerset BD Shape int16 tJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16←↩

t> > 201

parma polyhedra library.Pointset Powerset BD Shape int16 t IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16←↩

t> >:: iterator 203


t> > 204


t> >:: iterator 206


t> > 206


t> >:: iterator 209


t> > 209


t> >:: iterator 212

parma polyhedra library.Pointset Powerset BD Shape long doubleJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<longdouble> > 212

26

parma polyhedra library.Pointset Powerset BD Shape long double IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<longdouble> >:: iterator 214

parma polyhedra library.Pointset Powerset BD Shape mpq classJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq←↩

class> > 215

parma polyhedra library.Pointset Powerset BD Shape mpq class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq←↩

class> >:: iterator 217

parma polyhedra library.Pointset Powerset BD Shape mpz classJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz←↩

class> > 218

parma polyhedra library.Pointset Powerset BD Shape mpz class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz←↩

class> >:: iterator 220

parma polyhedra library.Pointset Powerset C PolyhedronJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>221

parma polyhedra library.Pointset Powerset C Polyhedron IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>←↩

:: iterator 223

parma polyhedra library.Pointset Powerset Double BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double ←↩

Box> 223

parma polyhedra library.Pointset Powerset Double Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double ←↩

Box>:: iterator 226

parma polyhedra library.Pointset Powerset Float BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box> 226

parma polyhedra library.Pointset Powerset Float Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>←↩

:: iterator 228

parma polyhedra library.Pointset Powerset GridJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid> 229

parma polyhedra library.Pointset Powerset Grid IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>:: it-erator 231

parma polyhedra library.Pointset Powerset Int16 BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box> 232

parma polyhedra library.Pointset Powerset Int16 Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>←↩

:: iterator 234

27



:: iterator 237



:: iterator 239



:: iterator 242

parma polyhedra library.Pointset Powerset Long Double BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double←↩

Box> 243

parma polyhedra library.Pointset Powerset Long Double Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double←↩

Box>:: iterator 245

parma polyhedra library.Pointset Powerset NNC PolyhedronJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>245

parma polyhedra library.Pointset Powerset NNC Polyhedron IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>←↩

:: iterator 248

parma polyhedra library.Pointset Powerset Octagonal Shape doubleJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<double> > 248

parma polyhedra library.Pointset Powerset Octagonal Shape double IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<double> >:: iterator 250

parma polyhedra library.Pointset Powerset Octagonal Shape floatJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<float> > 251

parma polyhedra library.Pointset Powerset Octagonal Shape float IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<float> >:: iterator 253

parma polyhedra library.Pointset Powerset Octagonal Shape int16 tJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<int16 t> > 254

28

parma polyhedra library.Pointset Powerset Octagonal Shape int16 t IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<int16 t> >:: iterator 256










Shape<int8 t> > 262



parma polyhedra library.Pointset Powerset Octagonal Shape long doubleJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<long double> > 265

parma polyhedra library.Pointset Powerset Octagonal Shape long double IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<long double> >:: iterator 268

parma polyhedra library.Pointset Powerset Octagonal Shape mpq classJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<mpq class> > 268

parma polyhedra library.Pointset Powerset Octagonal Shape mpq class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<mpq class> >:: iterator 271

parma polyhedra library.Pointset Powerset Octagonal Shape mpz classJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<mpz class> > 271

parma polyhedra library.Pointset Powerset Octagonal Shape mpz class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal←↩

Shape<mpz class> >:: iterator 273

parma polyhedra library.Pointset Powerset Rational BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational ←↩

Box> 274

29

parma polyhedra library.Pointset Powerset Rational Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational ←↩

Box>:: iterator 276

parma polyhedra library.Pointset Powerset Uint16 BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>277

parma polyhedra library.Pointset Powerset Uint16 Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>←↩

:: iterator 279



:: iterator 282



:: iterator 284

parma polyhedra library.Pointset Powerset Uint8 BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint8 Box> 285


:: iterator 287

parma polyhedra library.Pointset Powerset Z BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box> 288

parma polyhedra library.Pointset Powerset Z Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>:←↩

: iterator 290

parma polyhedra library.Poly Con RelationThe relation between a polyhedron and a constraint 290

parma polyhedra library.Poly Gen RelationThe relation between a polyhedron and a generator 291

parma polyhedra library.PolyhedronJava class interfacing C++ Parma Polyhedra Library::Polyhedron 292

parma polyhedra library.Rational BoxJava class interfacing C++ Parma Polyhedra Library::Rational Box 294

parma polyhedra library.Relation SymbolRelation symbols 298

30

parma polyhedra library.Timeout ExceptionExceptions caused by timeout expiring 298

parma polyhedra library.Uint16 BoxJava class interfacing C++ Parma Polyhedra Library::Uint16 Box 299




parma polyhedra library.VariableA dimension of the vector space 314

parma polyhedra library.Variable StringifierAn interface for objects converting a Variable id to a string 314

parma polyhedra library.Variables SetA java.util.TreeSet of variables' indexes 315

parma polyhedra library.Z BoxJava class interfacing C++ Parma Polyhedra Library::Z Box 315

8 Module Documentation

8.1 Java Language InterfacePackages

• package parma polyhedra libraryThe PPL Java interface package.

Classes

• class parma polyhedra library.Artificial Parameter SequenceA sequence of artificial parameters.

• enum parma polyhedra library.Bounded Integer Type OverflowOverflow behavior of bounded integer types.

• enum parma polyhedra library.Bounded Integer Type RepresentationRepresentation of bounded integer types.

• enum parma polyhedra library.Bounded Integer Type WidthWidths of bounded integer types.

• class parma polyhedra library.By Reference< T >

An utility class implementing mutable and non-mutable call-by-reference.• class parma polyhedra library.Coefficient

A PPL coefficient.• enum parma polyhedra library.Complexity Class

Possible Complexities.• class parma polyhedra library.Congruence

31

A linear congruence.• class parma polyhedra library.Congruence System

A system of congruences.• class parma polyhedra library.Constraint

A linear equality or inequality.• class parma polyhedra library.Constraint System

A system of constraints.• enum parma polyhedra library.Control Parameter Name

Names of MIP problems' control parameters.• enum parma polyhedra library.Control Parameter Value

Possible values for MIP problem's control parameters.• enum parma polyhedra library.Degenerate Element

Kinds of degenerate abstract elements.• class parma polyhedra library.Domain Error Exception

Exceptions caused by domain errors.• class parma polyhedra library.Generator

A line, ray, point or closure point.• class parma polyhedra library.Generator System

A system of generators.• enum parma polyhedra library.Generator Type

The generator type.• class parma polyhedra library.Grid Generator

A grid line, parameter or grid point.• class parma polyhedra library.Grid Generator System

A system of grid generators.• enum parma polyhedra library.Grid Generator Type

The grid generator type.• class parma polyhedra library.Invalid Argument Exception

Exceptions caused by invalid arguments.• class parma polyhedra library.IO

A class collecting I/O functions.• class parma polyhedra library.Length Error Exception

Exceptions caused by too big length/size values.• class parma polyhedra library.Linear Expression

A linear expression.• class parma polyhedra library.Linear Expression Coefficient

A linear expression built from a coefficient.• class parma polyhedra library.Linear Expression Difference

The difference of two linear expressions.• class parma polyhedra library.Linear Expression Sum

The sum of two linear expressions.• class parma polyhedra library.Linear Expression Times

The product of a linear expression and a coefficient.• class parma polyhedra library.Linear Expression Unary Minus

The negation of a linear expression.• class parma polyhedra library.Linear Expression Variable

32

A linear expression built from a variable.

• class parma polyhedra library.Logic Error Exception

Exceptions due to errors in low-level routines.

• class parma polyhedra library.MIP Problem

A Mixed Integer (linear) Programming problem.

• enum parma polyhedra library.MIP Problem Status

Possible outcomes of the MIP Problem solver.

• enum parma polyhedra library.Optimization Mode

Possible optimization modes.

• class parma polyhedra library.Overflow Error Exception

Exceptions due to overflow errors.

• class parma polyhedra library.Pair< K, V >

A pair of values of type K and V.

• class parma polyhedra library.Parma Polyhedra Library

A class collecting library-level functions.

• class parma polyhedra library.Partial Function

A partial function on space dimension indices.

• class parma polyhedra library.PIP Problem

A Parametric Integer Programming problem.

• enum parma polyhedra library.PIP Problem Control Parameter Name

Names of PIP problems' control parameters.

• enum parma polyhedra library.PIP Problem Control Parameter Value

Possible values for PIP problems' control parameters.

• enum parma polyhedra library.PIP Problem Status

Possible outcomes of the PIP Problem solver.

• class parma polyhedra library.Poly Con Relation

The relation between a polyhedron and a constraint.

• enum parma polyhedra library.Relation Symbol

Relation symbols.

• class parma polyhedra library.Timeout Exception

Exceptions caused by timeout expiring.

• class parma polyhedra library.Variable

A dimension of the vector space.

• interface parma polyhedra library.Variable Stringifier

An interface for objects converting a Variable id to a string.

8.1.1 Detailed Description

The Parma Polyhedra Library comes equipped with an interface for the Java language.

9 Namespace Documentation

9.1 Package parma polyhedra library

The PPL Java interface package.

33

Classes

• class Artificial Parameter• class Artificial Parameter Sequence

A sequence of artificial parameters.• class BD Shape double

Java class interfacing C++ Parma Polyhedra Library::BD Shape<double>• class BD Shape float

Java class interfacing C++ Parma Polyhedra Library::BD Shape<float>• class BD Shape int16 t

Java class interfacing C++ Parma Polyhedra Library::BD Shape<int16 t>• class BD Shape int32 t



Java class interfacing C++ Parma Polyhedra Library::BD Shape<int8 t>• class BD Shape long double

Java class interfacing C++ Parma Polyhedra Library::BD Shape<long double>• class BD Shape mpq class

Java class interfacing C++ Parma Polyhedra Library::BD Shape<mpq class>• class BD Shape mpz class

Java class interfacing C++ Parma Polyhedra Library::BD Shape<mpz class>• enum Bounded Integer Type Overflow

Overflow behavior of bounded integer types.• enum Bounded Integer Type Representation

Representation of bounded integer types.• enum Bounded Integer Type Width

Widths of bounded integer types.• class By Reference

An utility class implementing mutable and non-mutable call-by-reference.• class C Polyhedron

Java class interfacing C++ Parma Polyhedra Library::C Polyhedron.• class Coefficient

A PPL coefficient.• enum Complexity Class

Possible Complexities.• class Congruence

A linear congruence.• class Congruence System

A system of congruences.• class Constraint

A linear equality or inequality.• class Constraint System

A system of constraints.• class Constraints Product C Polyhedron Grid

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<C Polyhedron,Grid>

34

• class Constraints Product Grid C Polyhedron

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,C Polyhedron>• class Constraints Product Grid NNC Polyhedron

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,NNC Polyhedron>• class Constraints Product NNC Polyhedron Grid

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<NNC Polyhedron,Grid>• enum Control Parameter Name

Names of MIP problems' control parameters.• enum Control Parameter Value

Possible values for MIP problem's control parameters.• enum Degenerate Element

Kinds of degenerate abstract elements.• class Domain Error Exception

Exceptions caused by domain errors.• class Double Box

Java class interfacing C++ Parma Polyhedra Library::Double Box.• class Float Box

Java class interfacing C++ Parma Polyhedra Library::Float Box.• class Generator

A line, ray, point or closure point.• class Generator System

A system of generators.• enum Generator Type

The generator type.• class Grid

Java class interfacing C++ Parma Polyhedra Library::Grid.• class Grid Generator

A grid line, parameter or grid point.• class Grid Generator System

A system of grid generators.• enum Grid Generator Type

The grid generator type.• class Int16 Box

Java class interfacing C++ Parma Polyhedra Library::Int16 Box.• class Int32 Box



Java class interfacing C++ Parma Polyhedra Library::Int8 Box.• class Invalid Argument Exception

Exceptions caused by invalid arguments.• class IO

A class collecting I/O functions.• class Length Error Exception

Exceptions caused by too big length/size values.

35

• class Linear Expression

A linear expression.• class Linear Expression Coefficient

A linear expression built from a coefficient.• class Linear Expression Difference

The difference of two linear expressions.• class Linear Expression Sum

The sum of two linear expressions.• class Linear Expression Times

The product of a linear expression and a coefficient.• class Linear Expression Unary Minus

The negation of a linear expression.• class Linear Expression Variable

A linear expression built from a variable.• class Logic Error Exception

Exceptions due to errors in low-level routines.• class Long Double Box

Java class interfacing C++ Parma Polyhedra Library::Long Double Box.• class MIP Problem

A Mixed Integer (linear) Programming problem.• enum MIP Problem Status

Possible outcomes of the MIP Problem solver.• class NNC Polyhedron

Java class interfacing C++ Parma Polyhedra Library::NNC Polyhedron.• class Octagonal Shape double

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<double>• class Octagonal Shape float

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<float>• class Octagonal Shape int16 t

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<int16 t>• class Octagonal Shape int32 t



Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<int8 t>• class Octagonal Shape long double

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<long double>• class Octagonal Shape mpq class

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpq class>• class Octagonal Shape mpz class

Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpz class>• enum Optimization Mode

Possible optimization modes.• class Overflow Error Exception

Exceptions due to overflow errors.

36

• class Pair

A pair of values of type K and V.• class Parma Polyhedra Library

A class collecting library-level functions.• class Partial Function

A partial function on space dimension indices.• class PIP Decision Node

An internal node of the PIP solution tree.• class PIP Problem

A Parametric Integer Programming problem.• enum PIP Problem Control Parameter Name

Names of PIP problems' control parameters.• enum PIP Problem Control Parameter Value

Possible values for PIP problems' control parameters.• enum PIP Problem Status

Possible outcomes of the PIP Problem solver.• class PIP Solution Node

A leaf node of the PIP solution tree.• class PIP Tree Node

A node of the PIP solution tree.• class Pointset Powerset BD Shape double

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >

• class Pointset Powerset BD Shape double Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >:: iter-ator.

• class Pointset Powerset BD Shape float

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float> >

• class Pointset Powerset BD Shape float Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float>>:: iterator.• class Pointset Powerset BD Shape int16 t

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16 t> >

• class Pointset Powerset BD Shape int16 t Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16 t> >:: iter-ator.

• class Pointset Powerset BD Shape int32 t











37

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int8 t> >:: itera-tor.

• class Pointset Powerset BD Shape long doubleJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double> >

• class Pointset Powerset BD Shape long double IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double>>←↩

:: iterator.• class Pointset Powerset BD Shape mpq class

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >

• class Pointset Powerset BD Shape mpq class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >:←↩

: iterator.• class Pointset Powerset BD Shape mpz class

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >

• class Pointset Powerset BD Shape mpz class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >:←↩

: iterator.• class Pointset Powerset C Polyhedron

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>• class Pointset Powerset C Polyhedron Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>:: iterator.• class Pointset Powerset Double Box

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>• class Pointset Powerset Double Box Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>:: iterator.• class Pointset Powerset Float Box

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>• class Pointset Powerset Float Box Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>:: iterator.• class Pointset Powerset Grid

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>• class Pointset Powerset Grid Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>:: iterator.• class Pointset Powerset Int16 Box

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>• class Pointset Powerset Int16 Box Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>:: iterator.• class Pointset Powerset Int32 Box





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int8 Box>

38

• class Pointset Powerset Int8 Box Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int8 Box>:: iterator.• class Pointset Powerset Long Double Box

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>• class Pointset Powerset Long Double Box Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>:: iterator.• class Pointset Powerset NNC Polyhedron

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>• class Pointset Powerset NNC Polyhedron Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>:: iterator.• class Pointset Powerset Octagonal Shape double

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<double> >

• class Pointset Powerset Octagonal Shape double Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<double>>←↩

:: iterator.• class Pointset Powerset Octagonal Shape float

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >

• class Pointset Powerset Octagonal Shape float Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >←↩

:: iterator.• class Pointset Powerset Octagonal Shape int16 t

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int16 t> >

• class Pointset Powerset Octagonal Shape int16 t Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int16 t>>←↩













:: iterator.• class Pointset Powerset Octagonal Shape long double

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<long double>>

• class Pointset Powerset Octagonal Shape long double Iterator

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<long double>>:: iterator.

• class Pointset Powerset Octagonal Shape mpq class

39

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpq class>>

• class Pointset Powerset Octagonal Shape mpq class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpq class>>:: iterator.

• class Pointset Powerset Octagonal Shape mpz classJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>

• class Pointset Powerset Octagonal Shape mpz class IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>:: iterator.

• class Pointset Powerset Rational BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>

• class Pointset Powerset Rational Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>:: iterator.

• class Pointset Powerset Uint16 BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>

• class Pointset Powerset Uint16 Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>:: iterator.







• class Pointset Powerset Z BoxJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>

• class Pointset Powerset Z Box IteratorJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>:: iterator.

• class Poly Con RelationThe relation between a polyhedron and a constraint.

• class Poly Gen RelationThe relation between a polyhedron and a generator.

• class PolyhedronJava class interfacing C++ Parma Polyhedra Library::Polyhedron.

• class Rational BoxJava class interfacing C++ Parma Polyhedra Library::Rational Box.

• enum Relation SymbolRelation symbols.

• class Timeout ExceptionExceptions caused by timeout expiring.

40

• class Uint16 BoxJava class interfacing C++ Parma Polyhedra Library::Uint16 Box.




• class VariableA dimension of the vector space.

• interface Variable StringifierAn interface for objects converting a Variable id to a string.

• class Variables SetA java.util.TreeSet of variables' indexes.

• class Z BoxJava class interfacing C++ Parma Polyhedra Library::Z Box.


The PPL Java interface package.All classes, interfaces and enums related to the Parma Polyhedra Library Java interface are included in

this package.

10 Class Documentation

10.1 parma polyhedra library.Artificial Parameter Class ReferencePublic Member Functions

• Artificial Parameter (Linear Expression e, Coefficient d)Builds an artificial parameter from a linear expression and a denominator.

• Linear Expression linear expression ()Returns the linear expression in artificial parameter this.

• Coefficient denominator ()Returns the denominator in artificial parameter this.

• native String ascii dump ()Returns an ascii formatted internal representation of this.

• native String toString ()Returns a string representation of this.


An Artificial Parameter object represents the result of the integer division of a Linear Expression (on theother parameters, including the previously-defined artificials) by an integer denominator (a Coefficientobject). The dimensions of the artificial parameters (if any) in a tree node have consecutive indices startingfrom dim+1, where the value of dim is computed as follows:

• for the tree root node, dim is the space dimension of the PIP Problem;

• for any other node of the tree, it is recusrively obtained by adding the value of dim computed for theparent node to the number of artificial parameters defined in the parent node.

41

Since the numbering of dimensions for artificial parameters follows the rule above, the additionof new problem variables and/or new problem parameters to an already solved PIP Problemobject (as done when incrementally solving a problem) will result in the systematic renumberingof all the existing artificial parameters.

The documentation for this class was generated from the following file:

• Artificial Parameter.java

10.2 parma polyhedra library.Artificial Parameter Sequence Class ReferenceA sequence of artificial parameters.

Inherits ArrayList< Artificial Parameter >.

Public Member Functions

• Artificial Parameter Sequence ()

Default constructor: builds an empty sequence of artificial parameters.


A sequence of artificial parameters.An object of the class Artificial Parameter Sequence is a sequence of artificial parameters.The documentation for this class was generated from the following file:

• Artificial Parameter Sequence.java

10.3 parma polyhedra library.BD Shape double Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<double>

Inherits parma polyhedra library.PPL Object.


• BD Shape double (long num dimensions, Degenerate Element kind)• BD Shape double (Int8 Box y)• BD Shape double (Int16 Box y)• BD Shape double (Int32 Box y)• BD Shape double (Int64 Box y)• BD Shape double (Uint8 Box y)• BD Shape double (Uint16 Box y)• BD Shape double (Uint32 Box y)• BD Shape double (Uint64 Box y)• BD Shape double (Z Box y)• BD Shape double (Rational Box y)• BD Shape double (BD Shape int8 t y)• BD Shape double (BD Shape int16 t y)• BD Shape double (BD Shape int32 t y)• BD Shape double (BD Shape int64 t y)• BD Shape double (BD Shape mpz class y)• BD Shape double (BD Shape mpq class y)• BD Shape double (Octagonal Shape int8 t y)• BD Shape double (Octagonal Shape int16 t y)

42

• BD Shape double (Octagonal Shape int32 t y)• BD Shape double (Octagonal Shape int64 t y)• BD Shape double (Octagonal Shape mpz class y)• BD Shape double (Octagonal Shape mpq class y)• BD Shape double (C Polyhedron y)• BD Shape double (NNC Polyhedron y)• BD Shape double (Grid y)• BD Shape double (Float Box y)• BD Shape double (BD Shape float y)• BD Shape double (Octagonal Shape float y)• BD Shape double (Double Box y)• BD Shape double (BD Shape double y)• BD Shape double (Octagonal Shape double y)• BD Shape double (Long Double Box y)• BD Shape double (BD Shape long double y)• BD Shape double (Octagonal Shape long double y)• BD Shape double (Int8 Box y, Complexity Class complexity)• BD Shape double (Int16 Box y, Complexity Class complexity)• BD Shape double (Int32 Box y, Complexity Class complexity)• BD Shape double (Int64 Box y, Complexity Class complexity)• BD Shape double (Uint8 Box y, Complexity Class complexity)• BD Shape double (Uint16 Box y, Complexity Class complexity)• BD Shape double (Uint32 Box y, Complexity Class complexity)• BD Shape double (Uint64 Box y, Complexity Class complexity)• BD Shape double (Z Box y, Complexity Class complexity)• BD Shape double (Rational Box y, Complexity Class complexity)• BD Shape double (BD Shape int8 t y, Complexity Class complexity)• BD Shape double (BD Shape int16 t y, Complexity Class complexity)• BD Shape double (BD Shape int32 t y, Complexity Class complexity)• BD Shape double (BD Shape int64 t y, Complexity Class complexity)• BD Shape double (BD Shape mpz class y, Complexity Class complexity)• BD Shape double (BD Shape mpq class y, Complexity Class complexity)• BD Shape double (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape double (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape double (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape double (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape double (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape double (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape double (C Polyhedron y, Complexity Class complexity)• BD Shape double (NNC Polyhedron y, Complexity Class complexity)• BD Shape double (Grid y, Complexity Class complexity)• BD Shape double (Float Box y, Complexity Class complexity)• BD Shape double (BD Shape float y, Complexity Class complexity)• BD Shape double (Octagonal Shape float y, Complexity Class complexity)• BD Shape double (Double Box y, Complexity Class complexity)• BD Shape double (BD Shape double y, Complexity Class complexity)• BD Shape double (Octagonal Shape double y, Complexity Class complexity)• BD Shape double (Long Double Box y, Complexity Class complexity)• BD Shape double (BD Shape long double y, Complexity Class complexity)• BD Shape double (Octagonal Shape long double y, Complexity Class complexity)

43

• BD Shape double (Constraint System cs)• BD Shape double (Congruence System cs)• BD Shape double (Generator System cs)• native void swap (BD Shape double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)• native boolean minimize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum, Generator point)• native boolean minimize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum, Generator point)• native boolean frequency (Linear Expression expr, Coefficient freq n, Coefficient freq d, Coeffi-

cient val n, Coefficient val d)• native boolean contains (BD Shape double y)• native boolean strictly contains (BD Shape double y)• native boolean is disjoint from (BD Shape double y)• native boolean equals (BD Shape double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape double p)• native void upper bound assign (BD Shape double p)• native void difference assign (BD Shape double p)• native void concatenate assign (BD Shape double p)

44

• native void time elapse assign (BD Shape double p)• native boolean upper bound assign if exact (BD Shape double y)• native boolean simplify using context assign (BD Shape double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩

expr, Coefficient denominator)• native void bounded affine preimage (Variable var, Linear Expression lb expr, Linear Expression

ub expr, Coefficient denominator)• native void generalized affine image (Variable var, Relation Symbol relsym, Linear Expression

expr, Coefficient denominator)• native void generalized affine preimage (Variable var, Relation Symbol relsym, Linear Expression

expr, Coefficient denominator)• native void generalized affine image (Linear Expression lhs, Relation Symbol relsym, Linear ←↩

Expression rhs)• native void generalized affine preimage (Linear Expression lhs, Relation Symbol relsym, Linear←↩

Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape double y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape double y, By Reference< Integer > tp)• native void widening assign (BD Shape double y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape double y, Constraint System cs,

By Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape double y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void limited CC76 extrapolation assign (BD Shape double y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape double arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape double arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩

Type Representation r, Bounded Integer Type Overflow o, Constraint System cs, long complexity←↩

threshold, boolean wrap individually)• native void free ()• native int hashCode ()• native String toString ()

45

Static Public Member Functions

• static native Pair< BD Shape double, Pointset Powerset NNC Polyhedron > linear partition (B←↩

D Shape double p, BD Shape double q)

Protected Member Functions

• native void finalize ()


Java class interfacing C++ Parma Polyhedra Library::BD Shape<double>The documentation for this class was generated from the following file:

• BD Shape double.java

10.4 parma polyhedra library.BD Shape float Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<float>



• BD Shape float (long num dimensions, Degenerate Element kind)• BD Shape float (Int8 Box y)• BD Shape float (Int16 Box y)• BD Shape float (Int32 Box y)• BD Shape float (Int64 Box y)• BD Shape float (Uint8 Box y)• BD Shape float (Uint16 Box y)• BD Shape float (Uint32 Box y)• BD Shape float (Uint64 Box y)• BD Shape float (Z Box y)• BD Shape float (Rational Box y)• BD Shape float (BD Shape int8 t y)• BD Shape float (BD Shape int16 t y)• BD Shape float (BD Shape int32 t y)• BD Shape float (BD Shape int64 t y)• BD Shape float (BD Shape mpz class y)• BD Shape float (BD Shape mpq class y)• BD Shape float (Octagonal Shape int8 t y)• BD Shape float (Octagonal Shape int16 t y)• BD Shape float (Octagonal Shape int32 t y)• BD Shape float (Octagonal Shape int64 t y)• BD Shape float (Octagonal Shape mpz class y)• BD Shape float (Octagonal Shape mpq class y)• BD Shape float (C Polyhedron y)• BD Shape float (NNC Polyhedron y)• BD Shape float (Grid y)• BD Shape float (Float Box y)• BD Shape float (BD Shape float y)• BD Shape float (Octagonal Shape float y)• BD Shape float (Double Box y)

46

• BD Shape float (BD Shape double y)• BD Shape float (Octagonal Shape double y)• BD Shape float (Long Double Box y)• BD Shape float (BD Shape long double y)• BD Shape float (Octagonal Shape long double y)• BD Shape float (Int8 Box y, Complexity Class complexity)• BD Shape float (Int16 Box y, Complexity Class complexity)• BD Shape float (Int32 Box y, Complexity Class complexity)• BD Shape float (Int64 Box y, Complexity Class complexity)• BD Shape float (Uint8 Box y, Complexity Class complexity)• BD Shape float (Uint16 Box y, Complexity Class complexity)• BD Shape float (Uint32 Box y, Complexity Class complexity)• BD Shape float (Uint64 Box y, Complexity Class complexity)• BD Shape float (Z Box y, Complexity Class complexity)• BD Shape float (Rational Box y, Complexity Class complexity)• BD Shape float (BD Shape int8 t y, Complexity Class complexity)• BD Shape float (BD Shape int16 t y, Complexity Class complexity)• BD Shape float (BD Shape int32 t y, Complexity Class complexity)• BD Shape float (BD Shape int64 t y, Complexity Class complexity)• BD Shape float (BD Shape mpz class y, Complexity Class complexity)• BD Shape float (BD Shape mpq class y, Complexity Class complexity)• BD Shape float (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape float (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape float (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape float (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape float (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape float (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape float (C Polyhedron y, Complexity Class complexity)• BD Shape float (NNC Polyhedron y, Complexity Class complexity)• BD Shape float (Grid y, Complexity Class complexity)• BD Shape float (Float Box y, Complexity Class complexity)• BD Shape float (BD Shape float y, Complexity Class complexity)• BD Shape float (Octagonal Shape float y, Complexity Class complexity)• BD Shape float (Double Box y, Complexity Class complexity)• BD Shape float (BD Shape double y, Complexity Class complexity)• BD Shape float (Octagonal Shape double y, Complexity Class complexity)• BD Shape float (Long Double Box y, Complexity Class complexity)• BD Shape float (BD Shape long double y, Complexity Class complexity)• BD Shape float (Octagonal Shape long double y, Complexity Class complexity)• BD Shape float (Constraint System cs)• BD Shape float (Congruence System cs)• BD Shape float (Generator System cs)• native void swap (BD Shape float y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()

47

• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (BD Shape float y)• native boolean strictly contains (BD Shape float y)• native boolean is disjoint from (BD Shape float y)• native boolean equals (BD Shape float p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape float p)• native void upper bound assign (BD Shape float p)• native void difference assign (BD Shape float p)• native void concatenate assign (BD Shape float p)• native void time elapse assign (BD Shape float p)• native boolean upper bound assign if exact (BD Shape float y)• native boolean simplify using context assign (BD Shape float p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩


ub expr, Coefficient denominator)

48

• native void generalized affine image (Variable var, Relation Symbol relsym, Linear Expressionexpr, Coefficient denominator)

• native void generalized affine preimage (Variable var, Relation Symbol relsym, Linear Expressionexpr, Coefficient denominator)

• native void generalized affine image (Linear Expression lhs, Relation Symbol relsym, Linear ←↩


Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape float y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape float y, By Reference< Integer > tp)• native void widening assign (BD Shape float y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape float y, Constraint System cs, By←↩

Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape float y, Constraint System cs, By Reference<

Integer > tp)• native void limited CC76 extrapolation assign (BD Shape float y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape float arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape float arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< BD Shape float, Pointset Powerset NNC Polyhedron > linear partition (BD←↩

Shape float p, BD Shape float q)




Java class interfacing C++ Parma Polyhedra Library::BD Shape<float>The documentation for this class was generated from the following file:

• BD Shape float.java

49

10.5 parma polyhedra library.BD Shape int16 t Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<int16 t>



• BD Shape int16 t (long num dimensions, Degenerate Element kind)• BD Shape int16 t (Int8 Box y)• BD Shape int16 t (Int16 Box y)• BD Shape int16 t (Int32 Box y)• BD Shape int16 t (Int64 Box y)• BD Shape int16 t (Uint8 Box y)• BD Shape int16 t (Uint16 Box y)• BD Shape int16 t (Uint32 Box y)• BD Shape int16 t (Uint64 Box y)• BD Shape int16 t (Z Box y)• BD Shape int16 t (Rational Box y)• BD Shape int16 t (BD Shape int8 t y)• BD Shape int16 t (BD Shape int16 t y)• BD Shape int16 t (BD Shape int32 t y)• BD Shape int16 t (BD Shape int64 t y)• BD Shape int16 t (BD Shape mpz class y)• BD Shape int16 t (BD Shape mpq class y)• BD Shape int16 t (Octagonal Shape int8 t y)• BD Shape int16 t (Octagonal Shape int16 t y)• BD Shape int16 t (Octagonal Shape int32 t y)• BD Shape int16 t (Octagonal Shape int64 t y)• BD Shape int16 t (Octagonal Shape mpz class y)• BD Shape int16 t (Octagonal Shape mpq class y)• BD Shape int16 t (C Polyhedron y)• BD Shape int16 t (NNC Polyhedron y)• BD Shape int16 t (Grid y)• BD Shape int16 t (Float Box y)• BD Shape int16 t (BD Shape float y)• BD Shape int16 t (Octagonal Shape float y)• BD Shape int16 t (Double Box y)• BD Shape int16 t (BD Shape double y)• BD Shape int16 t (Octagonal Shape double y)• BD Shape int16 t (Long Double Box y)• BD Shape int16 t (BD Shape long double y)• BD Shape int16 t (Octagonal Shape long double y)• BD Shape int16 t (Int8 Box y, Complexity Class complexity)• BD Shape int16 t (Int16 Box y, Complexity Class complexity)• BD Shape int16 t (Int32 Box y, Complexity Class complexity)• BD Shape int16 t (Int64 Box y, Complexity Class complexity)• BD Shape int16 t (Uint8 Box y, Complexity Class complexity)• BD Shape int16 t (Uint16 Box y, Complexity Class complexity)• BD Shape int16 t (Uint32 Box y, Complexity Class complexity)• BD Shape int16 t (Uint64 Box y, Complexity Class complexity)• BD Shape int16 t (Z Box y, Complexity Class complexity)

50

• BD Shape int16 t (Rational Box y, Complexity Class complexity)• BD Shape int16 t (BD Shape int8 t y, Complexity Class complexity)• BD Shape int16 t (BD Shape int16 t y, Complexity Class complexity)• BD Shape int16 t (BD Shape int32 t y, Complexity Class complexity)• BD Shape int16 t (BD Shape int64 t y, Complexity Class complexity)• BD Shape int16 t (BD Shape mpz class y, Complexity Class complexity)• BD Shape int16 t (BD Shape mpq class y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape int16 t (C Polyhedron y, Complexity Class complexity)• BD Shape int16 t (NNC Polyhedron y, Complexity Class complexity)• BD Shape int16 t (Grid y, Complexity Class complexity)• BD Shape int16 t (Float Box y, Complexity Class complexity)• BD Shape int16 t (BD Shape float y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape float y, Complexity Class complexity)• BD Shape int16 t (Double Box y, Complexity Class complexity)• BD Shape int16 t (BD Shape double y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape double y, Complexity Class complexity)• BD Shape int16 t (Long Double Box y, Complexity Class complexity)• BD Shape int16 t (BD Shape long double y, Complexity Class complexity)• BD Shape int16 t (Octagonal Shape long double y, Complexity Class complexity)• BD Shape int16 t (Constraint System cs)• BD Shape int16 t (Congruence System cs)• BD Shape int16 t (Generator System cs)• native void swap (BD Shape int16 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)

51

• native boolean minimize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<Boolean > maximum)

• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<Boolean > maximum, Generator point)

• native boolean minimize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<Boolean > maximum, Generator point)

• native boolean frequency (Linear Expression expr, Coefficient freq n, Coefficient freq d, Coeffi-cient val n, Coefficient val d)

• native boolean contains (BD Shape int16 t y)• native boolean strictly contains (BD Shape int16 t y)• native boolean is disjoint from (BD Shape int16 t y)• native boolean equals (BD Shape int16 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape int16 t p)• native void upper bound assign (BD Shape int16 t p)• native void difference assign (BD Shape int16 t p)• native void concatenate assign (BD Shape int16 t p)• native void time elapse assign (BD Shape int16 t p)• native boolean upper bound assign if exact (BD Shape int16 t y)• native boolean simplify using context assign (BD Shape int16 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)

52

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape int16 t y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape int16 t y, By Reference< Integer > tp)• native void widening assign (BD Shape int16 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape int16 t y, Constraint System cs,

By Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape int16 t y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void limited CC76 extrapolation assign (BD Shape int16 t y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape int16 t arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape int16 t arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< BD Shape int16 t, Pointset Powerset NNC Polyhedron > linear partition (B←↩

D Shape int16 t p, BD Shape int16 t q)




Java class interfacing C++ Parma Polyhedra Library::BD Shape<int16 t>The documentation for this class was generated from the following file:

• BD Shape int16 t.java




• BD Shape int32 t (long num dimensions, Degenerate Element kind)• BD Shape int32 t (Int8 Box y)• BD Shape int32 t (Int16 Box y)• BD Shape int32 t (Int32 Box y)• BD Shape int32 t (Int64 Box y)

53

• BD Shape int32 t (Uint8 Box y)• BD Shape int32 t (Uint16 Box y)• BD Shape int32 t (Uint32 Box y)• BD Shape int32 t (Uint64 Box y)• BD Shape int32 t (Z Box y)• BD Shape int32 t (Rational Box y)• BD Shape int32 t (BD Shape int8 t y)• BD Shape int32 t (BD Shape int16 t y)• BD Shape int32 t (BD Shape int32 t y)• BD Shape int32 t (BD Shape int64 t y)• BD Shape int32 t (BD Shape mpz class y)• BD Shape int32 t (BD Shape mpq class y)• BD Shape int32 t (Octagonal Shape int8 t y)• BD Shape int32 t (Octagonal Shape int16 t y)• BD Shape int32 t (Octagonal Shape int32 t y)• BD Shape int32 t (Octagonal Shape int64 t y)• BD Shape int32 t (Octagonal Shape mpz class y)• BD Shape int32 t (Octagonal Shape mpq class y)• BD Shape int32 t (C Polyhedron y)• BD Shape int32 t (NNC Polyhedron y)• BD Shape int32 t (Grid y)• BD Shape int32 t (Float Box y)• BD Shape int32 t (BD Shape float y)• BD Shape int32 t (Octagonal Shape float y)• BD Shape int32 t (Double Box y)• BD Shape int32 t (BD Shape double y)• BD Shape int32 t (Octagonal Shape double y)• BD Shape int32 t (Long Double Box y)• BD Shape int32 t (BD Shape long double y)• BD Shape int32 t (Octagonal Shape long double y)• BD Shape int32 t (Int8 Box y, Complexity Class complexity)• BD Shape int32 t (Int16 Box y, Complexity Class complexity)• BD Shape int32 t (Int32 Box y, Complexity Class complexity)• BD Shape int32 t (Int64 Box y, Complexity Class complexity)• BD Shape int32 t (Uint8 Box y, Complexity Class complexity)• BD Shape int32 t (Uint16 Box y, Complexity Class complexity)• BD Shape int32 t (Uint32 Box y, Complexity Class complexity)• BD Shape int32 t (Uint64 Box y, Complexity Class complexity)• BD Shape int32 t (Z Box y, Complexity Class complexity)• BD Shape int32 t (Rational Box y, Complexity Class complexity)• BD Shape int32 t (BD Shape int8 t y, Complexity Class complexity)• BD Shape int32 t (BD Shape int16 t y, Complexity Class complexity)• BD Shape int32 t (BD Shape int32 t y, Complexity Class complexity)• BD Shape int32 t (BD Shape int64 t y, Complexity Class complexity)• BD Shape int32 t (BD Shape mpz class y, Complexity Class complexity)• BD Shape int32 t (BD Shape mpq class y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape int64 t y, Complexity Class complexity)

54

• BD Shape int32 t (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape int32 t (C Polyhedron y, Complexity Class complexity)• BD Shape int32 t (NNC Polyhedron y, Complexity Class complexity)• BD Shape int32 t (Grid y, Complexity Class complexity)• BD Shape int32 t (Float Box y, Complexity Class complexity)• BD Shape int32 t (BD Shape float y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape float y, Complexity Class complexity)• BD Shape int32 t (Double Box y, Complexity Class complexity)• BD Shape int32 t (BD Shape double y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape double y, Complexity Class complexity)• BD Shape int32 t (Long Double Box y, Complexity Class complexity)• BD Shape int32 t (BD Shape long double y, Complexity Class complexity)• BD Shape int32 t (Octagonal Shape long double y, Complexity Class complexity)• BD Shape int32 t (Constraint System cs)• BD Shape int32 t (Congruence System cs)• BD Shape int32 t (Generator System cs)• native void swap (BD Shape int32 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (BD Shape int32 t y)• native boolean strictly contains (BD Shape int32 t y)• native boolean is disjoint from (BD Shape int32 t y)• native boolean equals (BD Shape int32 t p)

55

• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape int32 t p)• native void upper bound assign (BD Shape int32 t p)• native void difference assign (BD Shape int32 t p)• native void concatenate assign (BD Shape int32 t p)• native void time elapse assign (BD Shape int32 t p)• native boolean upper bound assign if exact (BD Shape int32 t y)• native boolean simplify using context assign (BD Shape int32 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape int32 t y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape int32 t y, By Reference< Integer > tp)• native void widening assign (BD Shape int32 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape int32 t y, Constraint System cs,

By Reference< Integer > tp)

56

• native void limited H79 extrapolation assign (BD Shape int32 t y, Constraint System cs, By ←↩
















• BD Shape int64 t (long num dimensions, Degenerate Element kind)• BD Shape int64 t (Int8 Box y)• BD Shape int64 t (Int16 Box y)• BD Shape int64 t (Int32 Box y)• BD Shape int64 t (Int64 Box y)• BD Shape int64 t (Uint8 Box y)• BD Shape int64 t (Uint16 Box y)• BD Shape int64 t (Uint32 Box y)• BD Shape int64 t (Uint64 Box y)• BD Shape int64 t (Z Box y)• BD Shape int64 t (Rational Box y)• BD Shape int64 t (BD Shape int8 t y)• BD Shape int64 t (BD Shape int16 t y)• BD Shape int64 t (BD Shape int32 t y)• BD Shape int64 t (BD Shape int64 t y)• BD Shape int64 t (BD Shape mpz class y)• BD Shape int64 t (BD Shape mpq class y)

57

• BD Shape int64 t (Octagonal Shape int8 t y)• BD Shape int64 t (Octagonal Shape int16 t y)• BD Shape int64 t (Octagonal Shape int32 t y)• BD Shape int64 t (Octagonal Shape int64 t y)• BD Shape int64 t (Octagonal Shape mpz class y)• BD Shape int64 t (Octagonal Shape mpq class y)• BD Shape int64 t (C Polyhedron y)• BD Shape int64 t (NNC Polyhedron y)• BD Shape int64 t (Grid y)• BD Shape int64 t (Float Box y)• BD Shape int64 t (BD Shape float y)• BD Shape int64 t (Octagonal Shape float y)• BD Shape int64 t (Double Box y)• BD Shape int64 t (BD Shape double y)• BD Shape int64 t (Octagonal Shape double y)• BD Shape int64 t (Long Double Box y)• BD Shape int64 t (BD Shape long double y)• BD Shape int64 t (Octagonal Shape long double y)• BD Shape int64 t (Int8 Box y, Complexity Class complexity)• BD Shape int64 t (Int16 Box y, Complexity Class complexity)• BD Shape int64 t (Int32 Box y, Complexity Class complexity)• BD Shape int64 t (Int64 Box y, Complexity Class complexity)• BD Shape int64 t (Uint8 Box y, Complexity Class complexity)• BD Shape int64 t (Uint16 Box y, Complexity Class complexity)• BD Shape int64 t (Uint32 Box y, Complexity Class complexity)• BD Shape int64 t (Uint64 Box y, Complexity Class complexity)• BD Shape int64 t (Z Box y, Complexity Class complexity)• BD Shape int64 t (Rational Box y, Complexity Class complexity)• BD Shape int64 t (BD Shape int8 t y, Complexity Class complexity)• BD Shape int64 t (BD Shape int16 t y, Complexity Class complexity)• BD Shape int64 t (BD Shape int32 t y, Complexity Class complexity)• BD Shape int64 t (BD Shape int64 t y, Complexity Class complexity)• BD Shape int64 t (BD Shape mpz class y, Complexity Class complexity)• BD Shape int64 t (BD Shape mpq class y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape int64 t (C Polyhedron y, Complexity Class complexity)• BD Shape int64 t (NNC Polyhedron y, Complexity Class complexity)• BD Shape int64 t (Grid y, Complexity Class complexity)• BD Shape int64 t (Float Box y, Complexity Class complexity)• BD Shape int64 t (BD Shape float y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape float y, Complexity Class complexity)• BD Shape int64 t (Double Box y, Complexity Class complexity)• BD Shape int64 t (BD Shape double y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape double y, Complexity Class complexity)• BD Shape int64 t (Long Double Box y, Complexity Class complexity)

58

• BD Shape int64 t (BD Shape long double y, Complexity Class complexity)• BD Shape int64 t (Octagonal Shape long double y, Complexity Class complexity)• BD Shape int64 t (Constraint System cs)• BD Shape int64 t (Congruence System cs)• BD Shape int64 t (Generator System cs)• native void swap (BD Shape int64 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (BD Shape int64 t y)• native boolean strictly contains (BD Shape int64 t y)• native boolean is disjoint from (BD Shape int64 t y)• native boolean equals (BD Shape int64 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape int64 t p)• native void upper bound assign (BD Shape int64 t p)

59

• native void difference assign (BD Shape int64 t p)• native void concatenate assign (BD Shape int64 t p)• native void time elapse assign (BD Shape int64 t p)• native boolean upper bound assign if exact (BD Shape int64 t y)• native boolean simplify using context assign (BD Shape int64 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape int64 t y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape int64 t y, By Reference< Integer > tp)• native void widening assign (BD Shape int64 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape int64 t y, Constraint System cs,

By Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape int64 t y, Constraint System cs, By ←↩





60












• BD Shape int8 t (long num dimensions, Degenerate Element kind)• BD Shape int8 t (Int8 Box y)• BD Shape int8 t (Int16 Box y)• BD Shape int8 t (Int32 Box y)• BD Shape int8 t (Int64 Box y)• BD Shape int8 t (Uint8 Box y)• BD Shape int8 t (Uint16 Box y)• BD Shape int8 t (Uint32 Box y)• BD Shape int8 t (Uint64 Box y)• BD Shape int8 t (Z Box y)• BD Shape int8 t (Rational Box y)• BD Shape int8 t (BD Shape int8 t y)• BD Shape int8 t (BD Shape int16 t y)• BD Shape int8 t (BD Shape int32 t y)• BD Shape int8 t (BD Shape int64 t y)• BD Shape int8 t (BD Shape mpz class y)• BD Shape int8 t (BD Shape mpq class y)• BD Shape int8 t (Octagonal Shape int8 t y)• BD Shape int8 t (Octagonal Shape int16 t y)• BD Shape int8 t (Octagonal Shape int32 t y)• BD Shape int8 t (Octagonal Shape int64 t y)• BD Shape int8 t (Octagonal Shape mpz class y)• BD Shape int8 t (Octagonal Shape mpq class y)• BD Shape int8 t (C Polyhedron y)• BD Shape int8 t (NNC Polyhedron y)• BD Shape int8 t (Grid y)• BD Shape int8 t (Float Box y)• BD Shape int8 t (BD Shape float y)• BD Shape int8 t (Octagonal Shape float y)• BD Shape int8 t (Double Box y)

61

• BD Shape int8 t (BD Shape double y)• BD Shape int8 t (Octagonal Shape double y)• BD Shape int8 t (Long Double Box y)• BD Shape int8 t (BD Shape long double y)• BD Shape int8 t (Octagonal Shape long double y)• BD Shape int8 t (Int8 Box y, Complexity Class complexity)• BD Shape int8 t (Int16 Box y, Complexity Class complexity)• BD Shape int8 t (Int32 Box y, Complexity Class complexity)• BD Shape int8 t (Int64 Box y, Complexity Class complexity)• BD Shape int8 t (Uint8 Box y, Complexity Class complexity)• BD Shape int8 t (Uint16 Box y, Complexity Class complexity)• BD Shape int8 t (Uint32 Box y, Complexity Class complexity)• BD Shape int8 t (Uint64 Box y, Complexity Class complexity)• BD Shape int8 t (Z Box y, Complexity Class complexity)• BD Shape int8 t (Rational Box y, Complexity Class complexity)• BD Shape int8 t (BD Shape int8 t y, Complexity Class complexity)• BD Shape int8 t (BD Shape int16 t y, Complexity Class complexity)• BD Shape int8 t (BD Shape int32 t y, Complexity Class complexity)• BD Shape int8 t (BD Shape int64 t y, Complexity Class complexity)• BD Shape int8 t (BD Shape mpz class y, Complexity Class complexity)• BD Shape int8 t (BD Shape mpq class y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape int8 t (C Polyhedron y, Complexity Class complexity)• BD Shape int8 t (NNC Polyhedron y, Complexity Class complexity)• BD Shape int8 t (Grid y, Complexity Class complexity)• BD Shape int8 t (Float Box y, Complexity Class complexity)• BD Shape int8 t (BD Shape float y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape float y, Complexity Class complexity)• BD Shape int8 t (Double Box y, Complexity Class complexity)• BD Shape int8 t (BD Shape double y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape double y, Complexity Class complexity)• BD Shape int8 t (Long Double Box y, Complexity Class complexity)• BD Shape int8 t (BD Shape long double y, Complexity Class complexity)• BD Shape int8 t (Octagonal Shape long double y, Complexity Class complexity)• BD Shape int8 t (Constraint System cs)• BD Shape int8 t (Congruence System cs)• BD Shape int8 t (Generator System cs)• native void swap (BD Shape int8 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()

62






cient val n, Coefficient val d)• native boolean contains (BD Shape int8 t y)• native boolean strictly contains (BD Shape int8 t y)• native boolean is disjoint from (BD Shape int8 t y)• native boolean equals (BD Shape int8 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape int8 t p)• native void upper bound assign (BD Shape int8 t p)• native void difference assign (BD Shape int8 t p)• native void concatenate assign (BD Shape int8 t p)• native void time elapse assign (BD Shape int8 t p)• native boolean upper bound assign if exact (BD Shape int8 t y)• native boolean simplify using context assign (BD Shape int8 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



63





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape int8 t y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape int8 t y, By Reference< Integer > tp)• native void widening assign (BD Shape int8 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape int8 t y, Constraint System cs, By←↩

Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape int8 t y, Constraint System cs, By ←↩













64

10.9 parma polyhedra library.BD Shape long double Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<long double>



• BD Shape long double (long num dimensions, Degenerate Element kind)• BD Shape long double (Int8 Box y)• BD Shape long double (Int16 Box y)• BD Shape long double (Int32 Box y)• BD Shape long double (Int64 Box y)• BD Shape long double (Uint8 Box y)• BD Shape long double (Uint16 Box y)• BD Shape long double (Uint32 Box y)• BD Shape long double (Uint64 Box y)• BD Shape long double (Z Box y)• BD Shape long double (Rational Box y)• BD Shape long double (BD Shape int8 t y)• BD Shape long double (BD Shape int16 t y)• BD Shape long double (BD Shape int32 t y)• BD Shape long double (BD Shape int64 t y)• BD Shape long double (BD Shape mpz class y)• BD Shape long double (BD Shape mpq class y)• BD Shape long double (Octagonal Shape int8 t y)• BD Shape long double (Octagonal Shape int16 t y)• BD Shape long double (Octagonal Shape int32 t y)• BD Shape long double (Octagonal Shape int64 t y)• BD Shape long double (Octagonal Shape mpz class y)• BD Shape long double (Octagonal Shape mpq class y)• BD Shape long double (C Polyhedron y)• BD Shape long double (NNC Polyhedron y)• BD Shape long double (Grid y)• BD Shape long double (Float Box y)• BD Shape long double (BD Shape float y)• BD Shape long double (Octagonal Shape float y)• BD Shape long double (Double Box y)• BD Shape long double (BD Shape double y)• BD Shape long double (Octagonal Shape double y)• BD Shape long double (Long Double Box y)• BD Shape long double (BD Shape long double y)• BD Shape long double (Octagonal Shape long double y)• BD Shape long double (Int8 Box y, Complexity Class complexity)• BD Shape long double (Int16 Box y, Complexity Class complexity)• BD Shape long double (Int32 Box y, Complexity Class complexity)• BD Shape long double (Int64 Box y, Complexity Class complexity)• BD Shape long double (Uint8 Box y, Complexity Class complexity)• BD Shape long double (Uint16 Box y, Complexity Class complexity)• BD Shape long double (Uint32 Box y, Complexity Class complexity)• BD Shape long double (Uint64 Box y, Complexity Class complexity)• BD Shape long double (Z Box y, Complexity Class complexity)

65

• BD Shape long double (Rational Box y, Complexity Class complexity)• BD Shape long double (BD Shape int8 t y, Complexity Class complexity)• BD Shape long double (BD Shape int16 t y, Complexity Class complexity)• BD Shape long double (BD Shape int32 t y, Complexity Class complexity)• BD Shape long double (BD Shape int64 t y, Complexity Class complexity)• BD Shape long double (BD Shape mpz class y, Complexity Class complexity)• BD Shape long double (BD Shape mpq class y, Complexity Class complexity)• BD Shape long double (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape long double (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape long double (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape long double (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape long double (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape long double (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape long double (C Polyhedron y, Complexity Class complexity)• BD Shape long double (NNC Polyhedron y, Complexity Class complexity)• BD Shape long double (Grid y, Complexity Class complexity)• BD Shape long double (Float Box y, Complexity Class complexity)• BD Shape long double (BD Shape float y, Complexity Class complexity)• BD Shape long double (Octagonal Shape float y, Complexity Class complexity)• BD Shape long double (Double Box y, Complexity Class complexity)• BD Shape long double (BD Shape double y, Complexity Class complexity)• BD Shape long double (Octagonal Shape double y, Complexity Class complexity)• BD Shape long double (Long Double Box y, Complexity Class complexity)• BD Shape long double (BD Shape long double y, Complexity Class complexity)• BD Shape long double (Octagonal Shape long double y, Complexity Class complexity)• BD Shape long double (Constraint System cs)• BD Shape long double (Congruence System cs)• BD Shape long double (Generator System cs)• native void swap (BD Shape long double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)

66





• native boolean contains (BD Shape long double y)• native boolean strictly contains (BD Shape long double y)• native boolean is disjoint from (BD Shape long double y)• native boolean equals (BD Shape long double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape long double p)• native void upper bound assign (BD Shape long double p)• native void difference assign (BD Shape long double p)• native void concatenate assign (BD Shape long double p)• native void time elapse assign (BD Shape long double p)• native boolean upper bound assign if exact (BD Shape long double y)• native boolean simplify using context assign (BD Shape long double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







67

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape long double y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape long double y, By Reference< Integer > tp)• native void widening assign (BD Shape long double y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape long double y, Constraint System

cs, By Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape long double y, Constraint System cs,

By Reference< Integer > tp)• native void limited CC76 extrapolation assign (BD Shape long double y, Constraint System cs,

By Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape long double arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape long double arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< BD Shape long double, Pointset Powerset NNC Polyhedron > linear partition(BD Shape long double p, BD Shape long double q)




Java class interfacing C++ Parma Polyhedra Library::BD Shape<long double>The documentation for this class was generated from the following file:

• BD Shape long double.java

10.10 parma polyhedra library.BD Shape mpq class Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<mpq class>



• BD Shape mpq class (long num dimensions, Degenerate Element kind)• BD Shape mpq class (Int8 Box y)• BD Shape mpq class (Int16 Box y)• BD Shape mpq class (Int32 Box y)• BD Shape mpq class (Int64 Box y)

68

• BD Shape mpq class (Uint8 Box y)• BD Shape mpq class (Uint16 Box y)• BD Shape mpq class (Uint32 Box y)• BD Shape mpq class (Uint64 Box y)• BD Shape mpq class (Z Box y)• BD Shape mpq class (Rational Box y)• BD Shape mpq class (BD Shape int8 t y)• BD Shape mpq class (BD Shape int16 t y)• BD Shape mpq class (BD Shape int32 t y)• BD Shape mpq class (BD Shape int64 t y)• BD Shape mpq class (BD Shape mpz class y)• BD Shape mpq class (BD Shape mpq class y)• BD Shape mpq class (Octagonal Shape int8 t y)• BD Shape mpq class (Octagonal Shape int16 t y)• BD Shape mpq class (Octagonal Shape int32 t y)• BD Shape mpq class (Octagonal Shape int64 t y)• BD Shape mpq class (Octagonal Shape mpz class y)• BD Shape mpq class (Octagonal Shape mpq class y)• BD Shape mpq class (C Polyhedron y)• BD Shape mpq class (NNC Polyhedron y)• BD Shape mpq class (Grid y)• BD Shape mpq class (Float Box y)• BD Shape mpq class (BD Shape float y)• BD Shape mpq class (Octagonal Shape float y)• BD Shape mpq class (Double Box y)• BD Shape mpq class (BD Shape double y)• BD Shape mpq class (Octagonal Shape double y)• BD Shape mpq class (Long Double Box y)• BD Shape mpq class (BD Shape long double y)• BD Shape mpq class (Octagonal Shape long double y)• BD Shape mpq class (Int8 Box y, Complexity Class complexity)• BD Shape mpq class (Int16 Box y, Complexity Class complexity)• BD Shape mpq class (Int32 Box y, Complexity Class complexity)• BD Shape mpq class (Int64 Box y, Complexity Class complexity)• BD Shape mpq class (Uint8 Box y, Complexity Class complexity)• BD Shape mpq class (Uint16 Box y, Complexity Class complexity)• BD Shape mpq class (Uint32 Box y, Complexity Class complexity)• BD Shape mpq class (Uint64 Box y, Complexity Class complexity)• BD Shape mpq class (Z Box y, Complexity Class complexity)• BD Shape mpq class (Rational Box y, Complexity Class complexity)• BD Shape mpq class (BD Shape int8 t y, Complexity Class complexity)• BD Shape mpq class (BD Shape int16 t y, Complexity Class complexity)• BD Shape mpq class (BD Shape int32 t y, Complexity Class complexity)• BD Shape mpq class (BD Shape int64 t y, Complexity Class complexity)• BD Shape mpq class (BD Shape mpz class y, Complexity Class complexity)• BD Shape mpq class (BD Shape mpq class y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape int64 t y, Complexity Class complexity)

69

• BD Shape mpq class (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape mpq class (C Polyhedron y, Complexity Class complexity)• BD Shape mpq class (NNC Polyhedron y, Complexity Class complexity)• BD Shape mpq class (Grid y, Complexity Class complexity)• BD Shape mpq class (Float Box y, Complexity Class complexity)• BD Shape mpq class (BD Shape float y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape float y, Complexity Class complexity)• BD Shape mpq class (Double Box y, Complexity Class complexity)• BD Shape mpq class (BD Shape double y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape double y, Complexity Class complexity)• BD Shape mpq class (Long Double Box y, Complexity Class complexity)• BD Shape mpq class (BD Shape long double y, Complexity Class complexity)• BD Shape mpq class (Octagonal Shape long double y, Complexity Class complexity)• BD Shape mpq class (Constraint System cs)• BD Shape mpq class (Congruence System cs)• BD Shape mpq class (Generator System cs)• native void swap (BD Shape mpq class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (BD Shape mpq class y)• native boolean strictly contains (BD Shape mpq class y)• native boolean is disjoint from (BD Shape mpq class y)• native boolean equals (BD Shape mpq class p)

70

• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape mpq class p)• native void upper bound assign (BD Shape mpq class p)• native void difference assign (BD Shape mpq class p)• native void concatenate assign (BD Shape mpq class p)• native void time elapse assign (BD Shape mpq class p)• native boolean upper bound assign if exact (BD Shape mpq class y)• native boolean simplify using context assign (BD Shape mpq class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape mpq class y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape mpq class y, By Reference< Integer > tp)• native void widening assign (BD Shape mpq class y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape mpq class y, Constraint System

cs, By Reference< Integer > tp)

71

• native void limited H79 extrapolation assign (BD Shape mpq class y, Constraint System cs, By←↩

Reference< Integer > tp)• native void limited CC76 extrapolation assign (BD Shape mpq class y, Constraint System cs, By←↩

Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape mpq class arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape mpq class arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< BD Shape mpq class, Pointset Powerset NNC Polyhedron > linear partition(BD Shape mpq class p, BD Shape mpq class q)




Java class interfacing C++ Parma Polyhedra Library::BD Shape<mpq class>The documentation for this class was generated from the following file:

• BD Shape mpq class.java

10.11 parma polyhedra library.BD Shape mpz class Class ReferenceJava class interfacing C++ Parma Polyhedra Library::BD Shape<mpz class>



• BD Shape mpz class (long num dimensions, Degenerate Element kind)• BD Shape mpz class (Int8 Box y)• BD Shape mpz class (Int16 Box y)• BD Shape mpz class (Int32 Box y)• BD Shape mpz class (Int64 Box y)• BD Shape mpz class (Uint8 Box y)• BD Shape mpz class (Uint16 Box y)• BD Shape mpz class (Uint32 Box y)• BD Shape mpz class (Uint64 Box y)• BD Shape mpz class (Z Box y)• BD Shape mpz class (Rational Box y)• BD Shape mpz class (BD Shape int8 t y)• BD Shape mpz class (BD Shape int16 t y)• BD Shape mpz class (BD Shape int32 t y)• BD Shape mpz class (BD Shape int64 t y)• BD Shape mpz class (BD Shape mpz class y)• BD Shape mpz class (BD Shape mpq class y)

72

• BD Shape mpz class (Octagonal Shape int8 t y)• BD Shape mpz class (Octagonal Shape int16 t y)• BD Shape mpz class (Octagonal Shape int32 t y)• BD Shape mpz class (Octagonal Shape int64 t y)• BD Shape mpz class (Octagonal Shape mpz class y)• BD Shape mpz class (Octagonal Shape mpq class y)• BD Shape mpz class (C Polyhedron y)• BD Shape mpz class (NNC Polyhedron y)• BD Shape mpz class (Grid y)• BD Shape mpz class (Float Box y)• BD Shape mpz class (BD Shape float y)• BD Shape mpz class (Octagonal Shape float y)• BD Shape mpz class (Double Box y)• BD Shape mpz class (BD Shape double y)• BD Shape mpz class (Octagonal Shape double y)• BD Shape mpz class (Long Double Box y)• BD Shape mpz class (BD Shape long double y)• BD Shape mpz class (Octagonal Shape long double y)• BD Shape mpz class (Int8 Box y, Complexity Class complexity)• BD Shape mpz class (Int16 Box y, Complexity Class complexity)• BD Shape mpz class (Int32 Box y, Complexity Class complexity)• BD Shape mpz class (Int64 Box y, Complexity Class complexity)• BD Shape mpz class (Uint8 Box y, Complexity Class complexity)• BD Shape mpz class (Uint16 Box y, Complexity Class complexity)• BD Shape mpz class (Uint32 Box y, Complexity Class complexity)• BD Shape mpz class (Uint64 Box y, Complexity Class complexity)• BD Shape mpz class (Z Box y, Complexity Class complexity)• BD Shape mpz class (Rational Box y, Complexity Class complexity)• BD Shape mpz class (BD Shape int8 t y, Complexity Class complexity)• BD Shape mpz class (BD Shape int16 t y, Complexity Class complexity)• BD Shape mpz class (BD Shape int32 t y, Complexity Class complexity)• BD Shape mpz class (BD Shape int64 t y, Complexity Class complexity)• BD Shape mpz class (BD Shape mpz class y, Complexity Class complexity)• BD Shape mpz class (BD Shape mpq class y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape int8 t y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape int16 t y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape int32 t y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape int64 t y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape mpz class y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape mpq class y, Complexity Class complexity)• BD Shape mpz class (C Polyhedron y, Complexity Class complexity)• BD Shape mpz class (NNC Polyhedron y, Complexity Class complexity)• BD Shape mpz class (Grid y, Complexity Class complexity)• BD Shape mpz class (Float Box y, Complexity Class complexity)• BD Shape mpz class (BD Shape float y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape float y, Complexity Class complexity)• BD Shape mpz class (Double Box y, Complexity Class complexity)• BD Shape mpz class (BD Shape double y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape double y, Complexity Class complexity)• BD Shape mpz class (Long Double Box y, Complexity Class complexity)

73

• BD Shape mpz class (BD Shape long double y, Complexity Class complexity)• BD Shape mpz class (Octagonal Shape long double y, Complexity Class complexity)• BD Shape mpz class (Constraint System cs)• BD Shape mpz class (Congruence System cs)• BD Shape mpz class (Generator System cs)• native void swap (BD Shape mpz class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (BD Shape mpz class y)• native boolean strictly contains (BD Shape mpz class y)• native boolean is disjoint from (BD Shape mpz class y)• native boolean equals (BD Shape mpz class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (BD Shape mpz class p)• native void upper bound assign (BD Shape mpz class p)

74

• native void difference assign (BD Shape mpz class p)• native void concatenate assign (BD Shape mpz class p)• native void time elapse assign (BD Shape mpz class p)• native boolean upper bound assign if exact (BD Shape mpz class y)• native boolean simplify using context assign (BD Shape mpz class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (BD Shape mpz class y, By Reference< Integer > tp)• native void H79 widening assign (BD Shape mpz class y, By Reference< Integer > tp)• native void widening assign (BD Shape mpz class y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (BD Shape mpz class y, Constraint System cs,

By Reference< Integer > tp)• native void limited H79 extrapolation assign (BD Shape mpz class y, Constraint System cs, By←↩

Reference< Integer > tp)• native void limited CC76 extrapolation assign (BD Shape mpz class y, Constraint System cs, By←↩

Reference< Integer > tp)• native void CC76 extrapolation assign (BD Shape mpz class arg, By Reference< Integer > tp)• native void CC76 narrowing assign (BD Shape mpz class arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩



75


• static native Pair< BD Shape mpz class, Pointset Powerset NNC Polyhedron > linear partition(BD Shape mpz class p, BD Shape mpz class q)




Java class interfacing C++ Parma Polyhedra Library::BD Shape<mpz class>The documentation for this class was generated from the following file:

• BD Shape mpz class.java

10.12 parma polyhedra library.Bounded Integer Type Overflow Enum Reference

Overflow behavior of bounded integer types.


• [static initializer]

Public Attributes

• OVERFLOW WRAPS

On overflow, wrapping takes place.

• OVERFLOW UNDEFINED

On overflow, the result is undefined.


Overflow behavior of bounded integer types.The documentation for this enum was generated from the following file:

• Bounded Integer Type Overflow.java

10.13 parma polyhedra library.Bounded Integer Type Representation Enum Ref-erence

Representation of bounded integer types.



Public Attributes

• UNSIGNED

Unsigned binary.

76


Representation of bounded integer types.The documentation for this enum was generated from the following file:

• Bounded Integer Type Representation.java

10.14 parma polyhedra library.Bounded Integer Type Width Enum ReferenceWidths of bounded integer types.



Public Attributes

• BITS 8

Minimization is requested.

• BITS 16

16 bits.

• BITS 32

32 bits.

• BITS 64

64 bits.


Widths of bounded integer types.The documentation for this enum was generated from the following file:

• Bounded Integer Type Width.java

10.15 parma polyhedra library.By Reference< T > Class Template ReferenceAn utility class implementing mutable and non-mutable call-by-reference.


• By Reference (T object value)

Builds an object encapsulating object value.

• void set (T y)

Set an object to value object value.

• T get ()

Returns the value held by this.


An utility class implementing mutable and non-mutable call-by-reference.The documentation for this class was generated from the following file:

• By Reference.java

77

10.16 parma polyhedra library.C Polyhedron Class ReferenceJava class interfacing C++ Parma Polyhedra Library::C Polyhedron.

Inheritance diagram for parma polyhedra library.C Polyhedron:

parma_polyhedra_library.C_Polyhedron

parma_polyhedra_library.Polyhedron


• C Polyhedron (long num dimensions, Degenerate Element kind)• C Polyhedron (Int8 Box y)• C Polyhedron (Int16 Box y)• C Polyhedron (Int32 Box y)• C Polyhedron (Int64 Box y)• C Polyhedron (Uint8 Box y)• C Polyhedron (Uint16 Box y)• C Polyhedron (Uint32 Box y)• C Polyhedron (Uint64 Box y)• C Polyhedron (Z Box y)• C Polyhedron (Rational Box y)• C Polyhedron (BD Shape int8 t y)• C Polyhedron (BD Shape int16 t y)• C Polyhedron (BD Shape int32 t y)• C Polyhedron (BD Shape int64 t y)• C Polyhedron (BD Shape mpz class y)• C Polyhedron (BD Shape mpq class y)• C Polyhedron (Octagonal Shape int8 t y)• C Polyhedron (Octagonal Shape int16 t y)• C Polyhedron (Octagonal Shape int32 t y)• C Polyhedron (Octagonal Shape int64 t y)• C Polyhedron (Octagonal Shape mpz class y)• C Polyhedron (Octagonal Shape mpq class y)• C Polyhedron (C Polyhedron y)• C Polyhedron (NNC Polyhedron y)• C Polyhedron (Grid y)• C Polyhedron (Float Box y)• C Polyhedron (BD Shape float y)

78

• C Polyhedron (Octagonal Shape float y)• C Polyhedron (Double Box y)• C Polyhedron (BD Shape double y)• C Polyhedron (Octagonal Shape double y)• C Polyhedron (Long Double Box y)• C Polyhedron (BD Shape long double y)• C Polyhedron (Octagonal Shape long double y)• C Polyhedron (Int8 Box y, Complexity Class complexity)• C Polyhedron (Int16 Box y, Complexity Class complexity)• C Polyhedron (Int32 Box y, Complexity Class complexity)• C Polyhedron (Int64 Box y, Complexity Class complexity)• C Polyhedron (Uint8 Box y, Complexity Class complexity)• C Polyhedron (Uint16 Box y, Complexity Class complexity)• C Polyhedron (Uint32 Box y, Complexity Class complexity)• C Polyhedron (Uint64 Box y, Complexity Class complexity)• C Polyhedron (Z Box y, Complexity Class complexity)• C Polyhedron (Rational Box y, Complexity Class complexity)• C Polyhedron (BD Shape int8 t y, Complexity Class complexity)• C Polyhedron (BD Shape int16 t y, Complexity Class complexity)• C Polyhedron (BD Shape int32 t y, Complexity Class complexity)• C Polyhedron (BD Shape int64 t y, Complexity Class complexity)• C Polyhedron (BD Shape mpz class y, Complexity Class complexity)• C Polyhedron (BD Shape mpq class y, Complexity Class complexity)• C Polyhedron (Octagonal Shape int8 t y, Complexity Class complexity)• C Polyhedron (Octagonal Shape int16 t y, Complexity Class complexity)• C Polyhedron (Octagonal Shape int32 t y, Complexity Class complexity)• C Polyhedron (Octagonal Shape int64 t y, Complexity Class complexity)• C Polyhedron (Octagonal Shape mpz class y, Complexity Class complexity)• C Polyhedron (Octagonal Shape mpq class y, Complexity Class complexity)• C Polyhedron (C Polyhedron y, Complexity Class complexity)• C Polyhedron (NNC Polyhedron y, Complexity Class complexity)• C Polyhedron (Grid y, Complexity Class complexity)• C Polyhedron (Float Box y, Complexity Class complexity)• C Polyhedron (BD Shape float y, Complexity Class complexity)• C Polyhedron (Octagonal Shape float y, Complexity Class complexity)• C Polyhedron (Double Box y, Complexity Class complexity)• C Polyhedron (BD Shape double y, Complexity Class complexity)• C Polyhedron (Octagonal Shape double y, Complexity Class complexity)• C Polyhedron (Long Double Box y, Complexity Class complexity)• C Polyhedron (BD Shape long double y, Complexity Class complexity)• C Polyhedron (Octagonal Shape long double y, Complexity Class complexity)• C Polyhedron (Constraint System cs)• C Polyhedron (Congruence System cs)• C Polyhedron (Generator System cs)• native boolean upper bound assign if exact (C Polyhedron y)• native boolean poly hull assign if exact (C Polyhedron y)• native void positive time elapse assign (C Polyhedron p)• native void free ()

79


• static native Pair< C Polyhedron, Pointset Powerset NNC Polyhedron > linear partition (C ←↩

Polyhedron p, C Polyhedron q)




Java class interfacing C++ Parma Polyhedra Library::C Polyhedron.The documentation for this class was generated from the following file:

• C Polyhedron.java

10.17 parma polyhedra library.Coefficient Class ReferenceA PPL coefficient.


• Coefficient (int i)Builds a coefficient valued i.

• Coefficient (long l)Builds a coefficient valued l.

• Coefficient (BigInteger bi)Builds a coefficient valued bi.

• Coefficient (String s)Builds a coefficient from the decimal representation in s.

• Coefficient (Coefficient c)Builds a copy of c.

• String toString ()Returns a String representation of this.

• BigInteger getBigInteger ()Returns the value held by this.


• static native int bits ()Returns the number of bits of PPL coefficients; 0 if unbounded.


A PPL coefficient.Objects of type Coefficient are used to implement the integral valued coefficients occurring in linear

expressions, constraints, generators and so on.

10.17.2 Constructor & Destructor Documentation

parma polyhedra library.Coefficient.Coefficient ( String s ) [inline] Builds a coefficient fromthe decimal representation in s.

80

Exceptions

java.lang.Number←↩

FormatExceptionThrown if s does not contain a valid decimal representation.


• Coefficient.java

10.18 parma polyhedra library.Complexity Class Enum ReferencePossible Complexities.



Public Attributes

• POLYNOMIAL COMPLEXITYWorst-case polynomial complexity.

• SIMPLEX COMPLEXITYWorst-case exponential complexity but typically polynomial behavior.


Possible Complexities.The documentation for this enum was generated from the following file:

• Complexity Class.java

10.19 parma polyhedra library.Congruence Class ReferenceA linear congruence.


• Congruence (Linear Expression e1, Linear Expression e2, Coefficient m)Returns the congruence e1 = e2 (mod m).

• Linear Expression left hand side ()Returns the left hand side of this.

• Linear Expression right hand side ()Returns the right hand side of this.

• Coefficient modulus ()Returns the relation symbol of this.



Protected Attributes

• Coefficient modThe modulus of the congruence.

81


A linear congruence.An object of the class Congruence is an object represeting a congruence:

• cg =∑n−1

i=0 aixi + b = 0 (mod m)

where n is the dimension of the space, ai is the integer coefficient of variable xi, b is the integerinhomogeneous term and m is the integer modulus; if m = 0, then cg represents the equality congruence∑n−1

i=0 aixi + b = 0 and, if m 6= 0, then the congruence cg is said to be a proper congruence.The documentation for this class was generated from the following file:

• Congruence.java

10.20 parma polyhedra library.Congruence System Class ReferenceA system of congruences.

Inherits ArrayList< Congruence >.


• Congruence System ()Default constructor: builds an empty system of congruences.




A system of congruences.An object of the class Congruence System is a system of congruences, i.e., a multiset of objects of the

class Congruence.The documentation for this class was generated from the following file:

• Congruence System.java

10.21 parma polyhedra library.Constraint Class ReferenceA linear equality or inequality.


• Constraint (Linear Expression le1, Relation Symbol rel sym, Linear Expression le2)Builds a constraint from two linear expressions with a specified relation symbol.



• Relation Symbol kind ()Returns the relation symbol of this.



82


A linear equality or inequality.An object of the class Constraint is either:

• a linear equality;

• a non-strict linear inequality;

• a strict linear inequality.


• Constraint.java

10.22 parma polyhedra library.Constraint System Class ReferenceA system of constraints.

Inherits ArrayList< Constraint >.


• Constraint System ()

Default constructor: builds an empty system of constraints.• native String ascii dump ()

Returns an ascii formatted internal representation of this.• native String toString ()

Returns a string representation of this.


A system of constraints.An object of the class Constraint System is a system of constraints, i.e., a multiset of objects of the

class Constraint.The documentation for this class was generated from the following file:

• Constraint System.java

10.23 parma polyhedra library.Constraints Product C Polyhedron Grid Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<C Polyhedron,Grid>Inherits parma polyhedra library.PPL Object.


• Constraints Product C Polyhedron Grid (long num dimensions, Degenerate Element kind)• Constraints Product C Polyhedron Grid (Int8 Box y)• Constraints Product C Polyhedron Grid (Int16 Box y)• Constraints Product C Polyhedron Grid (Int32 Box y)• Constraints Product C Polyhedron Grid (Int64 Box y)• Constraints Product C Polyhedron Grid (Uint8 Box y)• Constraints Product C Polyhedron Grid (Uint16 Box y)• Constraints Product C Polyhedron Grid (Uint32 Box y)• Constraints Product C Polyhedron Grid (Uint64 Box y)

83

• Constraints Product C Polyhedron Grid (Z Box y)• Constraints Product C Polyhedron Grid (Rational Box y)• Constraints Product C Polyhedron Grid (BD Shape int8 t y)• Constraints Product C Polyhedron Grid (BD Shape int16 t y)• Constraints Product C Polyhedron Grid (BD Shape int32 t y)• Constraints Product C Polyhedron Grid (BD Shape int64 t y)• Constraints Product C Polyhedron Grid (BD Shape mpz class y)• Constraints Product C Polyhedron Grid (BD Shape mpq class y)• Constraints Product C Polyhedron Grid (Octagonal Shape int8 t y)• Constraints Product C Polyhedron Grid (Octagonal Shape int16 t y)• Constraints Product C Polyhedron Grid (Octagonal Shape int32 t y)• Constraints Product C Polyhedron Grid (Octagonal Shape int64 t y)• Constraints Product C Polyhedron Grid (Octagonal Shape mpz class y)• Constraints Product C Polyhedron Grid (Octagonal Shape mpq class y)• Constraints Product C Polyhedron Grid (C Polyhedron y)• Constraints Product C Polyhedron Grid (NNC Polyhedron y)• Constraints Product C Polyhedron Grid (Grid y)• Constraints Product C Polyhedron Grid (Float Box y)• Constraints Product C Polyhedron Grid (BD Shape float y)• Constraints Product C Polyhedron Grid (Octagonal Shape float y)• Constraints Product C Polyhedron Grid (Double Box y)• Constraints Product C Polyhedron Grid (BD Shape double y)• Constraints Product C Polyhedron Grid (Octagonal Shape double y)• Constraints Product C Polyhedron Grid (Long Double Box y)• Constraints Product C Polyhedron Grid (BD Shape long double y)• Constraints Product C Polyhedron Grid (Octagonal Shape long double y)• Constraints Product C Polyhedron Grid (Constraints Product C Polyhedron Grid y)• Constraints Product C Polyhedron Grid (Int8 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Int16 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Int32 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Int64 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Uint8 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Uint16 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Uint32 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Uint64 Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Z Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Rational Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape int8 t y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape int16 t y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape int32 t y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape int64 t y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape mpz class y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape mpq class y, Complexity Class complex-

ity)• Constraints Product C Polyhedron Grid (Octagonal Shape int8 t y, Complexity Class complex-



ity)

84

• Constraints Product C Polyhedron Grid (Octagonal Shape int64 t y, Complexity Class complex-ity)

• Constraints Product C Polyhedron Grid (Octagonal Shape mpz class y, Complexity Class com-plexity)

• Constraints Product C Polyhedron Grid (Octagonal Shape mpq class y, Complexity Class com-plexity)

• Constraints Product C Polyhedron Grid (C Polyhedron y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (NNC Polyhedron y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Grid y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Float Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape float y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Octagonal Shape float y, Complexity Class complex-

ity)• Constraints Product C Polyhedron Grid (Double Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape double y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (Octagonal Shape double y, Complexity Class complex-

ity)• Constraints Product C Polyhedron Grid (Long Double Box y, Complexity Class complexity)• Constraints Product C Polyhedron Grid (BD Shape long double y, Complexity Class complex-

ity)• Constraints Product C Polyhedron Grid (Octagonal Shape long double y, Complexity Class com-

plexity)• Constraints Product C Polyhedron Grid (Constraints Product C Polyhedron Grid y, Complexity←↩

Class complexity)• Constraints Product C Polyhedron Grid (Constraint System cs)• Constraints Product C Polyhedron Grid (Congruence System cs)• native void swap (Constraints Product C Polyhedron Grid y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Constraints Product C Polyhedron Grid y)• native boolean strictly contains (Constraints Product C Polyhedron Grid y)• native boolean is disjoint from (Constraints Product C Polyhedron Grid y)

85

• native boolean equals (Constraints Product C Polyhedron Grid p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Constraints Product C Polyhedron Grid p)• native void upper bound assign (Constraints Product C Polyhedron Grid p)• native void difference assign (Constraints Product C Polyhedron Grid p)• native void concatenate assign (Constraints Product C Polyhedron Grid p)• native void time elapse assign (Constraints Product C Polyhedron Grid p)• native boolean upper bound assign if exact (Constraints Product C Polyhedron Grid y)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void widening assign (Constraints Product C Polyhedron Grid y, By Reference< Integer >

tp)• native void free ()• native int hashCode ()• native String toString ()

86




Java class interfacing C++ Parma Polyhedra Library::Constraints Product<C Polyhedron,Grid>The documentation for this class was generated from the following file:

• Constraints Product C Polyhedron Grid.java

10.24 parma polyhedra library.Constraints Product Grid C Polyhedron Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,C Polyhedron>Inherits parma polyhedra library.PPL Object.


• Constraints Product Grid C Polyhedron (long num dimensions, Degenerate Element kind)• Constraints Product Grid C Polyhedron (Int8 Box y)• Constraints Product Grid C Polyhedron (Int16 Box y)• Constraints Product Grid C Polyhedron (Int32 Box y)• Constraints Product Grid C Polyhedron (Int64 Box y)• Constraints Product Grid C Polyhedron (Uint8 Box y)• Constraints Product Grid C Polyhedron (Uint16 Box y)• Constraints Product Grid C Polyhedron (Uint32 Box y)• Constraints Product Grid C Polyhedron (Uint64 Box y)• Constraints Product Grid C Polyhedron (Z Box y)• Constraints Product Grid C Polyhedron (Rational Box y)• Constraints Product Grid C Polyhedron (BD Shape int8 t y)• Constraints Product Grid C Polyhedron (BD Shape int16 t y)• Constraints Product Grid C Polyhedron (BD Shape int32 t y)• Constraints Product Grid C Polyhedron (BD Shape int64 t y)• Constraints Product Grid C Polyhedron (BD Shape mpz class y)• Constraints Product Grid C Polyhedron (BD Shape mpq class y)• Constraints Product Grid C Polyhedron (Octagonal Shape int8 t y)• Constraints Product Grid C Polyhedron (Octagonal Shape int16 t y)• Constraints Product Grid C Polyhedron (Octagonal Shape int32 t y)• Constraints Product Grid C Polyhedron (Octagonal Shape int64 t y)• Constraints Product Grid C Polyhedron (Octagonal Shape mpz class y)• Constraints Product Grid C Polyhedron (Octagonal Shape mpq class y)• Constraints Product Grid C Polyhedron (C Polyhedron y)• Constraints Product Grid C Polyhedron (NNC Polyhedron y)• Constraints Product Grid C Polyhedron (Grid y)• Constraints Product Grid C Polyhedron (Float Box y)• Constraints Product Grid C Polyhedron (BD Shape float y)• Constraints Product Grid C Polyhedron (Octagonal Shape float y)• Constraints Product Grid C Polyhedron (Double Box y)• Constraints Product Grid C Polyhedron (BD Shape double y)• Constraints Product Grid C Polyhedron (Octagonal Shape double y)• Constraints Product Grid C Polyhedron (Long Double Box y)

87

• Constraints Product Grid C Polyhedron (BD Shape long double y)• Constraints Product Grid C Polyhedron (Octagonal Shape long double y)• Constraints Product Grid C Polyhedron (Constraints Product Grid C Polyhedron y)• Constraints Product Grid C Polyhedron (Int8 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Int16 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Int32 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Int64 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Uint8 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Uint16 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Uint32 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Uint64 Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Z Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Rational Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape int8 t y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape int16 t y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape int32 t y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape int64 t y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape mpz class y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape mpq class y, Complexity Class complex-

ity)• Constraints Product Grid C Polyhedron (Octagonal Shape int8 t y, Complexity Class complex-




ity)• Constraints Product Grid C Polyhedron (Octagonal Shape mpz class y, Complexity Class com-

plexity)• Constraints Product Grid C Polyhedron (Octagonal Shape mpq class y, Complexity Class com-

plexity)• Constraints Product Grid C Polyhedron (C Polyhedron y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (NNC Polyhedron y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Grid y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Float Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape float y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Octagonal Shape float y, Complexity Class complex-

ity)• Constraints Product Grid C Polyhedron (Double Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape double y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (Octagonal Shape double y, Complexity Class complex-

ity)• Constraints Product Grid C Polyhedron (Long Double Box y, Complexity Class complexity)• Constraints Product Grid C Polyhedron (BD Shape long double y, Complexity Class complex-

ity)• Constraints Product Grid C Polyhedron (Octagonal Shape long double y, Complexity Class com-

plexity)• Constraints Product Grid C Polyhedron (Constraints Product Grid C Polyhedron y, Complexity←↩

Class complexity)• Constraints Product Grid C Polyhedron (Constraint System cs)

88

• Constraints Product Grid C Polyhedron (Congruence System cs)• native void swap (Constraints Product Grid C Polyhedron y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Constraints Product Grid C Polyhedron y)• native boolean strictly contains (Constraints Product Grid C Polyhedron y)• native boolean is disjoint from (Constraints Product Grid C Polyhedron y)• native boolean equals (Constraints Product Grid C Polyhedron p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Constraints Product Grid C Polyhedron p)• native void upper bound assign (Constraints Product Grid C Polyhedron p)• native void difference assign (Constraints Product Grid C Polyhedron p)• native void concatenate assign (Constraints Product Grid C Polyhedron p)• native void time elapse assign (Constraints Product Grid C Polyhedron p)• native boolean upper bound assign if exact (Constraints Product Grid C Polyhedron y)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩

expr, Coefficient denominator)

89

• native void bounded affine preimage (Variable var, Linear Expression lb expr, Linear Expressionub expr, Coefficient denominator)





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void widening assign (Constraints Product Grid C Polyhedron y, By Reference< Integer >

tp)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,C Polyhedron>The documentation for this class was generated from the following file:

• Constraints Product Grid C Polyhedron.java

10.25 parma polyhedra library.Constraints Product Grid NNC Polyhedron ClassReference

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,NNC Polyhedron>Inherits parma polyhedra library.PPL Object.


• Constraints Product Grid NNC Polyhedron (long num dimensions, Degenerate Element kind)• Constraints Product Grid NNC Polyhedron (Int8 Box y)• Constraints Product Grid NNC Polyhedron (Int16 Box y)• Constraints Product Grid NNC Polyhedron (Int32 Box y)• Constraints Product Grid NNC Polyhedron (Int64 Box y)• Constraints Product Grid NNC Polyhedron (Uint8 Box y)

90

• Constraints Product Grid NNC Polyhedron (Uint16 Box y)• Constraints Product Grid NNC Polyhedron (Uint32 Box y)• Constraints Product Grid NNC Polyhedron (Uint64 Box y)• Constraints Product Grid NNC Polyhedron (Z Box y)• Constraints Product Grid NNC Polyhedron (Rational Box y)• Constraints Product Grid NNC Polyhedron (BD Shape int8 t y)• Constraints Product Grid NNC Polyhedron (BD Shape int16 t y)• Constraints Product Grid NNC Polyhedron (BD Shape int32 t y)• Constraints Product Grid NNC Polyhedron (BD Shape int64 t y)• Constraints Product Grid NNC Polyhedron (BD Shape mpz class y)• Constraints Product Grid NNC Polyhedron (BD Shape mpq class y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape int8 t y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape int16 t y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape int32 t y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape int64 t y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape mpz class y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape mpq class y)• Constraints Product Grid NNC Polyhedron (C Polyhedron y)• Constraints Product Grid NNC Polyhedron (NNC Polyhedron y)• Constraints Product Grid NNC Polyhedron (Grid y)• Constraints Product Grid NNC Polyhedron (Float Box y)• Constraints Product Grid NNC Polyhedron (BD Shape float y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape float y)• Constraints Product Grid NNC Polyhedron (Double Box y)• Constraints Product Grid NNC Polyhedron (BD Shape double y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape double y)• Constraints Product Grid NNC Polyhedron (Long Double Box y)• Constraints Product Grid NNC Polyhedron (BD Shape long double y)• Constraints Product Grid NNC Polyhedron (Octagonal Shape long double y)• Constraints Product Grid NNC Polyhedron (Constraints Product Grid NNC Polyhedron y)• Constraints Product Grid NNC Polyhedron (Int8 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Int16 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Int32 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Int64 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Uint8 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Uint16 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Uint32 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Uint64 Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Z Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Rational Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (BD Shape int8 t y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (BD Shape int16 t y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (BD Shape int32 t y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (BD Shape int64 t y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (BD Shape mpz class y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (BD Shape mpq class y, Complexity Class complex-

ity)

91

• Constraints Product Grid NNC Polyhedron (Octagonal Shape int8 t y, Complexity Class com-plexity)




• Constraints Product Grid NNC Polyhedron (Octagonal Shape mpz class y, Complexity Class com-plexity)

• Constraints Product Grid NNC Polyhedron (Octagonal Shape mpq class y, Complexity Classcomplexity)

• Constraints Product Grid NNC Polyhedron (C Polyhedron y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (NNC Polyhedron y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Grid y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Float Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (BD Shape float y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (Octagonal Shape float y, Complexity Class com-

plexity)• Constraints Product Grid NNC Polyhedron (Double Box y, Complexity Class complexity)• Constraints Product Grid NNC Polyhedron (BD Shape double y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (Octagonal Shape double y, Complexity Class com-

plexity)• Constraints Product Grid NNC Polyhedron (Long Double Box y, Complexity Class complex-

ity)• Constraints Product Grid NNC Polyhedron (BD Shape long double y, Complexity Class com-

plexity)• Constraints Product Grid NNC Polyhedron (Octagonal Shape long double y, Complexity Class

complexity)• Constraints Product Grid NNC Polyhedron (Constraints Product Grid NNC Polyhedron y, Complexity←↩

Class complexity)• Constraints Product Grid NNC Polyhedron (Constraint System cs)• Constraints Product Grid NNC Polyhedron (Congruence System cs)• native void swap (Constraints Product Grid NNC Polyhedron y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)

92




• native boolean contains (Constraints Product Grid NNC Polyhedron y)• native boolean strictly contains (Constraints Product Grid NNC Polyhedron y)• native boolean is disjoint from (Constraints Product Grid NNC Polyhedron y)• native boolean equals (Constraints Product Grid NNC Polyhedron p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Constraints Product Grid NNC Polyhedron p)• native void upper bound assign (Constraints Product Grid NNC Polyhedron p)• native void difference assign (Constraints Product Grid NNC Polyhedron p)• native void concatenate assign (Constraints Product Grid NNC Polyhedron p)• native void time elapse assign (Constraints Product Grid NNC Polyhedron p)• native boolean upper bound assign if exact (Constraints Product Grid NNC Polyhedron y)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)

93

• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void widening assign (Constraints Product Grid NNC Polyhedron y, By Reference< Inte-

ger > tp)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Constraints Product<Grid,NNC Polyhedron>The documentation for this class was generated from the following file:

• Constraints Product Grid NNC Polyhedron.java

10.26 parma polyhedra library.Constraints Product NNC Polyhedron Grid ClassReference

Java class interfacing C++ Parma Polyhedra Library::Constraints Product<NNC Polyhedron,Grid>Inherits parma polyhedra library.PPL Object.


• Constraints Product NNC Polyhedron Grid (long num dimensions, Degenerate Element kind)• Constraints Product NNC Polyhedron Grid (Int8 Box y)• Constraints Product NNC Polyhedron Grid (Int16 Box y)• Constraints Product NNC Polyhedron Grid (Int32 Box y)• Constraints Product NNC Polyhedron Grid (Int64 Box y)• Constraints Product NNC Polyhedron Grid (Uint8 Box y)• Constraints Product NNC Polyhedron Grid (Uint16 Box y)• Constraints Product NNC Polyhedron Grid (Uint32 Box y)• Constraints Product NNC Polyhedron Grid (Uint64 Box y)• Constraints Product NNC Polyhedron Grid (Z Box y)• Constraints Product NNC Polyhedron Grid (Rational Box y)• Constraints Product NNC Polyhedron Grid (BD Shape int8 t y)• Constraints Product NNC Polyhedron Grid (BD Shape int16 t y)• Constraints Product NNC Polyhedron Grid (BD Shape int32 t y)• Constraints Product NNC Polyhedron Grid (BD Shape int64 t y)• Constraints Product NNC Polyhedron Grid (BD Shape mpz class y)• Constraints Product NNC Polyhedron Grid (BD Shape mpq class y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int8 t y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int16 t y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int32 t y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int64 t y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape mpz class y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape mpq class y)

94

• Constraints Product NNC Polyhedron Grid (C Polyhedron y)• Constraints Product NNC Polyhedron Grid (NNC Polyhedron y)• Constraints Product NNC Polyhedron Grid (Grid y)• Constraints Product NNC Polyhedron Grid (Float Box y)• Constraints Product NNC Polyhedron Grid (BD Shape float y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape float y)• Constraints Product NNC Polyhedron Grid (Double Box y)• Constraints Product NNC Polyhedron Grid (BD Shape double y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape double y)• Constraints Product NNC Polyhedron Grid (Long Double Box y)• Constraints Product NNC Polyhedron Grid (BD Shape long double y)• Constraints Product NNC Polyhedron Grid (Octagonal Shape long double y)• Constraints Product NNC Polyhedron Grid (Constraints Product NNC Polyhedron Grid y)• Constraints Product NNC Polyhedron Grid (Int8 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Int16 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Int32 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Int64 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Uint8 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Uint16 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Uint32 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Uint64 Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Z Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Rational Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (BD Shape int8 t y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (BD Shape int16 t y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (BD Shape int32 t y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (BD Shape int64 t y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (BD Shape mpz class y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (BD Shape mpq class y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int8 t y, Complexity Class com-

plexity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape int16 t y, Complexity Class com-



plexity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape mpz class y, Complexity Class com-

plexity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape mpq class y, Complexity Class

complexity)• Constraints Product NNC Polyhedron Grid (C Polyhedron y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (NNC Polyhedron y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Grid y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (Float Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (BD Shape float y, Complexity Class complexity)

95

• Constraints Product NNC Polyhedron Grid (Octagonal Shape float y, Complexity Class com-plexity)

• Constraints Product NNC Polyhedron Grid (Double Box y, Complexity Class complexity)• Constraints Product NNC Polyhedron Grid (BD Shape double y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape double y, Complexity Class com-

plexity)• Constraints Product NNC Polyhedron Grid (Long Double Box y, Complexity Class complex-

ity)• Constraints Product NNC Polyhedron Grid (BD Shape long double y, Complexity Class com-

plexity)• Constraints Product NNC Polyhedron Grid (Octagonal Shape long double y, Complexity Class

complexity)• Constraints Product NNC Polyhedron Grid (Constraints Product NNC Polyhedron Grid y, Complexity←↩

Class complexity)• Constraints Product NNC Polyhedron Grid (Constraint System cs)• Constraints Product NNC Polyhedron Grid (Congruence System cs)• native void swap (Constraints Product NNC Polyhedron Grid y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Constraints Product NNC Polyhedron Grid y)• native boolean strictly contains (Constraints Product NNC Polyhedron Grid y)• native boolean is disjoint from (Constraints Product NNC Polyhedron Grid y)• native boolean equals (Constraints Product NNC Polyhedron Grid p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)

96

• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Constraints Product NNC Polyhedron Grid p)• native void upper bound assign (Constraints Product NNC Polyhedron Grid p)• native void difference assign (Constraints Product NNC Polyhedron Grid p)• native void concatenate assign (Constraints Product NNC Polyhedron Grid p)• native void time elapse assign (Constraints Product NNC Polyhedron Grid p)• native boolean upper bound assign if exact (Constraints Product NNC Polyhedron Grid y)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void widening assign (Constraints Product NNC Polyhedron Grid y, By Reference< Inte-

ger > tp)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Constraints Product<NNC Polyhedron,Grid>The documentation for this class was generated from the following file:

• Constraints Product NNC Polyhedron Grid.java

97

10.27 parma polyhedra library.Control Parameter Name Enum ReferenceNames of MIP problems' control parameters.

Public Attributes

• PRICING

The pricing rule.


Names of MIP problems' control parameters.The documentation for this enum was generated from the following file:

• Control Parameter Name.java

10.28 parma polyhedra library.Control Parameter Value Enum ReferencePossible values for MIP problem's control parameters.

Public Attributes

• PRICING STEEPEST EDGE FLOAT

Steepest edge pricing method, using floating points (default).• PRICING STEEPEST EDGE EXACT

Steepest edge pricing method, using Coefficient.• PRICING TEXTBOOK

Textbook pricing method.


Possible values for MIP problem's control parameters.The documentation for this enum was generated from the following file:

• Control Parameter Value.java

10.29 parma polyhedra library.Degenerate Element Enum ReferenceKinds of degenerate abstract elements.



Public Attributes

• UNIVERSE

The universe element, i.e., the whole vector space.


Kinds of degenerate abstract elements.The documentation for this enum was generated from the following file:

• Degenerate Element.java

98

10.30 parma polyhedra library.Domain Error Exception Class ReferenceExceptions caused by domain errors.

Inherits RuntimeException.


• Domain Error Exception (String s)Constructor.


Exceptions caused by domain errors.The documentation for this class was generated from the following file:

• Domain Error Exception.java

10.31 parma polyhedra library.Double Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Double Box.



• Double Box (long num dimensions, Degenerate Element kind)• Double Box (Int8 Box y)• Double Box (Int16 Box y)• Double Box (Int32 Box y)• Double Box (Int64 Box y)• Double Box (Uint8 Box y)• Double Box (Uint16 Box y)• Double Box (Uint32 Box y)• Double Box (Uint64 Box y)• Double Box (Z Box y)• Double Box (Rational Box y)• Double Box (BD Shape int8 t y)• Double Box (BD Shape int16 t y)• Double Box (BD Shape int32 t y)• Double Box (BD Shape int64 t y)• Double Box (BD Shape mpz class y)• Double Box (BD Shape mpq class y)• Double Box (Octagonal Shape int8 t y)• Double Box (Octagonal Shape int16 t y)• Double Box (Octagonal Shape int32 t y)• Double Box (Octagonal Shape int64 t y)• Double Box (Octagonal Shape mpz class y)• Double Box (Octagonal Shape mpq class y)• Double Box (C Polyhedron y)• Double Box (NNC Polyhedron y)• Double Box (Grid y)• Double Box (Float Box y)• Double Box (BD Shape float y)• Double Box (Octagonal Shape float y)

99

• Double Box (Double Box y)• Double Box (BD Shape double y)• Double Box (Octagonal Shape double y)• Double Box (Long Double Box y)• Double Box (BD Shape long double y)• Double Box (Octagonal Shape long double y)• Double Box (Int8 Box y, Complexity Class complexity)• Double Box (Int16 Box y, Complexity Class complexity)• Double Box (Int32 Box y, Complexity Class complexity)• Double Box (Int64 Box y, Complexity Class complexity)• Double Box (Uint8 Box y, Complexity Class complexity)• Double Box (Uint16 Box y, Complexity Class complexity)• Double Box (Uint32 Box y, Complexity Class complexity)• Double Box (Uint64 Box y, Complexity Class complexity)• Double Box (Z Box y, Complexity Class complexity)• Double Box (Rational Box y, Complexity Class complexity)• Double Box (BD Shape int8 t y, Complexity Class complexity)• Double Box (BD Shape int16 t y, Complexity Class complexity)• Double Box (BD Shape int32 t y, Complexity Class complexity)• Double Box (BD Shape int64 t y, Complexity Class complexity)• Double Box (BD Shape mpz class y, Complexity Class complexity)• Double Box (BD Shape mpq class y, Complexity Class complexity)• Double Box (Octagonal Shape int8 t y, Complexity Class complexity)• Double Box (Octagonal Shape int16 t y, Complexity Class complexity)• Double Box (Octagonal Shape int32 t y, Complexity Class complexity)• Double Box (Octagonal Shape int64 t y, Complexity Class complexity)• Double Box (Octagonal Shape mpz class y, Complexity Class complexity)• Double Box (Octagonal Shape mpq class y, Complexity Class complexity)• Double Box (C Polyhedron y, Complexity Class complexity)• Double Box (NNC Polyhedron y, Complexity Class complexity)• Double Box (Grid y, Complexity Class complexity)• Double Box (Float Box y, Complexity Class complexity)• Double Box (BD Shape float y, Complexity Class complexity)• Double Box (Octagonal Shape float y, Complexity Class complexity)• Double Box (Double Box y, Complexity Class complexity)• Double Box (BD Shape double y, Complexity Class complexity)• Double Box (Octagonal Shape double y, Complexity Class complexity)• Double Box (Long Double Box y, Complexity Class complexity)• Double Box (BD Shape long double y, Complexity Class complexity)• Double Box (Octagonal Shape long double y, Complexity Class complexity)• Double Box (Constraint System cs)• Double Box (Congruence System cs)• Double Box (Generator System cs)• native void swap (Double Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()

100

• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩

Reference< Boolean > closed)• native boolean has lower bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩

Reference< Boolean > closed)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (Double Box y)• native boolean strictly contains (Double Box y)• native boolean is disjoint from (Double Box y)• native boolean equals (Double Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Double Box p)• native void upper bound assign (Double Box p)• native void difference assign (Double Box p)• native void concatenate assign (Double Box p)• native void time elapse assign (Double Box p)• native boolean upper bound assign if exact (Double Box y)• native boolean simplify using context assign (Double Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)

101

• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Double Box y, By Reference< Integer > tp)• native void widening assign (Double Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Double Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Double Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Double Box, Pointset Powerset NNC Polyhedron > linear partition (Double←↩

Box p, Double Box q)




Java class interfacing C++ Parma Polyhedra Library::Double Box.The documentation for this class was generated from the following file:

• Double Box.java

102

10.32 parma polyhedra library.Float Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Float Box.



• Float Box (long num dimensions, Degenerate Element kind)• Float Box (Int8 Box y)• Float Box (Int16 Box y)• Float Box (Int32 Box y)• Float Box (Int64 Box y)• Float Box (Uint8 Box y)• Float Box (Uint16 Box y)• Float Box (Uint32 Box y)• Float Box (Uint64 Box y)• Float Box (Z Box y)• Float Box (Rational Box y)• Float Box (BD Shape int8 t y)• Float Box (BD Shape int16 t y)• Float Box (BD Shape int32 t y)• Float Box (BD Shape int64 t y)• Float Box (BD Shape mpz class y)• Float Box (BD Shape mpq class y)• Float Box (Octagonal Shape int8 t y)• Float Box (Octagonal Shape int16 t y)• Float Box (Octagonal Shape int32 t y)• Float Box (Octagonal Shape int64 t y)• Float Box (Octagonal Shape mpz class y)• Float Box (Octagonal Shape mpq class y)• Float Box (C Polyhedron y)• Float Box (NNC Polyhedron y)• Float Box (Grid y)• Float Box (Float Box y)• Float Box (BD Shape float y)• Float Box (Octagonal Shape float y)• Float Box (Double Box y)• Float Box (BD Shape double y)• Float Box (Octagonal Shape double y)• Float Box (Long Double Box y)• Float Box (BD Shape long double y)• Float Box (Octagonal Shape long double y)• Float Box (Int8 Box y, Complexity Class complexity)• Float Box (Int16 Box y, Complexity Class complexity)• Float Box (Int32 Box y, Complexity Class complexity)• Float Box (Int64 Box y, Complexity Class complexity)• Float Box (Uint8 Box y, Complexity Class complexity)• Float Box (Uint16 Box y, Complexity Class complexity)• Float Box (Uint32 Box y, Complexity Class complexity)• Float Box (Uint64 Box y, Complexity Class complexity)• Float Box (Z Box y, Complexity Class complexity)

103

• Float Box (Rational Box y, Complexity Class complexity)• Float Box (BD Shape int8 t y, Complexity Class complexity)• Float Box (BD Shape int16 t y, Complexity Class complexity)• Float Box (BD Shape int32 t y, Complexity Class complexity)• Float Box (BD Shape int64 t y, Complexity Class complexity)• Float Box (BD Shape mpz class y, Complexity Class complexity)• Float Box (BD Shape mpq class y, Complexity Class complexity)• Float Box (Octagonal Shape int8 t y, Complexity Class complexity)• Float Box (Octagonal Shape int16 t y, Complexity Class complexity)• Float Box (Octagonal Shape int32 t y, Complexity Class complexity)• Float Box (Octagonal Shape int64 t y, Complexity Class complexity)• Float Box (Octagonal Shape mpz class y, Complexity Class complexity)• Float Box (Octagonal Shape mpq class y, Complexity Class complexity)• Float Box (C Polyhedron y, Complexity Class complexity)• Float Box (NNC Polyhedron y, Complexity Class complexity)• Float Box (Grid y, Complexity Class complexity)• Float Box (Float Box y, Complexity Class complexity)• Float Box (BD Shape float y, Complexity Class complexity)• Float Box (Octagonal Shape float y, Complexity Class complexity)• Float Box (Double Box y, Complexity Class complexity)• Float Box (BD Shape double y, Complexity Class complexity)• Float Box (Octagonal Shape double y, Complexity Class complexity)• Float Box (Long Double Box y, Complexity Class complexity)• Float Box (BD Shape long double y, Complexity Class complexity)• Float Box (Octagonal Shape long double y, Complexity Class complexity)• Float Box (Constraint System cs)• Float Box (Congruence System cs)• Float Box (Generator System cs)• native void swap (Float Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩

Reference< Boolean > closed)

104

• native boolean has lower bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩






cient val n, Coefficient val d)• native boolean contains (Float Box y)• native boolean strictly contains (Float Box y)• native boolean is disjoint from (Float Box y)• native boolean equals (Float Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Float Box p)• native void upper bound assign (Float Box p)• native void difference assign (Float Box p)• native void concatenate assign (Float Box p)• native void time elapse assign (Float Box p)• native boolean upper bound assign if exact (Float Box y)• native boolean simplify using context assign (Float Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)

105

• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Float Box y, By Reference< Integer > tp)• native void widening assign (Float Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Float Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Float Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Float Box, Pointset Powerset NNC Polyhedron > linear partition (Float Boxp, Float Box q)




Java class interfacing C++ Parma Polyhedra Library::Float Box.The documentation for this class was generated from the following file:

• Float Box.java

10.33 parma polyhedra library.Generator Class ReferenceA line, ray, point or closure point.


• Generator Type type ()

Returns the generator type.• Linear Expression linear expression ()

Returns the linear expression in this.• Coefficient divisor ()

If this is either a point or a closure point, returns its divisor.• native String ascii dump ()

106




• static Generator closure point (Linear Expression e, Coefficient d)Returns the closure point at e / d.

• static Generator line (Linear Expression e)Returns the line of direction e.

• static Generator point (Linear Expression e, Coefficient d)Returns the point at e / d.

• static Generator ray (Linear Expression e)Returns the ray of direction e.


A line, ray, point or closure point.An object of the class Generator is one of the following:

• a line;

• a ray;

• a point;

• a closure point.

10.33.2 Member Function Documentation

static Generator parma polyhedra library.Generator.closure point ( Linear Expression e, Coeffi-cient d ) [inline], [static] Returns the closure point at e / d.Exceptions

RuntimeErrorException Thrown if d is zero.

static Generator parma polyhedra library.Generator.line ( Linear Expression e ) [inline], [static]Returns the line of direction e.Exceptions

RuntimeErrorException Thrown if the homogeneous part of e represents the origin of the vectorspace.

static Generator parma polyhedra library.Generator.point ( Linear Expression e, Coefficient d )[inline], [static] Returns the point at e / d.Exceptions


static Generator parma polyhedra library.Generator.ray ( Linear Expression e ) [inline], [static]Returns the ray of direction e.

107

Exceptions


Coefficient parma polyhedra library.Generator.divisor ( ) [inline] If this is either a pointor a closure point, returns its divisor.Exceptions

RuntimeErrorException Thrown if this is neither a point nor a closure point.


• Generator.java

10.34 parma polyhedra library.Generator System Class ReferenceA system of generators.

Inherits ArrayList< Generator >.


• Generator System ()

Default constructor: builds an empty system of generators.• native String ascii dump ()




A system of generators.An object of the class Generator System is a system of generators, i.e., a multiset of objects of the class

Generator (lines, rays, points and closure points).The documentation for this class was generated from the following file:

• Generator System.java

10.35 parma polyhedra library.Generator Type Enum ReferenceThe generator type.



Public Attributes

• LINE

The generator is a line.• RAY

The generator is a ray.• POINT

The generator is a point.

108


The generator type.The documentation for this enum was generated from the following file:

• Generator Type.java

10.36 parma polyhedra library.Grid Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Grid.



• Grid (long num dimensions, Degenerate Element kind)• Grid (Int8 Box y)• Grid (Int16 Box y)• Grid (Int32 Box y)• Grid (Int64 Box y)• Grid (Uint8 Box y)• Grid (Uint16 Box y)• Grid (Uint32 Box y)• Grid (Uint64 Box y)• Grid (Z Box y)• Grid (Rational Box y)• Grid (BD Shape int8 t y)• Grid (BD Shape int16 t y)• Grid (BD Shape int32 t y)• Grid (BD Shape int64 t y)• Grid (BD Shape mpz class y)• Grid (BD Shape mpq class y)• Grid (Octagonal Shape int8 t y)• Grid (Octagonal Shape int16 t y)• Grid (Octagonal Shape int32 t y)• Grid (Octagonal Shape int64 t y)• Grid (Octagonal Shape mpz class y)• Grid (Octagonal Shape mpq class y)• Grid (C Polyhedron y)• Grid (NNC Polyhedron y)• Grid (Grid y)• Grid (Float Box y)• Grid (BD Shape float y)• Grid (Octagonal Shape float y)• Grid (Double Box y)• Grid (BD Shape double y)• Grid (Octagonal Shape double y)• Grid (Long Double Box y)• Grid (BD Shape long double y)• Grid (Octagonal Shape long double y)• Grid (Int8 Box y, Complexity Class complexity)• Grid (Int16 Box y, Complexity Class complexity)• Grid (Int32 Box y, Complexity Class complexity)

109

• Grid (Int64 Box y, Complexity Class complexity)• Grid (Uint8 Box y, Complexity Class complexity)• Grid (Uint16 Box y, Complexity Class complexity)• Grid (Uint32 Box y, Complexity Class complexity)• Grid (Uint64 Box y, Complexity Class complexity)• Grid (Z Box y, Complexity Class complexity)• Grid (Rational Box y, Complexity Class complexity)• Grid (BD Shape int8 t y, Complexity Class complexity)• Grid (BD Shape int16 t y, Complexity Class complexity)• Grid (BD Shape int32 t y, Complexity Class complexity)• Grid (BD Shape int64 t y, Complexity Class complexity)• Grid (BD Shape mpz class y, Complexity Class complexity)• Grid (BD Shape mpq class y, Complexity Class complexity)• Grid (Octagonal Shape int8 t y, Complexity Class complexity)• Grid (Octagonal Shape int16 t y, Complexity Class complexity)• Grid (Octagonal Shape int32 t y, Complexity Class complexity)• Grid (Octagonal Shape int64 t y, Complexity Class complexity)• Grid (Octagonal Shape mpz class y, Complexity Class complexity)• Grid (Octagonal Shape mpq class y, Complexity Class complexity)• Grid (C Polyhedron y, Complexity Class complexity)• Grid (NNC Polyhedron y, Complexity Class complexity)• Grid (Grid y, Complexity Class complexity)• Grid (Float Box y, Complexity Class complexity)• Grid (BD Shape float y, Complexity Class complexity)• Grid (Octagonal Shape float y, Complexity Class complexity)• Grid (Double Box y, Complexity Class complexity)• Grid (BD Shape double y, Complexity Class complexity)• Grid (Octagonal Shape double y, Complexity Class complexity)• Grid (Long Double Box y, Complexity Class complexity)• Grid (BD Shape long double y, Complexity Class complexity)• Grid (Octagonal Shape long double y, Complexity Class complexity)• Grid (Constraint System cs)• Grid (Congruence System cs)• Grid (Grid Generator System cs)• native void swap (Grid y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Poly Gen Relation relation with (Grid Generator c)• native Constraint System constraints ()• native Congruence System congruences ()• native Grid Generator System grid generators ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native Grid Generator System minimized grid generators ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()

110

• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (Grid y)• native boolean strictly contains (Grid y)• native boolean is disjoint from (Grid y)• native boolean equals (Grid p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add grid generator (Grid Generator c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void add grid generators (Grid Generator System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Grid p)• native void upper bound assign (Grid p)• native void difference assign (Grid p)• native void concatenate assign (Grid p)• native void time elapse assign (Grid p)• native boolean upper bound assign if exact (Grid y)• native boolean simplify using context assign (Grid p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩




111




Expression rhs)• native void generalized affine image with congruence (Variable var, Relation Symbol relsym, Linear←↩

Expression expr, Coefficient denominator, Coefficient modulus)• native void generalized affine preimage with congruence (Variable var, Relation Symbol relsym,

Linear Expression expr, Coefficient denominator, Coefficient modulus)• native void generalized affine image lhs rhs with congruence (Linear Expression lhs, Relation←↩

Symbol relsym, Linear Expression rhs, Coefficient modulus)• native void generalized affine preimage lhs rhs with congruence (Linear Expression lhs, Relation←↩

Symbol relsym, Linear Expression rhs, Coefficient modulus)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void congruence widening assign (Grid y, By Reference< Integer > tp)• native void generator widening assign (Grid y, By Reference< Integer > tp)• native void widening assign (Grid y, By Reference< Integer > tp)• native void limited congruence extrapolation assign (Grid y, Congruence System cs, By Reference<

Integer > tp)• native void limited generator extrapolation assign (Grid y, Congruence System cs, By Reference<

Integer > tp)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Grid, Pointset Powerset Grid > approximate partition (Grid p, Grid q, By ←↩

Reference< Boolean > finite)



112


Java class interfacing C++ Parma Polyhedra Library::Grid.The documentation for this class was generated from the following file:

• Grid.java

10.37 parma polyhedra library.Grid Generator Class ReferenceA grid line, parameter or grid point.


• Grid Generator Type type ()Returns the generator type.

• Linear Expression linear expression ()Returns the linear expression in this.

• Coefficient divisor ()If this is either a grid point or a parameter, returns its divisor.




• static Grid Generator grid line (Linear Expression e)Returns the line of direction e.

• static Grid Generator parameter (Linear Expression e, Coefficient d)Returns the parameter at e / d.

• static Grid Generator grid point (Linear Expression e, Coefficient d)Returns the point at e / d.


A grid line, parameter or grid point.An object of the class Grid Generator is one of the following:

• a grid line;

• a parameter;

• a grid point.


static Grid Generator parma polyhedra library.Grid Generator.grid line ( Linear Expression e )[inline], [static] Returns the line of direction e.Exceptions

113


static Grid Generator parma polyhedra library.Grid Generator.parameter ( Linear Expression e,Coefficient d ) [inline], [static] Returns the parameter at e / d.Exceptions


static Grid Generator parma polyhedra library.Grid Generator.grid point ( Linear Expression e,Coefficient d ) [inline], [static] Returns the point at e / d.Exceptions


Coefficient parma polyhedra library.Grid Generator.divisor ( ) [inline] If this is either agrid point or a parameter, returns its divisor.Exceptions

RuntimeErrorException Thrown if this is a line.


• Grid Generator.java

10.38 parma polyhedra library.Grid Generator System Class ReferenceA system of grid generators.

Inherits ArrayList< Grid Generator >.


• Grid Generator System ()

Default constructor: builds an empty system of grid generators.

• native String ascii dump ()

Returns an ascii formatted internal representation of this.

• native String toString ()



A system of grid generators.An object of the class Grid Generator System is a system of grid generators, i.e., a multiset of objects

of the class Grid Generator.The documentation for this class was generated from the following file:

• Grid Generator System.java

10.39 parma polyhedra library.Grid Generator Type Enum ReferenceThe grid generator type.

114



Public Attributes

• LINEThe generator is a line.

• PARAMETERThe generator is a parameter.


The grid generator type.The documentation for this enum was generated from the following file:

• Grid Generator Type.java

10.40 parma polyhedra library.Int16 Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Int16 Box.



• Int16 Box (long num dimensions, Degenerate Element kind)• Int16 Box (Int8 Box y)• Int16 Box (Int16 Box y)• Int16 Box (Int32 Box y)• Int16 Box (Int64 Box y)• Int16 Box (Uint8 Box y)• Int16 Box (Uint16 Box y)• Int16 Box (Uint32 Box y)• Int16 Box (Uint64 Box y)• Int16 Box (Z Box y)• Int16 Box (Rational Box y)• Int16 Box (BD Shape int8 t y)• Int16 Box (BD Shape int16 t y)• Int16 Box (BD Shape int32 t y)• Int16 Box (BD Shape int64 t y)• Int16 Box (BD Shape mpz class y)• Int16 Box (BD Shape mpq class y)• Int16 Box (Octagonal Shape int8 t y)• Int16 Box (Octagonal Shape int16 t y)• Int16 Box (Octagonal Shape int32 t y)• Int16 Box (Octagonal Shape int64 t y)• Int16 Box (Octagonal Shape mpz class y)• Int16 Box (Octagonal Shape mpq class y)• Int16 Box (C Polyhedron y)• Int16 Box (NNC Polyhedron y)• Int16 Box (Grid y)• Int16 Box (Float Box y)• Int16 Box (BD Shape float y)

115

• Int16 Box (Octagonal Shape float y)• Int16 Box (Double Box y)• Int16 Box (BD Shape double y)• Int16 Box (Octagonal Shape double y)• Int16 Box (Long Double Box y)• Int16 Box (BD Shape long double y)• Int16 Box (Octagonal Shape long double y)• Int16 Box (Int8 Box y, Complexity Class complexity)• Int16 Box (Int16 Box y, Complexity Class complexity)• Int16 Box (Int32 Box y, Complexity Class complexity)• Int16 Box (Int64 Box y, Complexity Class complexity)• Int16 Box (Uint8 Box y, Complexity Class complexity)• Int16 Box (Uint16 Box y, Complexity Class complexity)• Int16 Box (Uint32 Box y, Complexity Class complexity)• Int16 Box (Uint64 Box y, Complexity Class complexity)• Int16 Box (Z Box y, Complexity Class complexity)• Int16 Box (Rational Box y, Complexity Class complexity)• Int16 Box (BD Shape int8 t y, Complexity Class complexity)• Int16 Box (BD Shape int16 t y, Complexity Class complexity)• Int16 Box (BD Shape int32 t y, Complexity Class complexity)• Int16 Box (BD Shape int64 t y, Complexity Class complexity)• Int16 Box (BD Shape mpz class y, Complexity Class complexity)• Int16 Box (BD Shape mpq class y, Complexity Class complexity)• Int16 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Int16 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Int16 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Int16 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Int16 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Int16 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Int16 Box (C Polyhedron y, Complexity Class complexity)• Int16 Box (NNC Polyhedron y, Complexity Class complexity)• Int16 Box (Grid y, Complexity Class complexity)• Int16 Box (Float Box y, Complexity Class complexity)• Int16 Box (BD Shape float y, Complexity Class complexity)• Int16 Box (Octagonal Shape float y, Complexity Class complexity)• Int16 Box (Double Box y, Complexity Class complexity)• Int16 Box (BD Shape double y, Complexity Class complexity)• Int16 Box (Octagonal Shape double y, Complexity Class complexity)• Int16 Box (Long Double Box y, Complexity Class complexity)• Int16 Box (BD Shape long double y, Complexity Class complexity)• Int16 Box (Octagonal Shape long double y, Complexity Class complexity)• Int16 Box (Constraint System cs)• Int16 Box (Congruence System cs)• Int16 Box (Generator System cs)• native void swap (Int16 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)

116

• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Int16 Box y)• native boolean strictly contains (Int16 Box y)• native boolean is disjoint from (Int16 Box y)• native boolean equals (Int16 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Int16 Box p)• native void upper bound assign (Int16 Box p)• native void difference assign (Int16 Box p)• native void concatenate assign (Int16 Box p)• native void time elapse assign (Int16 Box p)• native boolean upper bound assign if exact (Int16 Box y)• native boolean simplify using context assign (Int16 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)

117

• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Int16 Box y, By Reference< Integer > tp)• native void widening assign (Int16 Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Int16 Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Int16 Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Int16 Box, Pointset Powerset NNC Polyhedron > linear partition (Int16 Boxp, Int16 Box q)




Java class interfacing C++ Parma Polyhedra Library::Int16 Box.The documentation for this class was generated from the following file:

• Int16 Box.java

118




• Int32 Box (long num dimensions, Degenerate Element kind)• Int32 Box (Int8 Box y)• Int32 Box (Int16 Box y)• Int32 Box (Int32 Box y)• Int32 Box (Int64 Box y)• Int32 Box (Uint8 Box y)• Int32 Box (Uint16 Box y)• Int32 Box (Uint32 Box y)• Int32 Box (Uint64 Box y)• Int32 Box (Z Box y)• Int32 Box (Rational Box y)• Int32 Box (BD Shape int8 t y)• Int32 Box (BD Shape int16 t y)• Int32 Box (BD Shape int32 t y)• Int32 Box (BD Shape int64 t y)• Int32 Box (BD Shape mpz class y)• Int32 Box (BD Shape mpq class y)• Int32 Box (Octagonal Shape int8 t y)• Int32 Box (Octagonal Shape int16 t y)• Int32 Box (Octagonal Shape int32 t y)• Int32 Box (Octagonal Shape int64 t y)• Int32 Box (Octagonal Shape mpz class y)• Int32 Box (Octagonal Shape mpq class y)• Int32 Box (C Polyhedron y)• Int32 Box (NNC Polyhedron y)• Int32 Box (Grid y)• Int32 Box (Float Box y)• Int32 Box (BD Shape float y)• Int32 Box (Octagonal Shape float y)• Int32 Box (Double Box y)• Int32 Box (BD Shape double y)• Int32 Box (Octagonal Shape double y)• Int32 Box (Long Double Box y)• Int32 Box (BD Shape long double y)• Int32 Box (Octagonal Shape long double y)• Int32 Box (Int8 Box y, Complexity Class complexity)• Int32 Box (Int16 Box y, Complexity Class complexity)• Int32 Box (Int32 Box y, Complexity Class complexity)• Int32 Box (Int64 Box y, Complexity Class complexity)• Int32 Box (Uint8 Box y, Complexity Class complexity)• Int32 Box (Uint16 Box y, Complexity Class complexity)• Int32 Box (Uint32 Box y, Complexity Class complexity)• Int32 Box (Uint64 Box y, Complexity Class complexity)• Int32 Box (Z Box y, Complexity Class complexity)

119

• Int32 Box (Rational Box y, Complexity Class complexity)• Int32 Box (BD Shape int8 t y, Complexity Class complexity)• Int32 Box (BD Shape int16 t y, Complexity Class complexity)• Int32 Box (BD Shape int32 t y, Complexity Class complexity)• Int32 Box (BD Shape int64 t y, Complexity Class complexity)• Int32 Box (BD Shape mpz class y, Complexity Class complexity)• Int32 Box (BD Shape mpq class y, Complexity Class complexity)• Int32 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Int32 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Int32 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Int32 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Int32 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Int32 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Int32 Box (C Polyhedron y, Complexity Class complexity)• Int32 Box (NNC Polyhedron y, Complexity Class complexity)• Int32 Box (Grid y, Complexity Class complexity)• Int32 Box (Float Box y, Complexity Class complexity)• Int32 Box (BD Shape float y, Complexity Class complexity)• Int32 Box (Octagonal Shape float y, Complexity Class complexity)• Int32 Box (Double Box y, Complexity Class complexity)• Int32 Box (BD Shape double y, Complexity Class complexity)• Int32 Box (Octagonal Shape double y, Complexity Class complexity)• Int32 Box (Long Double Box y, Complexity Class complexity)• Int32 Box (BD Shape long double y, Complexity Class complexity)• Int32 Box (Octagonal Shape long double y, Complexity Class complexity)• Int32 Box (Constraint System cs)• Int32 Box (Congruence System cs)• Int32 Box (Generator System cs)• native void swap (Int32 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩

Reference< Boolean > closed)

120

• native boolean has lower bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩






cient val n, Coefficient val d)• native boolean contains (Int32 Box y)• native boolean strictly contains (Int32 Box y)• native boolean is disjoint from (Int32 Box y)• native boolean equals (Int32 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Int32 Box p)• native void upper bound assign (Int32 Box p)• native void difference assign (Int32 Box p)• native void concatenate assign (Int32 Box p)• native void time elapse assign (Int32 Box p)• native boolean upper bound assign if exact (Int32 Box y)• native boolean simplify using context assign (Int32 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







121

• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Int32 Box y, By Reference< Integer > tp)• native void widening assign (Int32 Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Int32 Box y, Constraint System cs, By Reference<










• Int32 Box.java




• Int64 Box (long num dimensions, Degenerate Element kind)• Int64 Box (Int8 Box y)• Int64 Box (Int16 Box y)• Int64 Box (Int32 Box y)• Int64 Box (Int64 Box y)• Int64 Box (Uint8 Box y)• Int64 Box (Uint16 Box y)

122

• Int64 Box (Uint32 Box y)• Int64 Box (Uint64 Box y)• Int64 Box (Z Box y)• Int64 Box (Rational Box y)• Int64 Box (BD Shape int8 t y)• Int64 Box (BD Shape int16 t y)• Int64 Box (BD Shape int32 t y)• Int64 Box (BD Shape int64 t y)• Int64 Box (BD Shape mpz class y)• Int64 Box (BD Shape mpq class y)• Int64 Box (Octagonal Shape int8 t y)• Int64 Box (Octagonal Shape int16 t y)• Int64 Box (Octagonal Shape int32 t y)• Int64 Box (Octagonal Shape int64 t y)• Int64 Box (Octagonal Shape mpz class y)• Int64 Box (Octagonal Shape mpq class y)• Int64 Box (C Polyhedron y)• Int64 Box (NNC Polyhedron y)• Int64 Box (Grid y)• Int64 Box (Float Box y)• Int64 Box (BD Shape float y)• Int64 Box (Octagonal Shape float y)• Int64 Box (Double Box y)• Int64 Box (BD Shape double y)• Int64 Box (Octagonal Shape double y)• Int64 Box (Long Double Box y)• Int64 Box (BD Shape long double y)• Int64 Box (Octagonal Shape long double y)• Int64 Box (Int8 Box y, Complexity Class complexity)• Int64 Box (Int16 Box y, Complexity Class complexity)• Int64 Box (Int32 Box y, Complexity Class complexity)• Int64 Box (Int64 Box y, Complexity Class complexity)• Int64 Box (Uint8 Box y, Complexity Class complexity)• Int64 Box (Uint16 Box y, Complexity Class complexity)• Int64 Box (Uint32 Box y, Complexity Class complexity)• Int64 Box (Uint64 Box y, Complexity Class complexity)• Int64 Box (Z Box y, Complexity Class complexity)• Int64 Box (Rational Box y, Complexity Class complexity)• Int64 Box (BD Shape int8 t y, Complexity Class complexity)• Int64 Box (BD Shape int16 t y, Complexity Class complexity)• Int64 Box (BD Shape int32 t y, Complexity Class complexity)• Int64 Box (BD Shape int64 t y, Complexity Class complexity)• Int64 Box (BD Shape mpz class y, Complexity Class complexity)• Int64 Box (BD Shape mpq class y, Complexity Class complexity)• Int64 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Int64 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Int64 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Int64 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Int64 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Int64 Box (Octagonal Shape mpq class y, Complexity Class complexity)

123

• Int64 Box (C Polyhedron y, Complexity Class complexity)• Int64 Box (NNC Polyhedron y, Complexity Class complexity)• Int64 Box (Grid y, Complexity Class complexity)• Int64 Box (Float Box y, Complexity Class complexity)• Int64 Box (BD Shape float y, Complexity Class complexity)• Int64 Box (Octagonal Shape float y, Complexity Class complexity)• Int64 Box (Double Box y, Complexity Class complexity)• Int64 Box (BD Shape double y, Complexity Class complexity)• Int64 Box (Octagonal Shape double y, Complexity Class complexity)• Int64 Box (Long Double Box y, Complexity Class complexity)• Int64 Box (BD Shape long double y, Complexity Class complexity)• Int64 Box (Octagonal Shape long double y, Complexity Class complexity)• Int64 Box (Constraint System cs)• Int64 Box (Congruence System cs)• Int64 Box (Generator System cs)• native void swap (Int64 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Int64 Box y)• native boolean strictly contains (Int64 Box y)• native boolean is disjoint from (Int64 Box y)

124

• native boolean equals (Int64 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Int64 Box p)• native void upper bound assign (Int64 Box p)• native void difference assign (Int64 Box p)• native void concatenate assign (Int64 Box p)• native void time elapse assign (Int64 Box p)• native boolean upper bound assign if exact (Int64 Box y)• native boolean simplify using context assign (Int64 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







Integer > tp)

125

• native void CC76 narrowing assign (Int64 Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩









• Int64 Box.java




• Int8 Box (long num dimensions, Degenerate Element kind)• Int8 Box (Int8 Box y)• Int8 Box (Int16 Box y)• Int8 Box (Int32 Box y)• Int8 Box (Int64 Box y)• Int8 Box (Uint8 Box y)• Int8 Box (Uint16 Box y)• Int8 Box (Uint32 Box y)• Int8 Box (Uint64 Box y)• Int8 Box (Z Box y)• Int8 Box (Rational Box y)• Int8 Box (BD Shape int8 t y)• Int8 Box (BD Shape int16 t y)• Int8 Box (BD Shape int32 t y)• Int8 Box (BD Shape int64 t y)• Int8 Box (BD Shape mpz class y)• Int8 Box (BD Shape mpq class y)• Int8 Box (Octagonal Shape int8 t y)• Int8 Box (Octagonal Shape int16 t y)• Int8 Box (Octagonal Shape int32 t y)• Int8 Box (Octagonal Shape int64 t y)• Int8 Box (Octagonal Shape mpz class y)

126

• Int8 Box (Octagonal Shape mpq class y)• Int8 Box (C Polyhedron y)• Int8 Box (NNC Polyhedron y)• Int8 Box (Grid y)• Int8 Box (Float Box y)• Int8 Box (BD Shape float y)• Int8 Box (Octagonal Shape float y)• Int8 Box (Double Box y)• Int8 Box (BD Shape double y)• Int8 Box (Octagonal Shape double y)• Int8 Box (Long Double Box y)• Int8 Box (BD Shape long double y)• Int8 Box (Octagonal Shape long double y)• Int8 Box (Int8 Box y, Complexity Class complexity)• Int8 Box (Int16 Box y, Complexity Class complexity)• Int8 Box (Int32 Box y, Complexity Class complexity)• Int8 Box (Int64 Box y, Complexity Class complexity)• Int8 Box (Uint8 Box y, Complexity Class complexity)• Int8 Box (Uint16 Box y, Complexity Class complexity)• Int8 Box (Uint32 Box y, Complexity Class complexity)• Int8 Box (Uint64 Box y, Complexity Class complexity)• Int8 Box (Z Box y, Complexity Class complexity)• Int8 Box (Rational Box y, Complexity Class complexity)• Int8 Box (BD Shape int8 t y, Complexity Class complexity)• Int8 Box (BD Shape int16 t y, Complexity Class complexity)• Int8 Box (BD Shape int32 t y, Complexity Class complexity)• Int8 Box (BD Shape int64 t y, Complexity Class complexity)• Int8 Box (BD Shape mpz class y, Complexity Class complexity)• Int8 Box (BD Shape mpq class y, Complexity Class complexity)• Int8 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Int8 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Int8 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Int8 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Int8 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Int8 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Int8 Box (C Polyhedron y, Complexity Class complexity)• Int8 Box (NNC Polyhedron y, Complexity Class complexity)• Int8 Box (Grid y, Complexity Class complexity)• Int8 Box (Float Box y, Complexity Class complexity)• Int8 Box (BD Shape float y, Complexity Class complexity)• Int8 Box (Octagonal Shape float y, Complexity Class complexity)• Int8 Box (Double Box y, Complexity Class complexity)• Int8 Box (BD Shape double y, Complexity Class complexity)• Int8 Box (Octagonal Shape double y, Complexity Class complexity)• Int8 Box (Long Double Box y, Complexity Class complexity)• Int8 Box (BD Shape long double y, Complexity Class complexity)• Int8 Box (Octagonal Shape long double y, Complexity Class complexity)• Int8 Box (Constraint System cs)• Int8 Box (Congruence System cs)• Int8 Box (Generator System cs)

127

• native void swap (Int8 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Int8 Box y)• native boolean strictly contains (Int8 Box y)• native boolean is disjoint from (Int8 Box y)• native boolean equals (Int8 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Int8 Box p)• native void upper bound assign (Int8 Box p)• native void difference assign (Int8 Box p)• native void concatenate assign (Int8 Box p)

128

• native void time elapse assign (Int8 Box p)• native boolean upper bound assign if exact (Int8 Box y)• native boolean simplify using context assign (Int8 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩











• static native Pair< Int8 Box, Pointset Powerset NNC Polyhedron > linear partition (Int8 Box p,Int8 Box q)



129



• Int8 Box.java

10.44 parma polyhedra library.Invalid Argument Exception Class ReferenceExceptions caused by invalid arguments.



• Invalid Argument Exception (String s)Constructor.


Exceptions caused by invalid arguments.The documentation for this class was generated from the following file:

• Invalid Argument Exception.java

10.45 parma polyhedra library.IO Class ReferenceA class collecting I/O functions.


• static native String wrap string (String str, int indent depth, int preferred first line length, int preferred←↩

line length)Utility function for the wrapping of lines of text.


A class collecting I/O functions.


static native String parma polyhedra library.IO.wrap string ( String str, int indent depth, intpreferred first line length, int preferred line length ) [static] Utility function for the wrappingof lines of text.Parameters

str The source string holding the lines to wrap.indent depth The indentation depth.preferred ←↩

first line lengthThe preferred length for the first line of text.

preferred ←↩

line lengthThe preferred length for all the lines but the first one.

Returns

The wrapped string.


• IO.java

130

10.46 parma polyhedra library.Length Error Exception Class ReferenceExceptions caused by too big length/size values.



• Length Error Exception (String s)

Constructor.


Exceptions caused by too big length/size values.The documentation for this class was generated from the following file:

• Length Error Exception.java

10.47 parma polyhedra library.Linear Expression Class ReferenceA linear expression.

Inheritance diagram for parma polyhedra library.Linear Expression:

parma_polyhedra_library.Linear_Expression

parma_polyhedra_library.Linear_Expression_Coefficient

parma_polyhedra_library.Linear_Expression_Difference

parma_polyhedra_library.Linear_Expression_Sum

parma_polyhedra_library.Linear_Expression_Times

parma_polyhedra_library.Linear_Expression_Unary_Minus

parma_polyhedra_library.Linear_Expression_Variable


• Linear Expression sum (Linear Expression y)

Returns the sum of this and y.

131

• Linear Expression subtract (Linear Expression y)

Returns the difference of this and y.

• Linear Expression times (Coefficient c)

Returns the product of this times c.

• Linear Expression unary minus ()

Returns the negation of this.

• abstract Linear Expression clone ()

Returns a copy of the linear expression.

• native String ascii dump ()

Returns an ascii formatted internal representation of this.



• native boolean is zero ()

Returns true if and only if this is 0.

• native boolean all homogeneous terms are zero ()

Returns true if and only if all the homogeneous terms of this are 0.


A linear expression.An object of the class Linear Expression represents a linear expression that can be built from a Linear←↩

Expression Variable, Linear Expression Coefficient, Linear Expression Sum, Linear Expression Difference,Linear Expression Unary Minus.


• Linear Expression.java

10.48 parma polyhedra library.Linear Expression Coefficient Class Reference

A linear expression built from a coefficient.Inheritance diagram for parma polyhedra library.Linear Expression Coefficient:

parma_polyhedra_library.Linear_Expression_Coefficient


132


• Linear Expression Coefficient (Coefficient c)Builds the object corresponding to a copy of the coefficient c.

• Coefficient argument ()Returns coefficient representing the linear expression.

• Linear Expression Coefficient clone ()Builds a copy of this.


• Coefficient coeffThe coefficient representing the linear expression.


A linear expression built from a coefficient.The documentation for this class was generated from the following file:

• Linear Expression Coefficient.java

10.49 parma polyhedra library.Linear Expression Difference Class ReferenceThe difference of two linear expressions.

Inheritance diagram for parma polyhedra library.Linear Expression Difference:

parma_polyhedra_library.Linear_Expression_Difference



• Linear Expression Difference (Linear Expression x, Linear Expression y)Builds an object that represents the difference of the copy x and y.


• Linear Expression right hand side ()Returns the left hand side of this.

• Linear Expression Difference clone ()Builds a copy of this.

133


• Linear Expression lhsThe value of the left hand side of this.

• Linear Expression rhsThe value of the right hand side of this.


The difference of two linear expressions.The documentation for this class was generated from the following file:

• Linear Expression Difference.java

10.50 parma polyhedra library.Linear Expression Sum Class ReferenceThe sum of two linear expressions.

Inheritance diagram for parma polyhedra library.Linear Expression Sum:

parma_polyhedra_library.Linear_Expression_Sum



• Linear Expression Sum (Linear Expression x, Linear Expression y)Builds an object that represents the sum of the copy of x and y.



• Linear Expression Sum clone ()Builds a copy of this.


• Linear Expression lhsThe value of the left hand side of this.

• Linear Expression rhsThe value of the right hand side of this.

134


The sum of two linear expressions.The documentation for this class was generated from the following file:

• Linear Expression Sum.java

10.51 parma polyhedra library.Linear Expression Times Class Reference

The product of a linear expression and a coefficient.Inheritance diagram for parma polyhedra library.Linear Expression Times:

parma_polyhedra_library.Linear_Expression_Times



• Linear Expression Times (Coefficient c, Variable v)

Builds an object cloning the input arguments.

• Linear Expression Times (Coefficient c, Linear Expression l)


• Linear Expression Times (Linear Expression l, Coefficient c)


• Coefficient coefficient ()

Returns the coefficient of this.

• Linear Expression linear expression ()

Returns the linear expression subobject of this.

• Linear Expression Times clone ()

Builds a copy of this.


• Coefficient coeff

The value of the coefficient.

• Linear Expression lin expr

The value of the inner linear expression.

135


The product of a linear expression and a coefficient.The documentation for this class was generated from the following file:

• Linear Expression Times.java

10.52 parma polyhedra library.Linear Expression Unary Minus Class Reference

The negation of a linear expression.Inheritance diagram for parma polyhedra library.Linear Expression Unary Minus:

parma_polyhedra_library.Linear_Expression_Unary_Minus



• Linear Expression Unary Minus (Linear Expression x)

Builds an object that represents the negation of the copy x.

• Linear Expression argument ()

Returns the value that this negates.

• Linear Expression Unary Minus clone ()



• Linear Expression arg

The value that this negates.


The negation of a linear expression.The documentation for this class was generated from the following file:

• Linear Expression Unary Minus.java

136

10.53 parma polyhedra library.Linear Expression Variable Class Reference

A linear expression built from a variable.Inheritance diagram for parma polyhedra library.Linear Expression Variable:

parma_polyhedra_library.Linear_Expression_Variable



• Linear Expression Variable (Variable v)

Builds the object associated to the copy of v.

• Variable argument ()

Returns the variable representing the linear expression.

• Linear Expression Variable clone ()



• Variable arg


A linear expression built from a variable.The documentation for this class was generated from the following file:

• Linear Expression Variable.java

10.54 parma polyhedra library.Logic Error Exception Class Reference

Exceptions due to errors in low-level routines.Inherits RuntimeException.


• Logic Error Exception (String s)

Constructor.

137


Exceptions due to errors in low-level routines.These exceptions may be generated, for instance, by the inability of querying/controlling the FPU

behavior with respect to rounding modes.The documentation for this class was generated from the following file:

• Logic Error Exception.java

10.55 parma polyhedra library.Long Double Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Long Double Box.



• Long Double Box (long num dimensions, Degenerate Element kind)• Long Double Box (Int8 Box y)• Long Double Box (Int16 Box y)• Long Double Box (Int32 Box y)• Long Double Box (Int64 Box y)• Long Double Box (Uint8 Box y)• Long Double Box (Uint16 Box y)• Long Double Box (Uint32 Box y)• Long Double Box (Uint64 Box y)• Long Double Box (Z Box y)• Long Double Box (Rational Box y)• Long Double Box (BD Shape int8 t y)• Long Double Box (BD Shape int16 t y)• Long Double Box (BD Shape int32 t y)• Long Double Box (BD Shape int64 t y)• Long Double Box (BD Shape mpz class y)• Long Double Box (BD Shape mpq class y)• Long Double Box (Octagonal Shape int8 t y)• Long Double Box (Octagonal Shape int16 t y)• Long Double Box (Octagonal Shape int32 t y)• Long Double Box (Octagonal Shape int64 t y)• Long Double Box (Octagonal Shape mpz class y)• Long Double Box (Octagonal Shape mpq class y)• Long Double Box (C Polyhedron y)• Long Double Box (NNC Polyhedron y)• Long Double Box (Grid y)• Long Double Box (Float Box y)• Long Double Box (BD Shape float y)• Long Double Box (Octagonal Shape float y)• Long Double Box (Double Box y)• Long Double Box (BD Shape double y)• Long Double Box (Octagonal Shape double y)• Long Double Box (Long Double Box y)• Long Double Box (BD Shape long double y)• Long Double Box (Octagonal Shape long double y)• Long Double Box (Int8 Box y, Complexity Class complexity)

138

• Long Double Box (Int16 Box y, Complexity Class complexity)• Long Double Box (Int32 Box y, Complexity Class complexity)• Long Double Box (Int64 Box y, Complexity Class complexity)• Long Double Box (Uint8 Box y, Complexity Class complexity)• Long Double Box (Uint16 Box y, Complexity Class complexity)• Long Double Box (Uint32 Box y, Complexity Class complexity)• Long Double Box (Uint64 Box y, Complexity Class complexity)• Long Double Box (Z Box y, Complexity Class complexity)• Long Double Box (Rational Box y, Complexity Class complexity)• Long Double Box (BD Shape int8 t y, Complexity Class complexity)• Long Double Box (BD Shape int16 t y, Complexity Class complexity)• Long Double Box (BD Shape int32 t y, Complexity Class complexity)• Long Double Box (BD Shape int64 t y, Complexity Class complexity)• Long Double Box (BD Shape mpz class y, Complexity Class complexity)• Long Double Box (BD Shape mpq class y, Complexity Class complexity)• Long Double Box (Octagonal Shape int8 t y, Complexity Class complexity)• Long Double Box (Octagonal Shape int16 t y, Complexity Class complexity)• Long Double Box (Octagonal Shape int32 t y, Complexity Class complexity)• Long Double Box (Octagonal Shape int64 t y, Complexity Class complexity)• Long Double Box (Octagonal Shape mpz class y, Complexity Class complexity)• Long Double Box (Octagonal Shape mpq class y, Complexity Class complexity)• Long Double Box (C Polyhedron y, Complexity Class complexity)• Long Double Box (NNC Polyhedron y, Complexity Class complexity)• Long Double Box (Grid y, Complexity Class complexity)• Long Double Box (Float Box y, Complexity Class complexity)• Long Double Box (BD Shape float y, Complexity Class complexity)• Long Double Box (Octagonal Shape float y, Complexity Class complexity)• Long Double Box (Double Box y, Complexity Class complexity)• Long Double Box (BD Shape double y, Complexity Class complexity)• Long Double Box (Octagonal Shape double y, Complexity Class complexity)• Long Double Box (Long Double Box y, Complexity Class complexity)• Long Double Box (BD Shape long double y, Complexity Class complexity)• Long Double Box (Octagonal Shape long double y, Complexity Class complexity)• Long Double Box (Constraint System cs)• Long Double Box (Congruence System cs)• Long Double Box (Generator System cs)• native void swap (Long Double Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()

139

• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Long Double Box y)• native boolean strictly contains (Long Double Box y)• native boolean is disjoint from (Long Double Box y)• native boolean equals (Long Double Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Long Double Box p)• native void upper bound assign (Long Double Box p)• native void difference assign (Long Double Box p)• native void concatenate assign (Long Double Box p)• native void time elapse assign (Long Double Box p)• native boolean upper bound assign if exact (Long Double Box y)• native boolean simplify using context assign (Long Double Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩




140




Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Long Double Box y, By Reference< Integer > tp)• native void widening assign (Long Double Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Long Double Box y, Constraint System cs, By←↩

Reference< Integer > tp)• native void CC76 narrowing assign (Long Double Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Long Double Box, Pointset Powerset NNC Polyhedron > linear partition (Long←↩

Double Box p, Long Double Box q)




Java class interfacing C++ Parma Polyhedra Library::Long Double Box.The documentation for this class was generated from the following file:

• Long Double Box.java

10.56 parma polyhedra library.MIP Problem Class Reference

A Mixed Integer (linear) Programming problem.Inherits parma polyhedra library.PPL Object.

141


Functions that Do Not Modify the MIP Problem

• native long max space dimension ()Returns the maximum space dimension an MIP Problem can handle.

• native long space dimension ()Returns the space dimension of the MIP problem.

• native Variables Set integer space dimensions ()Returns a set containing all the variables' indexes constrained to be integral.

• native Constraint System constraints ()Returns the constraints .

• native Linear Expression objective function ()Returns the objective function.

• native Optimization Mode optimization mode ()Returns the optimization mode.



• native long total memory in bytes ()Returns the total size in bytes of the memory occupied by the underlying C++ object.

• native boolean OK ()Checks if all the invariants are satisfied.

Functions that May Modify the MIP Problem

• native void clear ()Resets this to be equal to the trivial MIP problem.

• native void add space dimensions and embed (long m)Adds m new space dimensions and embeds the old MIP problem in the new vector space.

• native void add to integer space dimensions (Variables Set i vars)Sets the variables whose indexes are in set i vars to be integer space dimensions.

• native void add constraint (Constraint c)Adds a copy of constraint c to the MIP problem.

• native void add constraints (Constraint System cs)Adds a copy of the constraints in cs to the MIP problem.

• native void set objective function (Linear Expression obj)Sets the objective function to obj.

• native void set optimization mode (Optimization Mode mode)Sets the optimization mode to mode.

Computing the Solution of the MIP Problem

• native boolean is satisfiable ()Checks satisfiability of this.

• native MIP Problem Status solve ()Optimizes the MIP problem.

• native void evaluate objective function (Generator evaluating point, Coefficient num, Coefficientden)

Sets num and den so that numden

is the result of evaluating the objective function on evaluating ←↩

point.• native Generator feasible point ()

Returns a feasible point for this, if it exists.

142

• native Generator optimizing point ()Returns an optimal point for this, if it exists.

• native void optimal value (Coefficient num, Coefficient den)Sets num and den so that num

denis the solution of the optimization problem.

Querying/Setting Control Parameters

• native Control Parameter Value get control parameter (Control Parameter Name name)Returns the value of control parameter name.

• native void set control parameter (Control Parameter Value value)Sets control parameter value.

Constructors and Destructor

• MIP Problem (long dim)

Builds a trivial MIP problem.

• MIP Problem (long dim, Constraint System cs, Linear Expression obj, Optimization Mode mode)

Builds an MIP problem having space dimension dim from the constraint system cs, the objective functionobj and optimization mode mode.

• MIP Problem (MIP Problem y)

Builds a copy of y.

• native void free ()

Releases all resources managed by this, also resetting it to a null reference.


Releases all resources managed by this.


A Mixed Integer (linear) Programming problem.An object of this class encodes a mixed integer (linear) programming problem. The MIP problem is

specified by providing:

• the dimension of the vector space;

• the feasible region, by means of a finite set of linear equality and non-strict inequality constraints;

• the subset of the unknown variables that range over the integers (the other variables implicitly rangingover the reals);

• the objective function, described by a Linear Expression;

• the optimization mode (either maximization or minimization).

The class provides support for the (incremental) solution of the MIP problem based on variations ofthe revised simplex method and on branch-and-bound techniques. The result of the resolution process isexpressed in terms of an enumeration, encoding the feasibility and the unboundedness of the optimizationproblem. The class supports simple feasibility tests (i.e., no optimization), as well as the extraction of anoptimal (resp., feasible) point, provided the MIP Problem is optimizable (resp., feasible).

By exploiting the incremental nature of the solver, it is possible to reuse part of the computational workalready done when solving variants of a given MIP Problem: currently, incremental resolution supports theaddition of space dimensions, the addition of constraints, the change of objective function and the changeof optimization mode.

143


parma polyhedra library.MIP Problem.MIP Problem ( long dim ) [inline] Builds a trivialMIP problem.

A trivial MIP problem requires to maximize the objective function 0 on a vector space under no con-straints at all: the origin of the vector space is an optimal solution.

144

Parameters

dim The dimension of the vector space enclosing this.

Exceptions

Length Error Exception Thrown if dim exceeds max space dimension().

parma polyhedra library.MIP Problem.MIP Problem ( long dim, Constraint System cs, Linear←↩

Expression obj, Optimization Mode mode ) [inline] Builds an MIP problem having space di-mension dim from the constraint system cs, the objective function obj and optimization mode mode.Parameters

dim The dimension of the vector space enclosing this.cs The constraint system defining the feasible region.

obj The objective function.mode The optimization mode.

Exceptions

Length Error Exception Thrown if dim exceeds max space dimension().Invalid Argument ←↩

ExceptionThrown if the constraint system contains any strict inequality or if the spacedimension of the constraint system (resp., the objective function) is strictlygreater than dim.


native void parma polyhedra library.MIP Problem.clear ( ) Resets this to be equal to the trivialMIP problem.

The space dimension is reset to 0.

native void parma polyhedra library.MIP Problem.add space dimensions and embed ( long m )Adds m new space dimensions and embeds the old MIP problem in the new vector space.Parameters

m The number of dimensions to add.

Exceptions

Length Error Exception Thrown if adding m new space dimensions would cause the vector space toexceed dimension max space dimension().

The new space dimensions will be those having the highest indexes in the new MIP problem; they are ini-tially unconstrained.

native void parma polyhedra library.MIP Problem.add to integer space dimensions ( Variables ←↩

Set i vars ) Sets the variables whose indexes are in set i vars to be integer space dimensions.Exceptions

Invalid Argument ←↩

ExceptionThrown if some index in i vars does not correspond to a space dimensionin this.

native void parma polyhedra library.MIP Problem.add constraint ( Constraint c ) Adds a copy ofconstraint c to the MIP problem.

145

Exceptions


ExceptionThrown if the constraint c is a strict inequality or if its space dimension isstrictly greater than the space dimension of this.

native void parma polyhedra library.MIP Problem.add constraints ( Constraint System cs ) Addsa copy of the constraints in cs to the MIP problem.Exceptions


ExceptionThrown if the constraint system cs contains any strict inequality or if itsspace dimension is strictly greater than the space dimension of this.

native void parma polyhedra library.MIP Problem.set objective function ( Linear Expression obj) Sets the objective function to obj.Exceptions


ExceptionThrown if the space dimension of obj is strictly greater than the spacedimension of this.

native boolean parma polyhedra library.MIP Problem.is satisfiable ( ) Checks satisfiability ofthis.

Returns

true if and only if the MIP problem is satisfiable.

native MIP Problem Status parma polyhedra library.MIP Problem.solve ( ) Optimizes the MIPproblem.

Returns

An MIP Problem Status flag indicating the outcome of the optimization attempt (unfeasible, un-bounded or optimized problem).

native void parma polyhedra library.MIP Problem.evaluate objective function ( Generator evaluating←↩

point, Coefficient num, Coefficient den ) Sets num and den so that numden is the result of evaluating

the objective function on evaluating point.Parameters

evaluating ←↩

pointThe point on which the objective function will be evaluated.

num On exit will contain the numerator of the evaluated value.den On exit will contain the denominator of the evaluated value.

Exceptions


ExceptionThrown if this and evaluating point are dimension-incompatibleor if the generator evaluating point is not a point.

native Generator parma polyhedra library.MIP Problem.feasible point ( ) Returns a feasible pointfor this, if it exists.

146

Exceptions

Domain Error Exception Thrown if the MIP problem is not satisfiable.

native Generator parma polyhedra library.MIP Problem.optimizing point ( ) Returns an optimalpoint for this, if it exists.Exceptions

Domain Error Exception Thrown if this doesn't not have an optimizing point, i.e., if the MI←↩

P problem is unbounded or not satisfiable.

native void parma polyhedra library.MIP Problem.optimal value ( Coefficient num, Coefficientden ) Sets num and den so that num

den is the solution of the optimization problem.Exceptions

Domain Error Exception Thrown if this doesn't not have an optimizing point, i.e., if the MI←↩

P problem is unbounded or not satisfiable.


• MIP Problem.java

10.57 parma polyhedra library.MIP Problem Status Enum Reference

Possible outcomes of the MIP Problem solver.



Public Attributes

• UNFEASIBLE MIP PROBLEM

The problem is unfeasible.

• UNBOUNDED MIP PROBLEM

The problem is unbounded.


Possible outcomes of the MIP Problem solver.The documentation for this enum was generated from the following file:

• MIP Problem Status.java

10.58 parma polyhedra library.NNC Polyhedron Class Reference

Java class interfacing C++ Parma Polyhedra Library::NNC Polyhedron.

147

Inheritance diagram for parma polyhedra library.NNC Polyhedron:

parma_polyhedra_library.NNC_Polyhedron



• NNC Polyhedron (long num dimensions, Degenerate Element kind)• NNC Polyhedron (Int8 Box y)• NNC Polyhedron (Int16 Box y)• NNC Polyhedron (Int32 Box y)• NNC Polyhedron (Int64 Box y)• NNC Polyhedron (Uint8 Box y)• NNC Polyhedron (Uint16 Box y)• NNC Polyhedron (Uint32 Box y)• NNC Polyhedron (Uint64 Box y)• NNC Polyhedron (Z Box y)• NNC Polyhedron (Rational Box y)• NNC Polyhedron (BD Shape int8 t y)• NNC Polyhedron (BD Shape int16 t y)• NNC Polyhedron (BD Shape int32 t y)• NNC Polyhedron (BD Shape int64 t y)• NNC Polyhedron (BD Shape mpz class y)• NNC Polyhedron (BD Shape mpq class y)• NNC Polyhedron (Octagonal Shape int8 t y)• NNC Polyhedron (Octagonal Shape int16 t y)• NNC Polyhedron (Octagonal Shape int32 t y)• NNC Polyhedron (Octagonal Shape int64 t y)• NNC Polyhedron (Octagonal Shape mpz class y)• NNC Polyhedron (Octagonal Shape mpq class y)• NNC Polyhedron (C Polyhedron y)• NNC Polyhedron (NNC Polyhedron y)• NNC Polyhedron (Grid y)• NNC Polyhedron (Float Box y)• NNC Polyhedron (BD Shape float y)• NNC Polyhedron (Octagonal Shape float y)• NNC Polyhedron (Double Box y)• NNC Polyhedron (BD Shape double y)

148

• NNC Polyhedron (Octagonal Shape double y)• NNC Polyhedron (Long Double Box y)• NNC Polyhedron (BD Shape long double y)• NNC Polyhedron (Octagonal Shape long double y)• NNC Polyhedron (Int8 Box y, Complexity Class complexity)• NNC Polyhedron (Int16 Box y, Complexity Class complexity)• NNC Polyhedron (Int32 Box y, Complexity Class complexity)• NNC Polyhedron (Int64 Box y, Complexity Class complexity)• NNC Polyhedron (Uint8 Box y, Complexity Class complexity)• NNC Polyhedron (Uint16 Box y, Complexity Class complexity)• NNC Polyhedron (Uint32 Box y, Complexity Class complexity)• NNC Polyhedron (Uint64 Box y, Complexity Class complexity)• NNC Polyhedron (Z Box y, Complexity Class complexity)• NNC Polyhedron (Rational Box y, Complexity Class complexity)• NNC Polyhedron (BD Shape int8 t y, Complexity Class complexity)• NNC Polyhedron (BD Shape int16 t y, Complexity Class complexity)• NNC Polyhedron (BD Shape int32 t y, Complexity Class complexity)• NNC Polyhedron (BD Shape int64 t y, Complexity Class complexity)• NNC Polyhedron (BD Shape mpz class y, Complexity Class complexity)• NNC Polyhedron (BD Shape mpq class y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape int8 t y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape int16 t y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape int32 t y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape int64 t y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape mpz class y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape mpq class y, Complexity Class complexity)• NNC Polyhedron (C Polyhedron y, Complexity Class complexity)• NNC Polyhedron (NNC Polyhedron y, Complexity Class complexity)• NNC Polyhedron (Grid y, Complexity Class complexity)• NNC Polyhedron (Float Box y, Complexity Class complexity)• NNC Polyhedron (BD Shape float y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape float y, Complexity Class complexity)• NNC Polyhedron (Double Box y, Complexity Class complexity)• NNC Polyhedron (BD Shape double y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape double y, Complexity Class complexity)• NNC Polyhedron (Long Double Box y, Complexity Class complexity)• NNC Polyhedron (BD Shape long double y, Complexity Class complexity)• NNC Polyhedron (Octagonal Shape long double y, Complexity Class complexity)• NNC Polyhedron (Constraint System cs)• NNC Polyhedron (Congruence System cs)• NNC Polyhedron (Generator System cs)• native boolean upper bound assign if exact (NNC Polyhedron y)• native boolean poly hull assign if exact (NNC Polyhedron y)• native void positive time elapse assign (NNC Polyhedron p)• native void free ()


• static native Pair< NNC Polyhedron, Pointset Powerset NNC Polyhedron > linear partition (N←↩

NC Polyhedron p, NNC Polyhedron q)

149




Java class interfacing C++ Parma Polyhedra Library::NNC Polyhedron.The documentation for this class was generated from the following file:

• NNC Polyhedron.java

10.59 parma polyhedra library.Octagonal Shape double Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<double>



• Octagonal Shape double (long num dimensions, Degenerate Element kind)• Octagonal Shape double (Int8 Box y)• Octagonal Shape double (Int16 Box y)• Octagonal Shape double (Int32 Box y)• Octagonal Shape double (Int64 Box y)• Octagonal Shape double (Uint8 Box y)• Octagonal Shape double (Uint16 Box y)• Octagonal Shape double (Uint32 Box y)• Octagonal Shape double (Uint64 Box y)• Octagonal Shape double (Z Box y)• Octagonal Shape double (Rational Box y)• Octagonal Shape double (BD Shape int8 t y)• Octagonal Shape double (BD Shape int16 t y)• Octagonal Shape double (BD Shape int32 t y)• Octagonal Shape double (BD Shape int64 t y)• Octagonal Shape double (BD Shape mpz class y)• Octagonal Shape double (BD Shape mpq class y)• Octagonal Shape double (Octagonal Shape int8 t y)• Octagonal Shape double (Octagonal Shape int16 t y)• Octagonal Shape double (Octagonal Shape int32 t y)• Octagonal Shape double (Octagonal Shape int64 t y)• Octagonal Shape double (Octagonal Shape mpz class y)• Octagonal Shape double (Octagonal Shape mpq class y)• Octagonal Shape double (C Polyhedron y)• Octagonal Shape double (NNC Polyhedron y)• Octagonal Shape double (Grid y)• Octagonal Shape double (Float Box y)• Octagonal Shape double (BD Shape float y)• Octagonal Shape double (Octagonal Shape float y)• Octagonal Shape double (Double Box y)• Octagonal Shape double (BD Shape double y)• Octagonal Shape double (Octagonal Shape double y)• Octagonal Shape double (Long Double Box y)• Octagonal Shape double (BD Shape long double y)• Octagonal Shape double (Octagonal Shape long double y)

150

• Octagonal Shape double (Int8 Box y, Complexity Class complexity)• Octagonal Shape double (Int16 Box y, Complexity Class complexity)• Octagonal Shape double (Int32 Box y, Complexity Class complexity)• Octagonal Shape double (Int64 Box y, Complexity Class complexity)• Octagonal Shape double (Uint8 Box y, Complexity Class complexity)• Octagonal Shape double (Uint16 Box y, Complexity Class complexity)• Octagonal Shape double (Uint32 Box y, Complexity Class complexity)• Octagonal Shape double (Uint64 Box y, Complexity Class complexity)• Octagonal Shape double (Z Box y, Complexity Class complexity)• Octagonal Shape double (Rational Box y, Complexity Class complexity)• Octagonal Shape double (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape double (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape double (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape double (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape double (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape double (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape double (C Polyhedron y, Complexity Class complexity)• Octagonal Shape double (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape double (Grid y, Complexity Class complexity)• Octagonal Shape double (Float Box y, Complexity Class complexity)• Octagonal Shape double (BD Shape float y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape double (Double Box y, Complexity Class complexity)• Octagonal Shape double (BD Shape double y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape double (Long Double Box y, Complexity Class complexity)• Octagonal Shape double (BD Shape long double y, Complexity Class complexity)• Octagonal Shape double (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape double (Constraint System cs)• Octagonal Shape double (Congruence System cs)• Octagonal Shape double (Generator System cs)• native void swap (Octagonal Shape double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()

151






cient val n, Coefficient val d)• native boolean contains (Octagonal Shape double y)• native boolean strictly contains (Octagonal Shape double y)• native boolean is disjoint from (Octagonal Shape double y)• native boolean equals (Octagonal Shape double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape double p)• native void upper bound assign (Octagonal Shape double p)• native void difference assign (Octagonal Shape double p)• native void concatenate assign (Octagonal Shape double p)• native void time elapse assign (Octagonal Shape double p)• native boolean upper bound assign if exact (Octagonal Shape double y)• native boolean simplify using context assign (Octagonal Shape double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





152



Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape double y, By Reference< Integer > tp)• native void widening assign (Octagonal Shape double y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape double y, Constraint System

cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape double y, Constraint System cs,

By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape double arg, By Reference< Integer >

tp)• native void CC76 narrowing assign (Octagonal Shape double arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Octagonal Shape double, Pointset Powerset NNC Polyhedron > linear partition(Octagonal Shape double p, Octagonal Shape double q)




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<double>The documentation for this class was generated from the following file:

• Octagonal Shape double.java

10.60 parma polyhedra library.Octagonal Shape float Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<float>


153


• Octagonal Shape float (long num dimensions, Degenerate Element kind)• Octagonal Shape float (Int8 Box y)• Octagonal Shape float (Int16 Box y)• Octagonal Shape float (Int32 Box y)• Octagonal Shape float (Int64 Box y)• Octagonal Shape float (Uint8 Box y)• Octagonal Shape float (Uint16 Box y)• Octagonal Shape float (Uint32 Box y)• Octagonal Shape float (Uint64 Box y)• Octagonal Shape float (Z Box y)• Octagonal Shape float (Rational Box y)• Octagonal Shape float (BD Shape int8 t y)• Octagonal Shape float (BD Shape int16 t y)• Octagonal Shape float (BD Shape int32 t y)• Octagonal Shape float (BD Shape int64 t y)• Octagonal Shape float (BD Shape mpz class y)• Octagonal Shape float (BD Shape mpq class y)• Octagonal Shape float (Octagonal Shape int8 t y)• Octagonal Shape float (Octagonal Shape int16 t y)• Octagonal Shape float (Octagonal Shape int32 t y)• Octagonal Shape float (Octagonal Shape int64 t y)• Octagonal Shape float (Octagonal Shape mpz class y)• Octagonal Shape float (Octagonal Shape mpq class y)• Octagonal Shape float (C Polyhedron y)• Octagonal Shape float (NNC Polyhedron y)• Octagonal Shape float (Grid y)• Octagonal Shape float (Float Box y)• Octagonal Shape float (BD Shape float y)• Octagonal Shape float (Octagonal Shape float y)• Octagonal Shape float (Double Box y)• Octagonal Shape float (BD Shape double y)• Octagonal Shape float (Octagonal Shape double y)• Octagonal Shape float (Long Double Box y)• Octagonal Shape float (BD Shape long double y)• Octagonal Shape float (Octagonal Shape long double y)• Octagonal Shape float (Int8 Box y, Complexity Class complexity)• Octagonal Shape float (Int16 Box y, Complexity Class complexity)• Octagonal Shape float (Int32 Box y, Complexity Class complexity)• Octagonal Shape float (Int64 Box y, Complexity Class complexity)• Octagonal Shape float (Uint8 Box y, Complexity Class complexity)• Octagonal Shape float (Uint16 Box y, Complexity Class complexity)• Octagonal Shape float (Uint32 Box y, Complexity Class complexity)• Octagonal Shape float (Uint64 Box y, Complexity Class complexity)• Octagonal Shape float (Z Box y, Complexity Class complexity)• Octagonal Shape float (Rational Box y, Complexity Class complexity)• Octagonal Shape float (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape float (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape float (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape float (BD Shape int64 t y, Complexity Class complexity)

154

• Octagonal Shape float (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape float (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape float (C Polyhedron y, Complexity Class complexity)• Octagonal Shape float (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape float (Grid y, Complexity Class complexity)• Octagonal Shape float (Float Box y, Complexity Class complexity)• Octagonal Shape float (BD Shape float y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape float (Double Box y, Complexity Class complexity)• Octagonal Shape float (BD Shape double y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape float (Long Double Box y, Complexity Class complexity)• Octagonal Shape float (BD Shape long double y, Complexity Class complexity)• Octagonal Shape float (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape float (Constraint System cs)• Octagonal Shape float (Congruence System cs)• Octagonal Shape float (Generator System cs)• native void swap (Octagonal Shape float y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)

155


• native boolean contains (Octagonal Shape float y)• native boolean strictly contains (Octagonal Shape float y)• native boolean is disjoint from (Octagonal Shape float y)• native boolean equals (Octagonal Shape float p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape float p)• native void upper bound assign (Octagonal Shape float p)• native void difference assign (Octagonal Shape float p)• native void concatenate assign (Octagonal Shape float p)• native void time elapse assign (Octagonal Shape float p)• native boolean upper bound assign if exact (Octagonal Shape float y)• native boolean simplify using context assign (Octagonal Shape float p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()

156

• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape float y, By Reference< Integer > tp)• native void widening assign (Octagonal Shape float y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape float y, Constraint System

cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape float y, Constraint System cs,

By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape float arg, By Reference< Integer > tp)• native void CC76 narrowing assign (Octagonal Shape float arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Octagonal Shape float, Pointset Powerset NNC Polyhedron > linear partition(Octagonal Shape float p, Octagonal Shape float q)




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<float>The documentation for this class was generated from the following file:

• Octagonal Shape float.java

10.61 parma polyhedra library.Octagonal Shape int16 t Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<int16 t>



• Octagonal Shape int16 t (long num dimensions, Degenerate Element kind)• Octagonal Shape int16 t (Int8 Box y)• Octagonal Shape int16 t (Int16 Box y)• Octagonal Shape int16 t (Int32 Box y)• Octagonal Shape int16 t (Int64 Box y)• Octagonal Shape int16 t (Uint8 Box y)• Octagonal Shape int16 t (Uint16 Box y)• Octagonal Shape int16 t (Uint32 Box y)• Octagonal Shape int16 t (Uint64 Box y)• Octagonal Shape int16 t (Z Box y)• Octagonal Shape int16 t (Rational Box y)• Octagonal Shape int16 t (BD Shape int8 t y)• Octagonal Shape int16 t (BD Shape int16 t y)• Octagonal Shape int16 t (BD Shape int32 t y)

157

• Octagonal Shape int16 t (BD Shape int64 t y)• Octagonal Shape int16 t (BD Shape mpz class y)• Octagonal Shape int16 t (BD Shape mpq class y)• Octagonal Shape int16 t (Octagonal Shape int8 t y)• Octagonal Shape int16 t (Octagonal Shape int16 t y)• Octagonal Shape int16 t (Octagonal Shape int32 t y)• Octagonal Shape int16 t (Octagonal Shape int64 t y)• Octagonal Shape int16 t (Octagonal Shape mpz class y)• Octagonal Shape int16 t (Octagonal Shape mpq class y)• Octagonal Shape int16 t (C Polyhedron y)• Octagonal Shape int16 t (NNC Polyhedron y)• Octagonal Shape int16 t (Grid y)• Octagonal Shape int16 t (Float Box y)• Octagonal Shape int16 t (BD Shape float y)• Octagonal Shape int16 t (Octagonal Shape float y)• Octagonal Shape int16 t (Double Box y)• Octagonal Shape int16 t (BD Shape double y)• Octagonal Shape int16 t (Octagonal Shape double y)• Octagonal Shape int16 t (Long Double Box y)• Octagonal Shape int16 t (BD Shape long double y)• Octagonal Shape int16 t (Octagonal Shape long double y)• Octagonal Shape int16 t (Int8 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Int16 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Int32 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Int64 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Uint8 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Uint16 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Uint32 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Uint64 Box y, Complexity Class complexity)• Octagonal Shape int16 t (Z Box y, Complexity Class complexity)• Octagonal Shape int16 t (Rational Box y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape int16 t (C Polyhedron y, Complexity Class complexity)• Octagonal Shape int16 t (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape int16 t (Grid y, Complexity Class complexity)• Octagonal Shape int16 t (Float Box y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape float y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape int16 t (Double Box y, Complexity Class complexity)

158

• Octagonal Shape int16 t (BD Shape double y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape int16 t (Long Double Box y, Complexity Class complexity)• Octagonal Shape int16 t (BD Shape long double y, Complexity Class complexity)• Octagonal Shape int16 t (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape int16 t (Constraint System cs)• Octagonal Shape int16 t (Congruence System cs)• Octagonal Shape int16 t (Generator System cs)• native void swap (Octagonal Shape int16 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (Octagonal Shape int16 t y)• native boolean strictly contains (Octagonal Shape int16 t y)• native boolean is disjoint from (Octagonal Shape int16 t y)• native boolean equals (Octagonal Shape int16 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)

159

• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape int16 t p)• native void upper bound assign (Octagonal Shape int16 t p)• native void difference assign (Octagonal Shape int16 t p)• native void concatenate assign (Octagonal Shape int16 t p)• native void time elapse assign (Octagonal Shape int16 t p)• native boolean upper bound assign if exact (Octagonal Shape int16 t y)• native boolean simplify using context assign (Octagonal Shape int16 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape int16 t y, By Reference< Integer > tp)• native void widening assign (Octagonal Shape int16 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape int16 t y, Constraint System

cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape int16 t y, Constraint System cs,

By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape int16 t arg, By Reference< Integer >

tp)• native void CC76 narrowing assign (Octagonal Shape int16 t arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩



160


• static native Pair< Octagonal Shape int16 t, Pointset Powerset NNC Polyhedron > linear partition(Octagonal Shape int16 t p, Octagonal Shape int16 t q)




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<int16 t>The documentation for this class was generated from the following file:

• Octagonal Shape int16 t.java




• Octagonal Shape int32 t (long num dimensions, Degenerate Element kind)• Octagonal Shape int32 t (Int8 Box y)• Octagonal Shape int32 t (Int16 Box y)• Octagonal Shape int32 t (Int32 Box y)• Octagonal Shape int32 t (Int64 Box y)• Octagonal Shape int32 t (Uint8 Box y)• Octagonal Shape int32 t (Uint16 Box y)• Octagonal Shape int32 t (Uint32 Box y)• Octagonal Shape int32 t (Uint64 Box y)• Octagonal Shape int32 t (Z Box y)• Octagonal Shape int32 t (Rational Box y)• Octagonal Shape int32 t (BD Shape int8 t y)• Octagonal Shape int32 t (BD Shape int16 t y)• Octagonal Shape int32 t (BD Shape int32 t y)• Octagonal Shape int32 t (BD Shape int64 t y)• Octagonal Shape int32 t (BD Shape mpz class y)• Octagonal Shape int32 t (BD Shape mpq class y)• Octagonal Shape int32 t (Octagonal Shape int8 t y)• Octagonal Shape int32 t (Octagonal Shape int16 t y)• Octagonal Shape int32 t (Octagonal Shape int32 t y)• Octagonal Shape int32 t (Octagonal Shape int64 t y)• Octagonal Shape int32 t (Octagonal Shape mpz class y)• Octagonal Shape int32 t (Octagonal Shape mpq class y)• Octagonal Shape int32 t (C Polyhedron y)• Octagonal Shape int32 t (NNC Polyhedron y)• Octagonal Shape int32 t (Grid y)• Octagonal Shape int32 t (Float Box y)• Octagonal Shape int32 t (BD Shape float y)• Octagonal Shape int32 t (Octagonal Shape float y)• Octagonal Shape int32 t (Double Box y)

161

• Octagonal Shape int32 t (BD Shape double y)• Octagonal Shape int32 t (Octagonal Shape double y)• Octagonal Shape int32 t (Long Double Box y)• Octagonal Shape int32 t (BD Shape long double y)• Octagonal Shape int32 t (Octagonal Shape long double y)• Octagonal Shape int32 t (Int8 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Int16 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Int32 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Int64 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Uint8 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Uint16 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Uint32 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Uint64 Box y, Complexity Class complexity)• Octagonal Shape int32 t (Z Box y, Complexity Class complexity)• Octagonal Shape int32 t (Rational Box y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape int32 t (C Polyhedron y, Complexity Class complexity)• Octagonal Shape int32 t (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape int32 t (Grid y, Complexity Class complexity)• Octagonal Shape int32 t (Float Box y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape float y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape int32 t (Double Box y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape double y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape int32 t (Long Double Box y, Complexity Class complexity)• Octagonal Shape int32 t (BD Shape long double y, Complexity Class complexity)• Octagonal Shape int32 t (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape int32 t (Constraint System cs)• Octagonal Shape int32 t (Congruence System cs)• Octagonal Shape int32 t (Generator System cs)• native void swap (Octagonal Shape int32 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()

162






cient val n, Coefficient val d)• native boolean contains (Octagonal Shape int32 t y)• native boolean strictly contains (Octagonal Shape int32 t y)• native boolean is disjoint from (Octagonal Shape int32 t y)• native boolean equals (Octagonal Shape int32 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape int32 t p)• native void upper bound assign (Octagonal Shape int32 t p)• native void difference assign (Octagonal Shape int32 t p)• native void concatenate assign (Octagonal Shape int32 t p)• native void time elapse assign (Octagonal Shape int32 t p)• native boolean upper bound assign if exact (Octagonal Shape int32 t y)• native boolean simplify using context assign (Octagonal Shape int32 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



163


















164




• Octagonal Shape int64 t (long num dimensions, Degenerate Element kind)• Octagonal Shape int64 t (Int8 Box y)• Octagonal Shape int64 t (Int16 Box y)• Octagonal Shape int64 t (Int32 Box y)• Octagonal Shape int64 t (Int64 Box y)• Octagonal Shape int64 t (Uint8 Box y)• Octagonal Shape int64 t (Uint16 Box y)• Octagonal Shape int64 t (Uint32 Box y)• Octagonal Shape int64 t (Uint64 Box y)• Octagonal Shape int64 t (Z Box y)• Octagonal Shape int64 t (Rational Box y)• Octagonal Shape int64 t (BD Shape int8 t y)• Octagonal Shape int64 t (BD Shape int16 t y)• Octagonal Shape int64 t (BD Shape int32 t y)• Octagonal Shape int64 t (BD Shape int64 t y)• Octagonal Shape int64 t (BD Shape mpz class y)• Octagonal Shape int64 t (BD Shape mpq class y)• Octagonal Shape int64 t (Octagonal Shape int8 t y)• Octagonal Shape int64 t (Octagonal Shape int16 t y)• Octagonal Shape int64 t (Octagonal Shape int32 t y)• Octagonal Shape int64 t (Octagonal Shape int64 t y)• Octagonal Shape int64 t (Octagonal Shape mpz class y)• Octagonal Shape int64 t (Octagonal Shape mpq class y)• Octagonal Shape int64 t (C Polyhedron y)• Octagonal Shape int64 t (NNC Polyhedron y)• Octagonal Shape int64 t (Grid y)• Octagonal Shape int64 t (Float Box y)• Octagonal Shape int64 t (BD Shape float y)• Octagonal Shape int64 t (Octagonal Shape float y)• Octagonal Shape int64 t (Double Box y)• Octagonal Shape int64 t (BD Shape double y)• Octagonal Shape int64 t (Octagonal Shape double y)• Octagonal Shape int64 t (Long Double Box y)• Octagonal Shape int64 t (BD Shape long double y)• Octagonal Shape int64 t (Octagonal Shape long double y)• Octagonal Shape int64 t (Int8 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Int16 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Int32 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Int64 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Uint8 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Uint16 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Uint32 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Uint64 Box y, Complexity Class complexity)• Octagonal Shape int64 t (Z Box y, Complexity Class complexity)

165

• Octagonal Shape int64 t (Rational Box y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape int64 t (C Polyhedron y, Complexity Class complexity)• Octagonal Shape int64 t (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape int64 t (Grid y, Complexity Class complexity)• Octagonal Shape int64 t (Float Box y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape float y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape int64 t (Double Box y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape double y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape int64 t (Long Double Box y, Complexity Class complexity)• Octagonal Shape int64 t (BD Shape long double y, Complexity Class complexity)• Octagonal Shape int64 t (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape int64 t (Constraint System cs)• Octagonal Shape int64 t (Congruence System cs)• Octagonal Shape int64 t (Generator System cs)• native void swap (Octagonal Shape int64 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)

166





• native boolean contains (Octagonal Shape int64 t y)• native boolean strictly contains (Octagonal Shape int64 t y)• native boolean is disjoint from (Octagonal Shape int64 t y)• native boolean equals (Octagonal Shape int64 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape int64 t p)• native void upper bound assign (Octagonal Shape int64 t p)• native void difference assign (Octagonal Shape int64 t p)• native void concatenate assign (Octagonal Shape int64 t p)• native void time elapse assign (Octagonal Shape int64 t p)• native boolean upper bound assign if exact (Octagonal Shape int64 t y)• native boolean simplify using context assign (Octagonal Shape int64 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







167

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape int64 t y, By Reference< Integer > tp)• native void widening assign (Octagonal Shape int64 t y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape int64 t y, Constraint System
















• Octagonal Shape int8 t (long num dimensions, Degenerate Element kind)• Octagonal Shape int8 t (Int8 Box y)• Octagonal Shape int8 t (Int16 Box y)• Octagonal Shape int8 t (Int32 Box y)• Octagonal Shape int8 t (Int64 Box y)• Octagonal Shape int8 t (Uint8 Box y)• Octagonal Shape int8 t (Uint16 Box y)

168

• Octagonal Shape int8 t (Uint32 Box y)• Octagonal Shape int8 t (Uint64 Box y)• Octagonal Shape int8 t (Z Box y)• Octagonal Shape int8 t (Rational Box y)• Octagonal Shape int8 t (BD Shape int8 t y)• Octagonal Shape int8 t (BD Shape int16 t y)• Octagonal Shape int8 t (BD Shape int32 t y)• Octagonal Shape int8 t (BD Shape int64 t y)• Octagonal Shape int8 t (BD Shape mpz class y)• Octagonal Shape int8 t (BD Shape mpq class y)• Octagonal Shape int8 t (Octagonal Shape int8 t y)• Octagonal Shape int8 t (Octagonal Shape int16 t y)• Octagonal Shape int8 t (Octagonal Shape int32 t y)• Octagonal Shape int8 t (Octagonal Shape int64 t y)• Octagonal Shape int8 t (Octagonal Shape mpz class y)• Octagonal Shape int8 t (Octagonal Shape mpq class y)• Octagonal Shape int8 t (C Polyhedron y)• Octagonal Shape int8 t (NNC Polyhedron y)• Octagonal Shape int8 t (Grid y)• Octagonal Shape int8 t (Float Box y)• Octagonal Shape int8 t (BD Shape float y)• Octagonal Shape int8 t (Octagonal Shape float y)• Octagonal Shape int8 t (Double Box y)• Octagonal Shape int8 t (BD Shape double y)• Octagonal Shape int8 t (Octagonal Shape double y)• Octagonal Shape int8 t (Long Double Box y)• Octagonal Shape int8 t (BD Shape long double y)• Octagonal Shape int8 t (Octagonal Shape long double y)• Octagonal Shape int8 t (Int8 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Int16 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Int32 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Int64 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Uint8 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Uint16 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Uint32 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Uint64 Box y, Complexity Class complexity)• Octagonal Shape int8 t (Z Box y, Complexity Class complexity)• Octagonal Shape int8 t (Rational Box y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape mpq class y, Complexity Class complexity)

169

• Octagonal Shape int8 t (C Polyhedron y, Complexity Class complexity)• Octagonal Shape int8 t (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape int8 t (Grid y, Complexity Class complexity)• Octagonal Shape int8 t (Float Box y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape float y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape int8 t (Double Box y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape double y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape int8 t (Long Double Box y, Complexity Class complexity)• Octagonal Shape int8 t (BD Shape long double y, Complexity Class complexity)• Octagonal Shape int8 t (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape int8 t (Constraint System cs)• Octagonal Shape int8 t (Congruence System cs)• Octagonal Shape int8 t (Generator System cs)• native void swap (Octagonal Shape int8 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (Octagonal Shape int8 t y)• native boolean strictly contains (Octagonal Shape int8 t y)• native boolean is disjoint from (Octagonal Shape int8 t y)• native boolean equals (Octagonal Shape int8 t p)• boolean equals (Object y)• native boolean OK ()

170

• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape int8 t p)• native void upper bound assign (Octagonal Shape int8 t p)• native void difference assign (Octagonal Shape int8 t p)• native void concatenate assign (Octagonal Shape int8 t p)• native void time elapse assign (Octagonal Shape int8 t p)• native boolean upper bound assign if exact (Octagonal Shape int8 t y)• native boolean simplify using context assign (Octagonal Shape int8 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩








By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape int8 t arg, By Reference< Integer > tp)

171

• native void CC76 narrowing assign (Octagonal Shape int8 t arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩










10.65 parma polyhedra library.Octagonal Shape long double Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<long double>



• Octagonal Shape long double (long num dimensions, Degenerate Element kind)• Octagonal Shape long double (Int8 Box y)• Octagonal Shape long double (Int16 Box y)• Octagonal Shape long double (Int32 Box y)• Octagonal Shape long double (Int64 Box y)• Octagonal Shape long double (Uint8 Box y)• Octagonal Shape long double (Uint16 Box y)• Octagonal Shape long double (Uint32 Box y)• Octagonal Shape long double (Uint64 Box y)• Octagonal Shape long double (Z Box y)• Octagonal Shape long double (Rational Box y)• Octagonal Shape long double (BD Shape int8 t y)• Octagonal Shape long double (BD Shape int16 t y)• Octagonal Shape long double (BD Shape int32 t y)• Octagonal Shape long double (BD Shape int64 t y)• Octagonal Shape long double (BD Shape mpz class y)• Octagonal Shape long double (BD Shape mpq class y)• Octagonal Shape long double (Octagonal Shape int8 t y)• Octagonal Shape long double (Octagonal Shape int16 t y)• Octagonal Shape long double (Octagonal Shape int32 t y)• Octagonal Shape long double (Octagonal Shape int64 t y)• Octagonal Shape long double (Octagonal Shape mpz class y)

172

• Octagonal Shape long double (Octagonal Shape mpq class y)• Octagonal Shape long double (C Polyhedron y)• Octagonal Shape long double (NNC Polyhedron y)• Octagonal Shape long double (Grid y)• Octagonal Shape long double (Float Box y)• Octagonal Shape long double (BD Shape float y)• Octagonal Shape long double (Octagonal Shape float y)• Octagonal Shape long double (Double Box y)• Octagonal Shape long double (BD Shape double y)• Octagonal Shape long double (Octagonal Shape double y)• Octagonal Shape long double (Long Double Box y)• Octagonal Shape long double (BD Shape long double y)• Octagonal Shape long double (Octagonal Shape long double y)• Octagonal Shape long double (Int8 Box y, Complexity Class complexity)• Octagonal Shape long double (Int16 Box y, Complexity Class complexity)• Octagonal Shape long double (Int32 Box y, Complexity Class complexity)• Octagonal Shape long double (Int64 Box y, Complexity Class complexity)• Octagonal Shape long double (Uint8 Box y, Complexity Class complexity)• Octagonal Shape long double (Uint16 Box y, Complexity Class complexity)• Octagonal Shape long double (Uint32 Box y, Complexity Class complexity)• Octagonal Shape long double (Uint64 Box y, Complexity Class complexity)• Octagonal Shape long double (Z Box y, Complexity Class complexity)• Octagonal Shape long double (Rational Box y, Complexity Class complexity)• Octagonal Shape long double (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape long double (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape long double (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape long double (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape long double (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape long double (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape long double (C Polyhedron y, Complexity Class complexity)• Octagonal Shape long double (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape long double (Grid y, Complexity Class complexity)• Octagonal Shape long double (Float Box y, Complexity Class complexity)• Octagonal Shape long double (BD Shape float y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape long double (Double Box y, Complexity Class complexity)• Octagonal Shape long double (BD Shape double y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape long double (Long Double Box y, Complexity Class complexity)• Octagonal Shape long double (BD Shape long double y, Complexity Class complexity)• Octagonal Shape long double (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape long double (Constraint System cs)• Octagonal Shape long double (Congruence System cs)• Octagonal Shape long double (Generator System cs)

173

• native void swap (Octagonal Shape long double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





cient val n, Coefficient val d)• native boolean contains (Octagonal Shape long double y)• native boolean strictly contains (Octagonal Shape long double y)• native boolean is disjoint from (Octagonal Shape long double y)• native boolean equals (Octagonal Shape long double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape long double p)• native void upper bound assign (Octagonal Shape long double p)• native void difference assign (Octagonal Shape long double p)• native void concatenate assign (Octagonal Shape long double p)• native void time elapse assign (Octagonal Shape long double p)• native boolean upper bound assign if exact (Octagonal Shape long double y)• native boolean simplify using context assign (Octagonal Shape long double p)

174

• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape long double y, By Reference< Integer> tp)

• native void widening assign (Octagonal Shape long double y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape long double y, Constraint←↩

System cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape long double y, Constraint System

cs, By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape long double arg, By Reference< Inte-

ger > tp)• native void CC76 narrowing assign (Octagonal Shape long double arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Octagonal Shape long double, Pointset Powerset NNC Polyhedron > linear ←↩

partition (Octagonal Shape long double p, Octagonal Shape long double q)

175




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<long double>The documentation for this class was generated from the following file:

• Octagonal Shape long double.java

10.66 parma polyhedra library.Octagonal Shape mpq class Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpq class>



• Octagonal Shape mpq class (long num dimensions, Degenerate Element kind)• Octagonal Shape mpq class (Int8 Box y)• Octagonal Shape mpq class (Int16 Box y)• Octagonal Shape mpq class (Int32 Box y)• Octagonal Shape mpq class (Int64 Box y)• Octagonal Shape mpq class (Uint8 Box y)• Octagonal Shape mpq class (Uint16 Box y)• Octagonal Shape mpq class (Uint32 Box y)• Octagonal Shape mpq class (Uint64 Box y)• Octagonal Shape mpq class (Z Box y)• Octagonal Shape mpq class (Rational Box y)• Octagonal Shape mpq class (BD Shape int8 t y)• Octagonal Shape mpq class (BD Shape int16 t y)• Octagonal Shape mpq class (BD Shape int32 t y)• Octagonal Shape mpq class (BD Shape int64 t y)• Octagonal Shape mpq class (BD Shape mpz class y)• Octagonal Shape mpq class (BD Shape mpq class y)• Octagonal Shape mpq class (Octagonal Shape int8 t y)• Octagonal Shape mpq class (Octagonal Shape int16 t y)• Octagonal Shape mpq class (Octagonal Shape int32 t y)• Octagonal Shape mpq class (Octagonal Shape int64 t y)• Octagonal Shape mpq class (Octagonal Shape mpz class y)• Octagonal Shape mpq class (Octagonal Shape mpq class y)• Octagonal Shape mpq class (C Polyhedron y)• Octagonal Shape mpq class (NNC Polyhedron y)• Octagonal Shape mpq class (Grid y)• Octagonal Shape mpq class (Float Box y)• Octagonal Shape mpq class (BD Shape float y)• Octagonal Shape mpq class (Octagonal Shape float y)• Octagonal Shape mpq class (Double Box y)• Octagonal Shape mpq class (BD Shape double y)• Octagonal Shape mpq class (Octagonal Shape double y)• Octagonal Shape mpq class (Long Double Box y)• Octagonal Shape mpq class (BD Shape long double y)• Octagonal Shape mpq class (Octagonal Shape long double y)

176

• Octagonal Shape mpq class (Int8 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Int16 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Int32 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Int64 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Uint8 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Uint16 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Uint32 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Uint64 Box y, Complexity Class complexity)• Octagonal Shape mpq class (Z Box y, Complexity Class complexity)• Octagonal Shape mpq class (Rational Box y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape int64 t y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape mpq class (C Polyhedron y, Complexity Class complexity)• Octagonal Shape mpq class (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape mpq class (Grid y, Complexity Class complexity)• Octagonal Shape mpq class (Float Box y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape float y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape mpq class (Double Box y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape double y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape mpq class (Long Double Box y, Complexity Class complexity)• Octagonal Shape mpq class (BD Shape long double y, Complexity Class complexity)• Octagonal Shape mpq class (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape mpq class (Constraint System cs)• Octagonal Shape mpq class (Congruence System cs)• Octagonal Shape mpq class (Generator System cs)• native void swap (Octagonal Shape mpq class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()

177






cient val n, Coefficient val d)• native boolean contains (Octagonal Shape mpq class y)• native boolean strictly contains (Octagonal Shape mpq class y)• native boolean is disjoint from (Octagonal Shape mpq class y)• native boolean equals (Octagonal Shape mpq class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape mpq class p)• native void upper bound assign (Octagonal Shape mpq class p)• native void difference assign (Octagonal Shape mpq class p)• native void concatenate assign (Octagonal Shape mpq class p)• native void time elapse assign (Octagonal Shape mpq class p)• native boolean upper bound assign if exact (Octagonal Shape mpq class y)• native boolean simplify using context assign (Octagonal Shape mpq class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





178



Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape mpq class y, By Reference< Integer >

tp)• native void widening assign (Octagonal Shape mpq class y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape mpq class y, Constraint ←↩

System cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape mpq class y, Constraint System

cs, By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape mpq class arg, By Reference< Integer> tp)

• native void CC76 narrowing assign (Octagonal Shape mpq class arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Octagonal Shape mpq class, Pointset Powerset NNC Polyhedron > linear ←↩

partition (Octagonal Shape mpq class p, Octagonal Shape mpq class q)




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpq class>The documentation for this class was generated from the following file:

• Octagonal Shape mpq class.java

10.67 parma polyhedra library.Octagonal Shape mpz class Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpz class>


179


• Octagonal Shape mpz class (long num dimensions, Degenerate Element kind)• Octagonal Shape mpz class (Int8 Box y)• Octagonal Shape mpz class (Int16 Box y)• Octagonal Shape mpz class (Int32 Box y)• Octagonal Shape mpz class (Int64 Box y)• Octagonal Shape mpz class (Uint8 Box y)• Octagonal Shape mpz class (Uint16 Box y)• Octagonal Shape mpz class (Uint32 Box y)• Octagonal Shape mpz class (Uint64 Box y)• Octagonal Shape mpz class (Z Box y)• Octagonal Shape mpz class (Rational Box y)• Octagonal Shape mpz class (BD Shape int8 t y)• Octagonal Shape mpz class (BD Shape int16 t y)• Octagonal Shape mpz class (BD Shape int32 t y)• Octagonal Shape mpz class (BD Shape int64 t y)• Octagonal Shape mpz class (BD Shape mpz class y)• Octagonal Shape mpz class (BD Shape mpq class y)• Octagonal Shape mpz class (Octagonal Shape int8 t y)• Octagonal Shape mpz class (Octagonal Shape int16 t y)• Octagonal Shape mpz class (Octagonal Shape int32 t y)• Octagonal Shape mpz class (Octagonal Shape int64 t y)• Octagonal Shape mpz class (Octagonal Shape mpz class y)• Octagonal Shape mpz class (Octagonal Shape mpq class y)• Octagonal Shape mpz class (C Polyhedron y)• Octagonal Shape mpz class (NNC Polyhedron y)• Octagonal Shape mpz class (Grid y)• Octagonal Shape mpz class (Float Box y)• Octagonal Shape mpz class (BD Shape float y)• Octagonal Shape mpz class (Octagonal Shape float y)• Octagonal Shape mpz class (Double Box y)• Octagonal Shape mpz class (BD Shape double y)• Octagonal Shape mpz class (Octagonal Shape double y)• Octagonal Shape mpz class (Long Double Box y)• Octagonal Shape mpz class (BD Shape long double y)• Octagonal Shape mpz class (Octagonal Shape long double y)• Octagonal Shape mpz class (Int8 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Int16 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Int32 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Int64 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Uint8 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Uint16 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Uint32 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Uint64 Box y, Complexity Class complexity)• Octagonal Shape mpz class (Z Box y, Complexity Class complexity)• Octagonal Shape mpz class (Rational Box y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape int8 t y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape int16 t y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape int32 t y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape int64 t y, Complexity Class complexity)

180

• Octagonal Shape mpz class (BD Shape mpz class y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape mpq class y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape int8 t y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape int16 t y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape int32 t y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape int64 t y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape mpz class y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape mpq class y, Complexity Class complexity)• Octagonal Shape mpz class (C Polyhedron y, Complexity Class complexity)• Octagonal Shape mpz class (NNC Polyhedron y, Complexity Class complexity)• Octagonal Shape mpz class (Grid y, Complexity Class complexity)• Octagonal Shape mpz class (Float Box y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape float y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape float y, Complexity Class complexity)• Octagonal Shape mpz class (Double Box y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape double y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape double y, Complexity Class complexity)• Octagonal Shape mpz class (Long Double Box y, Complexity Class complexity)• Octagonal Shape mpz class (BD Shape long double y, Complexity Class complexity)• Octagonal Shape mpz class (Octagonal Shape long double y, Complexity Class complexity)• Octagonal Shape mpz class (Constraint System cs)• Octagonal Shape mpz class (Congruence System cs)• Octagonal Shape mpz class (Generator System cs)• native void swap (Octagonal Shape mpz class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





181


• native boolean contains (Octagonal Shape mpz class y)• native boolean strictly contains (Octagonal Shape mpz class y)• native boolean is disjoint from (Octagonal Shape mpz class y)• native boolean equals (Octagonal Shape mpz class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Octagonal Shape mpz class p)• native void upper bound assign (Octagonal Shape mpz class p)• native void difference assign (Octagonal Shape mpz class p)• native void concatenate assign (Octagonal Shape mpz class p)• native void time elapse assign (Octagonal Shape mpz class p)• native boolean upper bound assign if exact (Octagonal Shape mpz class y)• native boolean simplify using context assign (Octagonal Shape mpz class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







182

• native long total memory in bytes ()• native void BHMZ05 widening assign (Octagonal Shape mpz class y, By Reference< Integer >

tp)• native void widening assign (Octagonal Shape mpz class y, By Reference< Integer > tp)• native void limited BHMZ05 extrapolation assign (Octagonal Shape mpz class y, Constraint ←↩

System cs, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Octagonal Shape mpz class y, Constraint System

cs, By Reference< Integer > tp)• native void CC76 extrapolation assign (Octagonal Shape mpz class arg, By Reference< Integer> tp)

• native void CC76 narrowing assign (Octagonal Shape mpz class arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Octagonal Shape mpz class, Pointset Powerset NNC Polyhedron > linear ←↩

partition (Octagonal Shape mpz class p, Octagonal Shape mpz class q)




Java class interfacing C++ Parma Polyhedra Library::Octagonal Shape<mpz class>The documentation for this class was generated from the following file:

• Octagonal Shape mpz class.java

10.68 parma polyhedra library.Optimization Mode Enum ReferencePossible optimization modes.



Public Attributes

• MINIMIZATION

Minimization is requested.


Possible optimization modes.The documentation for this enum was generated from the following file:

• Optimization Mode.java

183

10.69 parma polyhedra library.Overflow Error Exception Class ReferenceExceptions due to overflow errors.



• Overflow Error Exception (String s)Constructor.


Exceptions due to overflow errors.These exceptions can be obtained when the library has been configured to use integer coefficients

having bounded size.The documentation for this class was generated from the following file:

• Overflow Error Exception.java

10.70 parma polyhedra library.Pair< K, V > Class Template ReferenceA pair of values of type K and V.


• K getFirst ()Returns the object of type K.

• V getSecond ()Returns the object of type V.


A pair of values of type K and V.An object of this class holds an ordered pair of values of type K and V.The documentation for this class was generated from the following file:

• Pair.java

10.71 parma polyhedra library.Parma Polyhedra Library Class ReferenceA class collecting library-level functions.


Library initialization and finalization

• static native void initialize library ()Initializes the Parma Polyhedra Library.

• static native void finalize library ()Finalizes the Parma Polyhedra Library.

Version Checking

• static native int version major ()Returns the major number of the PPL version.

• static native int version minor ()

184

Returns the minor number of the PPL version.• static native int version revision ()

Returns the revision number of the PPL version.• static native int version beta ()

Returns the beta number of the PPL version.• static native String version ()

Returns a string containing the PPL version.• static native String banner ()

Returns a string containing the PPL banner.

Floating-point rounding and precision settings.

• static native void set rounding for PPL ()Sets the FPU rounding mode so that the PPL abstractions based on floating point numbers work cor-rectly.

• static native void restore pre PPL rounding ()Sets the FPU rounding mode as it was before initialization of the PPL.

• static native int irrational precision ()Returns the precision parameter for irrational calculations.

• static native void set irrational precision (int p)Sets the precision parameter used for irrational calculations.

Timeout handling

• static native void set timeout (int csecs)Sets the timeout for computations whose completion could require an exponential amount of time.

• static native void reset timeout ()Resets the timeout time so that the computation is not interrupted.

• static native void set deterministic timeout (int unscaled weight, int scale)Sets a threshold for computations whose completion could require an exponential amount of time.

• static native void reset deterministic timeout ()Resets the deterministic timeout so that the computation is not interrupted.


A class collecting library-level functions.


static native void parma polyhedra library.Parma Polyhedra Library.initialize library ( ) [static]Initializes the Parma Polyhedra Library.

This method must be called after loading the library and before calling any other method from anyother PPL package class.

static native void parma polyhedra library.Parma Polyhedra Library.finalize library ( ) [static]Finalizes the Parma Polyhedra Library.

This method must be called when work with the library is done. After finalization, no other librarymethod can be called (except those in class Parma Polyhedra Library), unless the library is re-initializedby calling initialize library().

static native String parma polyhedra library.Parma Polyhedra Library.banner ( ) [static]Returns a string containing the PPL banner.

The banner provides information about the PPL version, the licensing, the lack of any warranty what-soever, the C++ compiler used to build the library, where to report bugs and where to look for furtherinformation.

185

static native void parma polyhedra library.Parma Polyhedra Library.set rounding for PPL ( )[static] Sets the FPU rounding mode so that the PPL abstractions based on floating point numberswork correctly.

This is performed automatically at initialization-time. Calling this function is needed only if restore←↩

pre PPL rounding() has been previously called.

static native void parma polyhedra library.Parma Polyhedra Library.restore pre PPL rounding () [static] Sets the FPU rounding mode as it was before initialization of the PPL.

After calling this function it is absolutely necessary to call set rounding for PPL() before using anyPPL abstractions based on floating point numbers. This is performed automatically at finalization-time.

static native void parma polyhedra library.Parma Polyhedra Library.set irrational precision ( intp ) [static] Sets the precision parameter used for irrational calculations.

If p is less than or equal to INT MAX, sets the precision parameter used for irrational calculations to p.Then, in the irrational calculations returning an unbounded rational, (e.g., when computing a square root),the lesser between numerator and denominator will be limited to 2∗∗p.

static native void parma polyhedra library.Parma Polyhedra Library.set timeout ( int csecs ) [static]Sets the timeout for computations whose completion could require an exponential amount of time.Parameters

csecs The number of centiseconds sometimes after which a timeout will occur; it must bestrictly greater than zero.

Computations taking exponential time will be interrupted some time after csecs centiseconds have elapsedsince the call to the timeout setting function, by throwing a Timeout Exception object. Otherwise, ifthe computation completes without being interrupted, then the timeout should be reset by calling reset←↩

timeout().

static native void parma polyhedra library.Parma Polyhedra Library.set deterministic timeout ( intunscaled weight, int scale ) [static] Sets a threshold for computations whose completion couldrequire an exponential amount of time.

If unscaled weight has value u and scale has value s, then the (scaled) weight threshold iscomputed as w = u·2s. Computations taking exponential time will be interrupted some time after reachingthe complexity threshold w, by throwing a Timeout Exception object. Otherwise, if the computationcompletes without being interrupted, then the deterministic timeout should be reset by calling reset ←↩

deterministic timeout().Parameters

unscaled ←↩

weightThe unscaled maximum computational weight; it has to be strictly greater than zero.

scale The scaling factor to be applied to unscaled weight; it has to be non-negative.

Exceptions


ExceptionThrown if the computation of the weight threshold exceeds the maximumallowed value.

Note

This ”timeout” checking functionality is said to be deterministic because it is not based on actualelapsed time. Its behavior will only depend on (some of the) computations performed in the PP←↩

L library and it will be otherwise independent from the computation environment (CPU, operatingsystem, compiler, etc.).

186

Warning

The weight mechanism is under beta testing. In particular, there is still no clear relation betweenthe weight threshold and the actual computational complexity. As a consequence, client applicationsshould be ready to reconsider the tuning of these weight thresholds when upgrading to newer versionof the PPL.


• Parma Polyhedra Library.java

10.72 parma polyhedra library.Partial Function Class ReferenceA partial function on space dimension indices.



• Partial Function ()Builds the empty map.

• native void insert (long i, long j)Inserts mapping from i to j.

• native boolean has empty codomain ()Returns true if and only if the partial function has an empty codomain (i.e., it is always undefined).

• native long max in codomain ()Returns the maximum value that belongs to the codomain of the partial function.

• native long maps (long i)If the partial function is defined on index i, returns its value.

• native void free ()Releases all resources managed by this, also resetting it to a null reference.


• native void finalize ()Releases all resources managed by this.


A partial function on space dimension indices.This class is used in order to specify how space dimensions should be mapped by methods named

map space dimensions.


native boolean parma polyhedra library.Partial Function.has empty codomain ( ) Returns trueif and only if the partial function has an empty codomain (i.e., it is always undefined).

This method will always be called before the other methods of the interface. Moreover, if true isreturned, then none of the other interface methods will be called.

native long parma polyhedra library.Partial Function.maps ( long i ) If the partial function is de-fined on index i, returns its value.

The function returns a negative value if the partial function is not defined on domain value i.The documentation for this class was generated from the following file:

• Partial Function.java

187

10.73 parma polyhedra library.PIP Decision Node Class ReferenceAn internal node of the PIP solution tree.

Inheritance diagram for parma polyhedra library.PIP Decision Node:

parma_polyhedra_library.PIP_Decision_Node

parma_polyhedra_library.PIP_Tree_Node


• native PIP Tree Node child node (boolean branch)Returns the true branch (if branch is true) or the false branch (if branch is false) of this.


An internal node of the PIP solution tree.The documentation for this class was generated from the following file:

• PIP Decision Node.java

10.74 parma polyhedra library.PIP Problem Class ReferenceA Parametric Integer Programming problem.



• PIP Problem (long dim)Builds a trivial PIP problem.

• PIP Problem (long dim, Constraint System cs, Variables Set params)Builds a PIP problem from a sequence of constraints.

• PIP Problem (PIP Problem y)Builds a copy of y.

• native void free ()Releases all resources managed by this, also resetting it to a null reference.

Functions that Do Not Modify the PIP Problem

• native long max space dimension ()Returns the maximum space dimension an PIP Problem can handle.

188

• native long space dimension ()Returns the space dimension of the PIP problem.

• native long number of parameter space dimensions ()Returns the number of parameter space dimensions of the PIP problem.

• native Variables Set parameter space dimensions ()Returns all the parameter space dimensions of problem pip.

• native long get big parameter dimension ()Returns the big parameter dimension of PIP problem pip.

• native long number of constraints ()Returns the number of constraints defining the feasible region of pip.

• native Constraint constraint at index (long dim)Returns the i-th constraint defining the feasible region of the PIP problem pip.

• native Constraint System constraints ()Returns the constraints .



• native long total memory in bytes ()Returns the size in bytes of the memory occupied by the underlying C++ object.

• native long external memory in bytes ()Returns the size in bytes of the memory managed by the underlying C++ object.

• native boolean OK ()Returns true if the pip problem is well formed, i.e., if it satisfies all its implementation invariants; returns0 and perhaps makes some noise if broken. Useful for debugging purposes.

Functions that May Modify the PIP Problem

• native void clear ()Resets this to be equal to the trivial PIP problem.

• native void add space dimensions and embed (long pip vars, long pip params)Adds pip vars + pip params new space dimensions and embeds the PIP problem in the new vec-tor space.

• native void add to parameter space dimensions (Variables Set vars)Sets the space dimensions in vars to be parameter dimensions of the PIP problem.

• native void set big parameter dimension (long d)Sets the big parameter dimension of PIP problem to d.

• native void add constraint (Constraint c)Adds a copy of constraint c to the PIP problem.

• native void add constraints (Constraint System cs)Adds a copy of the constraints in cs to the PIP problem.

Computing the Solution of the PIP Problem

• native boolean is satisfiable ()Checks satisfiability of this.

• native PIP Problem Status solve ()Optimizes the PIP problem.

• native PIP Tree Node solution ()Returns a solution for the PIP problem, if it exists.

• native PIP Tree Node optimizing solution ()Returns an optimizing solution for the PIP problem, if it exists.

Querying/Setting Control Parameters

• native PIP Problem Control Parameter Value get pip problem control parameter (PIP Problem←↩

Control Parameter Name name)Returns the value of control parameter name.

• native void set pip problem control parameter (PIP Problem Control Parameter Value value)Sets control parameter value.

189



Releases all resources managed by this.


A Parametric Integer Programming problem.An object of this class encodes a parametric integer (linear) programming problem. The PIP problem

is specified by providing:

• the dimension of the vector space;

• the subset of those dimensions of the vector space that are interpreted as integer parameters (the otherspace dimensions are interpreted as non-parameter integer variables);

• a finite set of linear equality and (strict or non-strict) inequality constraints involving variables and/orparameters; these constraints are used to define:

– the feasible region, if they involve one or more problem variable (and maybe some parameters);

– the initial context, if they only involve the parameters;

• optionally, the so-called big parameter, i.e., a problem parameter to be considered arbitrarily big.

Note that all problem variables and problem parameters are assumed to take non-negative integer val-ues, so that there is no need to specify non-negativity constraints.

The class provides support for the (incremental) solution of the PIP problem based on variations of therevised simplex method and on Gomory cut generation techniques.

The solution for a PIP problem is the lexicographic minimum of the integer points of the feasible region,expressed in terms of the parameters. As the problem to be solved only involves non-negative variablesand parameters, the problem will always be either unfeasible or optimizable.

As the feasibility and the solution value of a PIP problem depend on the values of the parameters, thesolution is a binary decision tree, dividing the context parameter set into subsets. The tree nodes are of twokinds:

• Decision nodes. These are internal tree nodes encoding one or more linear tests on the parameters;if all the tests are satisfied, then the solution is the node's true child; otherwise, the solution is thenode's false child;

• Solution nodes. These are leaf nodes in the tree, encoding the solution of the problem in the currentcontext subset, where each variable is defined in terms of a linear expression of the parameters.Solution nodes also optionally embed a set of parameter constraints: if all these constraints aresatisfied, the solution is described by the node, otherwise the problem has no solution.

It may happen that a decision node has no false child. This means that there is no solution if at leastone of the corresponding constraints is not satisfied. Decision nodes having two or more linear tests on theparameters cannot have a false child. Decision nodes always have a true child.

Both kinds of tree nodes may also contain the definition of extra parameters which are artificiallyintroduced by the solver to enforce an integral solution. Such artificial parameters are defined by theinteger division of a linear expression on the parameters by an integer coefficient.

By exploiting the incremental nature of the solver, it is possible to reuse part of the computational workalready done when solving variants of a given PIP Problem: currently, incremental resolution supports theaddition of space dimensions, the addition of parameters and the addition of constraints.

190


parma polyhedra library.PIP Problem.PIP Problem ( long dim ) [inline] Builds a trivial PIPproblem.

A trivial PIP problem requires to compute the lexicographic minimum on a vector space under noconstraints and with no parameters: due to the implicit non-negativity constraints, the origin of the vectorspace is an optimal solution.Parameters

dim The dimension of the vector space enclosing this (optional argument with defaultvalue 0).

Exceptions

Length Error Exception Thrown if dim exceeds max space dimension().

parma polyhedra library.PIP Problem.PIP Problem ( long dim, Constraint System cs, Variables←↩

Set params ) [inline] Builds a PIP problem from a sequence of constraints.Builds a PIP problem having space dimension dim from the constraint system cs; the dimensions vars

are interpreted as parameters.


native void parma polyhedra library.PIP Problem.clear ( ) Resets this to be equal to the trivialPIP problem.

The space dimension is reset to 0.

native void parma polyhedra library.PIP Problem.add space dimensions and embed ( long pip ←↩

vars, long pip params ) Adds pip vars + pip params new space dimensions and embeds thePIP problem in the new vector space.Parameters

pip vars The number of space dimensions to add that are interpreted as PIP problem variables(i.e., non parameters). These are added before adding the pip params parameters.

pip params The number of space dimensions to add that are interpreted as PIP problem parame-ters. These are added after having added the pip vars problem variables.

The new space dimensions will be those having the highest indexes in the new PIP problem; they are ini-tially unconstrained.

native void parma polyhedra library.PIP Problem.add constraint ( Constraint c ) Adds a copy ofconstraint c to the PIP problem.Exceptions


ExceptionThrown if the constraint c is a strict inequality or if its space dimension isstrictly greater than the space dimension of this.

native void parma polyhedra library.PIP Problem.add constraints ( Constraint System cs ) Addsa copy of the constraints in cs to the PIP problem.Exceptions

191


ExceptionThrown if the constraint system cs contains any strict inequality or if itsspace dimension is strictly greater than the space dimension of this.

native boolean parma polyhedra library.PIP Problem.is satisfiable ( ) Checks satisfiability of this.

Returns

true if and only if the PIP problem is satisfiable.

native PIP Problem Status parma polyhedra library.PIP Problem.solve ( ) Optimizes the PI←↩

P problem.Solves the PIP problem, returning an exit status.

Returns

UNFEASIBLE PIP PROBLEM if the PIP problem is not satisfiable; OPTIMIZED PIP PROBLEMif the PIP problem admits an optimal solution.


• PIP Problem.java

10.75 parma polyhedra library.PIP Problem Control Parameter Name Enum Ref-erence

Names of PIP problems' control parameters.

Public Attributes

• CUTTING STRATEGY

The cutting strategy rule.• PIVOT ROW STRATEGY

The pivot row strategy rule.


Names of PIP problems' control parameters.The documentation for this enum was generated from the following file:

• PIP Problem Control Parameter Name.java

10.76 parma polyhedra library.PIP Problem Control Parameter Value Enum Ref-erence

Possible values for PIP problems' control parameters.

Public Attributes

• CUTTING STRATEGY FIRST

Choose the first non-integer row.• CUTTING STRATEGY DEEPEST

Choose row which generates the deepest cut.• CUTTING STRATEGY ALL

192

Always generate all possible cuts.• PIVOT ROW STRATEGY FIRST

Choose the first row with negative parameter sign.• PIVOT ROW STRATEGY MAX COLUMN

Choose the row which generates the lexico-maximal pivot column.


Possible values for PIP problems' control parameters.The documentation for this enum was generated from the following file:

• PIP Problem Control Parameter Value.java

10.77 parma polyhedra library.PIP Problem Status Enum ReferencePossible outcomes of the PIP Problem solver.



Public Attributes

• UNFEASIBLE PIP PROBLEM

The problem is unsatisfiable.


Possible outcomes of the PIP Problem solver.The documentation for this enum was generated from the following file:

• PIP Problem Status.java

10.78 parma polyhedra library.PIP Solution Node Class ReferenceA leaf node of the PIP solution tree.

Inheritance diagram for parma polyhedra library.PIP Solution Node:

parma_polyhedra_library.PIP_Solution_Node


193


• native Linear Expression parametric values (Variable var)Returns the parametric expression of the values of variable var in solution node this.


A leaf node of the PIP solution tree.


native Linear Expression parma polyhedra library.PIP Solution Node.parametric values ( Vari-able var ) Returns the parametric expression of the values of variable var in solution node this.

The returned parametric expression will only refer to (problem or artificial) parameters.Parameters

var The variable being queried.


• PIP Solution Node.java

10.79 parma polyhedra library.PIP Tree Node Class ReferenceA node of the PIP solution tree.

Inheritance diagram for parma polyhedra library.PIP Tree Node:


parma_polyhedra_library.PIP_Decision_Node

parma_polyhedra_library.PIP_Solution_Node


• native PIP Solution Node as solution ()Returns the solution node if this is a solution node, and 0 otherwise.

• native PIP Decision Node as decision ()Returns the decision node if this is a decision node, and 0 otherwise.

• native boolean OK ()Returns true if the pip tree is well formed, i.e., if it satisfies all its implementation invariants; returns 0 andperhaps makes some noise if broken. Useful for debugging purposes.

• native long number of artificials ()Returns the number of artificial parameters in the PIP Tree Node.

• native Artificial Parameter Sequence artificials ()Returns the sequence of (Java) artificial parameters in the PIP Tree Node.

194

• native Constraint System constraints ()

Returns the system of parameter constraints controlling the PIP Tree Node.• native String toString ()



A node of the PIP solution tree.This is the base class for the nodes of the binary trees representing the solutions of PIP problems. From

this one, two classes are derived:

• PIP Decision Node, for the internal nodes of the tree;

• PIP Solution Node, for the leaves of the tree.


native Constraint System parma polyhedra library.PIP Tree Node.constraints ( ) Returns the sys-tem of parameter constraints controlling the PIP Tree Node.

The indices in the constraints are the same as the original variables and parameters. Coefficients inindices corresponding to variables always are zero.


• PIP Tree Node.java

10.80 parma polyhedra library.Pointset Powerset BD Shape double Class Refer-ence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape double (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape double (Pointset Powerset BD Shape double y)• Pointset Powerset BD Shape double (BD Shape double y)• Pointset Powerset BD Shape double (Pointset Powerset BD Shape double y, Complexity Class

complexity)• Pointset Powerset BD Shape double (BD Shape double y, Complexity Class complexity)• Pointset Powerset BD Shape double (Constraint System cs)• Pointset Powerset BD Shape double (Congruence System cs)• native void swap (Pointset Powerset BD Shape double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()

195

• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape double y)• native boolean strictly contains (Pointset Powerset BD Shape double y)• native boolean is disjoint from (Pointset Powerset BD Shape double y)• native boolean geometrically covers (Pointset Powerset BD Shape double y)• native boolean geometrically equals (Pointset Powerset BD Shape double y)• native boolean equals (Pointset Powerset BD Shape double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape double p)• native void upper bound assign (Pointset Powerset BD Shape double p)• native void difference assign (Pointset Powerset BD Shape double p)• native void concatenate assign (Pointset Powerset BD Shape double p)• native void time elapse assign (Pointset Powerset BD Shape double p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape double y)• native boolean simplify using context assign (Pointset Powerset BD Shape double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





Expression rhs)

196

• native void generalized affine preimage (Linear Expression lhs, Relation Symbol relsym, Linear←↩

Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape double Iterator begin iterator ()• native Pointset Powerset BD Shape double Iterator end iterator ()• native void add disjunct (BD Shape double j disj)• native void drop disjunct (Pointset Powerset BD Shape double Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape double Iterator itr1, Pointset Powerset←↩

BD Shape double Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape double y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape double y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape double y, Inte-

ger d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape double y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >


• Pointset Powerset BD Shape double.java

10.81 parma polyhedra library.Pointset Powerset BD Shape double Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >:: itera-tor.


197


• Pointset Powerset BD Shape double Iterator (Pointset Powerset BD Shape double Iterator y)• native boolean equals (Pointset Powerset BD Shape double Iterator itr)• native void next ()• native void prev ()• native BD Shape double get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<double> >:: itera-tor.


• Pointset Powerset BD Shape double Iterator.java

10.82 parma polyhedra library.Pointset Powerset BD Shape float Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float> >



• Pointset Powerset BD Shape float (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape float (Pointset Powerset BD Shape float y)• Pointset Powerset BD Shape float (BD Shape float y)• Pointset Powerset BD Shape float (Pointset Powerset BD Shape float y, Complexity Class com-

plexity)• Pointset Powerset BD Shape float (BD Shape float y, Complexity Class complexity)• Pointset Powerset BD Shape float (Constraint System cs)• Pointset Powerset BD Shape float (Congruence System cs)• native void swap (Pointset Powerset BD Shape float y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)

198

• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<Boolean > maximum)




• native boolean contains (Pointset Powerset BD Shape float y)• native boolean strictly contains (Pointset Powerset BD Shape float y)• native boolean is disjoint from (Pointset Powerset BD Shape float y)• native boolean geometrically covers (Pointset Powerset BD Shape float y)• native boolean geometrically equals (Pointset Powerset BD Shape float y)• native boolean equals (Pointset Powerset BD Shape float p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape float p)• native void upper bound assign (Pointset Powerset BD Shape float p)• native void difference assign (Pointset Powerset BD Shape float p)• native void concatenate assign (Pointset Powerset BD Shape float p)• native void time elapse assign (Pointset Powerset BD Shape float p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape float y)• native boolean simplify using context assign (Pointset Powerset BD Shape float p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)

199

• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape float Iterator begin iterator ()• native Pointset Powerset BD Shape float Iterator end iterator ()• native void add disjunct (BD Shape float j disj)• native void drop disjunct (Pointset Powerset BD Shape float Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape float Iterator itr1, Pointset Powerset B←↩

D Shape float Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape float y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape float y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape float y, Integer

d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape float y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float> >The documentation for this class was generated from the following file:

• Pointset Powerset BD Shape float.java

10.83 parma polyhedra library.Pointset Powerset BD Shape float Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float> >:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape float Iterator (Pointset Powerset BD Shape float Iterator y)• native boolean equals (Pointset Powerset BD Shape float Iterator itr)• native void next ()• native void prev ()• native BD Shape float get disjunct ()• native void free ()

200




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<float> >:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset BD Shape float Iterator.java

10.84 parma polyhedra library.Pointset Powerset BD Shape int16 t Class Refer-ence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16 t> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape int16 t (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape int16 t (Pointset Powerset BD Shape int16 t y)• Pointset Powerset BD Shape int16 t (BD Shape int16 t y)• Pointset Powerset BD Shape int16 t (Pointset Powerset BD Shape int16 t y, Complexity Class

complexity)• Pointset Powerset BD Shape int16 t (BD Shape int16 t y, Complexity Class complexity)• Pointset Powerset BD Shape int16 t (Constraint System cs)• Pointset Powerset BD Shape int16 t (Congruence System cs)• native void swap (Pointset Powerset BD Shape int16 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape int16 t y)

201

• native boolean strictly contains (Pointset Powerset BD Shape int16 t y)• native boolean is disjoint from (Pointset Powerset BD Shape int16 t y)• native boolean geometrically covers (Pointset Powerset BD Shape int16 t y)• native boolean geometrically equals (Pointset Powerset BD Shape int16 t y)• native boolean equals (Pointset Powerset BD Shape int16 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape int16 t p)• native void upper bound assign (Pointset Powerset BD Shape int16 t p)• native void difference assign (Pointset Powerset BD Shape int16 t p)• native void concatenate assign (Pointset Powerset BD Shape int16 t p)• native void time elapse assign (Pointset Powerset BD Shape int16 t p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape int16 t y)• native boolean simplify using context assign (Pointset Powerset BD Shape int16 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







202

• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape int16 t Iterator begin iterator ()• native Pointset Powerset BD Shape int16 t Iterator end iterator ()• native void add disjunct (BD Shape int16 t j disj)• native void drop disjunct (Pointset Powerset BD Shape int16 t Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape int16 t Iterator itr1, Pointset Powerset←↩

BD Shape int16 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape int16 t y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape int16 t y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape int16 t y, Inte-

ger d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape int16 t y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int16 t> >The documentation for this class was generated from the following file:

• Pointset Powerset BD Shape int16 t.java

10.85 parma polyhedra library.Pointset Powerset BD Shape int16 t Iterator ClassReference




• Pointset Powerset BD Shape int16 t Iterator (Pointset Powerset BD Shape int16 t Iterator y)• native boolean equals (Pointset Powerset BD Shape int16 t Iterator itr)• native void next ()• native void prev ()• native BD Shape int16 t get disjunct ()• native void free ()






• Pointset Powerset BD Shape int16 t Iterator.java

203


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int32 t> >Inherits parma polyhedra library.PPL Object.







Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape int32 t y)• native boolean strictly contains (Pointset Powerset BD Shape int32 t y)• native boolean is disjoint from (Pointset Powerset BD Shape int32 t y)• native boolean geometrically covers (Pointset Powerset BD Shape int32 t y)• native boolean geometrically equals (Pointset Powerset BD Shape int32 t y)• native boolean equals (Pointset Powerset BD Shape int32 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)

204

• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape int32 t p)• native void upper bound assign (Pointset Powerset BD Shape int32 t p)• native void difference assign (Pointset Powerset BD Shape int32 t p)• native void concatenate assign (Pointset Powerset BD Shape int32 t p)• native void time elapse assign (Pointset Powerset BD Shape int32 t p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape int32 t y)• native boolean simplify using context assign (Pointset Powerset BD Shape int32 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape int32 t Iterator begin iterator ()• native Pointset Powerset BD Shape int32 t Iterator end iterator ()• native void add disjunct (BD Shape int32 t j disj)• native void drop disjunct (Pointset Powerset BD Shape int32 t Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape int32 t Iterator itr1, Pointset Powerset←↩

BD Shape int32 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape int32 t y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape int32 t y)

205

• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape int32 t y, Inte-ger d)

• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape int32 t y, Integer d)• native void free ()• native int hashCode ()• native String toString ()





















206







Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape int64 t y)• native boolean strictly contains (Pointset Powerset BD Shape int64 t y)• native boolean is disjoint from (Pointset Powerset BD Shape int64 t y)• native boolean geometrically covers (Pointset Powerset BD Shape int64 t y)• native boolean geometrically equals (Pointset Powerset BD Shape int64 t y)• native boolean equals (Pointset Powerset BD Shape int64 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)

207

• native void intersection assign (Pointset Powerset BD Shape int64 t p)• native void upper bound assign (Pointset Powerset BD Shape int64 t p)• native void difference assign (Pointset Powerset BD Shape int64 t p)• native void concatenate assign (Pointset Powerset BD Shape int64 t p)• native void time elapse assign (Pointset Powerset BD Shape int64 t p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape int64 t y)• native boolean simplify using context assign (Pointset Powerset BD Shape int64 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape int64 t Iterator begin iterator ()• native Pointset Powerset BD Shape int64 t Iterator end iterator ()• native void add disjunct (BD Shape int64 t j disj)• native void drop disjunct (Pointset Powerset BD Shape int64 t Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape int64 t Iterator itr1, Pointset Powerset←↩

BD Shape int64 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape int64 t y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape int64 t y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape int64 t y, Inte-

ger d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape int64 t y, Integer d)• native void free ()• native int hashCode ()• native String toString ()

208

















10.90 parma polyhedra library.Pointset Powerset BD Shape int8 t Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int8 t> >



• Pointset Powerset BD Shape int8 t (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape int8 t (Pointset Powerset BD Shape int8 t y)• Pointset Powerset BD Shape int8 t (BD Shape int8 t y)• Pointset Powerset BD Shape int8 t (Pointset Powerset BD Shape int8 t y, Complexity Class com-

plexity)• Pointset Powerset BD Shape int8 t (BD Shape int8 t y, Complexity Class complexity)• Pointset Powerset BD Shape int8 t (Constraint System cs)• Pointset Powerset BD Shape int8 t (Congruence System cs)• native void swap (Pointset Powerset BD Shape int8 t y)

209

• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape int8 t y)• native boolean strictly contains (Pointset Powerset BD Shape int8 t y)• native boolean is disjoint from (Pointset Powerset BD Shape int8 t y)• native boolean geometrically covers (Pointset Powerset BD Shape int8 t y)• native boolean geometrically equals (Pointset Powerset BD Shape int8 t y)• native boolean equals (Pointset Powerset BD Shape int8 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape int8 t p)• native void upper bound assign (Pointset Powerset BD Shape int8 t p)• native void difference assign (Pointset Powerset BD Shape int8 t p)• native void concatenate assign (Pointset Powerset BD Shape int8 t p)• native void time elapse assign (Pointset Powerset BD Shape int8 t p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape int8 t y)• native boolean simplify using context assign (Pointset Powerset BD Shape int8 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)

210

• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape int8 t Iterator begin iterator ()• native Pointset Powerset BD Shape int8 t Iterator end iterator ()• native void add disjunct (BD Shape int8 t j disj)• native void drop disjunct (Pointset Powerset BD Shape int8 t Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape int8 t Iterator itr1, Pointset Powerset ←↩

BD Shape int8 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape int8 t y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape int8 t y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape int8 t y, Integer

d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape int8 t y, Integer d)• native void free ()• native int hashCode ()• native String toString ()






211


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int8 t>>:: iterator.Inherits parma polyhedra library.PPL Object.






Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<int8 t>>:: iterator.The documentation for this class was generated from the following file:


10.92 parma polyhedra library.Pointset Powerset BD Shape long double Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape long double (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape long double (Pointset Powerset BD Shape long double y)• Pointset Powerset BD Shape long double (BD Shape long double y)• Pointset Powerset BD Shape long double (Pointset Powerset BD Shape long double y, Complexity←↩

Class complexity)• Pointset Powerset BD Shape long double (BD Shape long double y, Complexity Class complex-

ity)• Pointset Powerset BD Shape long double (Constraint System cs)• Pointset Powerset BD Shape long double (Congruence System cs)• native void swap (Pointset Powerset BD Shape long double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()

212

• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape long double y)• native boolean strictly contains (Pointset Powerset BD Shape long double y)• native boolean is disjoint from (Pointset Powerset BD Shape long double y)• native boolean geometrically covers (Pointset Powerset BD Shape long double y)• native boolean geometrically equals (Pointset Powerset BD Shape long double y)• native boolean equals (Pointset Powerset BD Shape long double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape long double p)• native void upper bound assign (Pointset Powerset BD Shape long double p)• native void difference assign (Pointset Powerset BD Shape long double p)• native void concatenate assign (Pointset Powerset BD Shape long double p)• native void time elapse assign (Pointset Powerset BD Shape long double p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape long double y)• native boolean simplify using context assign (Pointset Powerset BD Shape long double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





213



Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape long double Iterator begin iterator ()• native Pointset Powerset BD Shape long double Iterator end iterator ()• native void add disjunct (BD Shape long double j disj)• native void drop disjunct (Pointset Powerset BD Shape long double Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape long double Iterator itr1, Pointset Powerset←↩

BD Shape long double Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape long double y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape long double y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape long double y,

Integer d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape long double y, Inte-

ger d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double> >The documentation for this class was generated from the following file:

• Pointset Powerset BD Shape long double.java

10.93 parma polyhedra library.Pointset Powerset BD Shape long double IteratorClass Reference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double> >::iterator.


214


• Pointset Powerset BD Shape long double Iterator (Pointset Powerset BD Shape long double←↩

Iterator y)• native boolean equals (Pointset Powerset BD Shape long double Iterator itr)• native void next ()• native void prev ()• native BD Shape long double get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<long double> >::iterator.


• Pointset Powerset BD Shape long double Iterator.java

10.94 parma polyhedra library.Pointset Powerset BD Shape mpq class Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape mpq class (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape mpq class (Pointset Powerset BD Shape mpq class y)• Pointset Powerset BD Shape mpq class (BD Shape mpq class y)• Pointset Powerset BD Shape mpq class (Pointset Powerset BD Shape mpq class y, Complexity←↩

Class complexity)• Pointset Powerset BD Shape mpq class (BD Shape mpq class y, Complexity Class complexity)• Pointset Powerset BD Shape mpq class (Constraint System cs)• Pointset Powerset BD Shape mpq class (Congruence System cs)• native void swap (Pointset Powerset BD Shape mpq class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()

215

• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset BD Shape mpq class y)• native boolean strictly contains (Pointset Powerset BD Shape mpq class y)• native boolean is disjoint from (Pointset Powerset BD Shape mpq class y)• native boolean geometrically covers (Pointset Powerset BD Shape mpq class y)• native boolean geometrically equals (Pointset Powerset BD Shape mpq class y)• native boolean equals (Pointset Powerset BD Shape mpq class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape mpq class p)• native void upper bound assign (Pointset Powerset BD Shape mpq class p)• native void difference assign (Pointset Powerset BD Shape mpq class p)• native void concatenate assign (Pointset Powerset BD Shape mpq class p)• native void time elapse assign (Pointset Powerset BD Shape mpq class p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape mpq class y)• native boolean simplify using context assign (Pointset Powerset BD Shape mpq class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







216

• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape mpq class Iterator begin iterator ()• native Pointset Powerset BD Shape mpq class Iterator end iterator ()• native void add disjunct (BD Shape mpq class j disj)• native void drop disjunct (Pointset Powerset BD Shape mpq class Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape mpq class Iterator itr1, Pointset Powerset←↩

BD Shape mpq class Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape mpq class y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape mpq class y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape mpq class y, In-

teger d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape mpq class y, Integer

d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >The documentation for this class was generated from the following file:

• Pointset Powerset BD Shape mpq class.java

10.95 parma polyhedra library.Pointset Powerset BD Shape mpq class Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >:: it-erator.



• Pointset Powerset BD Shape mpq class Iterator (Pointset Powerset BD Shape mpq class Iteratory)

• native boolean equals (Pointset Powerset BD Shape mpq class Iterator itr)• native void next ()• native void prev ()• native BD Shape mpq class get disjunct ()• native void free ()

217




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpq class> >:: it-erator.


• Pointset Powerset BD Shape mpq class Iterator.java

10.96 parma polyhedra library.Pointset Powerset BD Shape mpz class Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset BD Shape mpz class (long num dimensions, Degenerate Element kind)• Pointset Powerset BD Shape mpz class (Pointset Powerset BD Shape mpz class y)• Pointset Powerset BD Shape mpz class (BD Shape mpz class y)• Pointset Powerset BD Shape mpz class (Pointset Powerset BD Shape mpz class y, Complexity←↩

Class complexity)• Pointset Powerset BD Shape mpz class (BD Shape mpz class y, Complexity Class complexity)• Pointset Powerset BD Shape mpz class (Constraint System cs)• Pointset Powerset BD Shape mpz class (Congruence System cs)• native void swap (Pointset Powerset BD Shape mpz class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





218

• native boolean contains (Pointset Powerset BD Shape mpz class y)• native boolean strictly contains (Pointset Powerset BD Shape mpz class y)• native boolean is disjoint from (Pointset Powerset BD Shape mpz class y)• native boolean geometrically covers (Pointset Powerset BD Shape mpz class y)• native boolean geometrically equals (Pointset Powerset BD Shape mpz class y)• native boolean equals (Pointset Powerset BD Shape mpz class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset BD Shape mpz class p)• native void upper bound assign (Pointset Powerset BD Shape mpz class p)• native void difference assign (Pointset Powerset BD Shape mpz class p)• native void concatenate assign (Pointset Powerset BD Shape mpz class p)• native void time elapse assign (Pointset Powerset BD Shape mpz class p)• native boolean upper bound assign if exact (Pointset Powerset BD Shape mpz class y)• native boolean simplify using context assign (Pointset Powerset BD Shape mpz class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()

219

• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset BD Shape mpz class Iterator begin iterator ()• native Pointset Powerset BD Shape mpz class Iterator end iterator ()• native void add disjunct (BD Shape mpz class j disj)• native void drop disjunct (Pointset Powerset BD Shape mpz class Iterator itr)• native void drop disjuncts (Pointset Powerset BD Shape mpz class Iterator itr1, Pointset Powerset←↩

BD Shape mpz class Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset BD Shape mpz class y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset BD Shape mpz class y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset BD Shape mpz class y, In-

teger d)• native void BGP99 H79 extrapolation assign (Pointset Powerset BD Shape mpz class y, Integer

d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >


• Pointset Powerset BD Shape mpz class.java

10.97 parma polyhedra library.Pointset Powerset BD Shape mpz class Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >:: it-erator.



• Pointset Powerset BD Shape mpz class Iterator (Pointset Powerset BD Shape mpz class Iteratory)

• native boolean equals (Pointset Powerset BD Shape mpz class Iterator itr)• native void next ()• native void prev ()• native BD Shape mpz class get disjunct ()• native void free ()



220


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<BD Shape<mpz class> >:: it-erator.


• Pointset Powerset BD Shape mpz class Iterator.java

10.98 parma polyhedra library.Pointset Powerset C Polyhedron Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>



• Pointset Powerset C Polyhedron (long num dimensions, Degenerate Element kind)• Pointset Powerset C Polyhedron (Pointset Powerset C Polyhedron y)• Pointset Powerset C Polyhedron (C Polyhedron y)• Pointset Powerset C Polyhedron (Pointset Powerset C Polyhedron y, Complexity Class complex-

ity)• Pointset Powerset C Polyhedron (C Polyhedron y, Complexity Class complexity)• Pointset Powerset C Polyhedron (Constraint System cs)• Pointset Powerset C Polyhedron (Congruence System cs)• native void swap (Pointset Powerset C Polyhedron y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset C Polyhedron y)• native boolean strictly contains (Pointset Powerset C Polyhedron y)• native boolean is disjoint from (Pointset Powerset C Polyhedron y)• native boolean geometrically covers (Pointset Powerset C Polyhedron y)

221

• native boolean geometrically equals (Pointset Powerset C Polyhedron y)• native boolean equals (Pointset Powerset C Polyhedron p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset C Polyhedron p)• native void upper bound assign (Pointset Powerset C Polyhedron p)• native void difference assign (Pointset Powerset C Polyhedron p)• native void concatenate assign (Pointset Powerset C Polyhedron p)• native void time elapse assign (Pointset Powerset C Polyhedron p)• native boolean upper bound assign if exact (Pointset Powerset C Polyhedron y)• native boolean simplify using context assign (Pointset Powerset C Polyhedron p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset C Polyhedron Iterator begin iterator ()

222

• native Pointset Powerset C Polyhedron Iterator end iterator ()• native void add disjunct (C Polyhedron j disj)• native void drop disjunct (Pointset Powerset C Polyhedron Iterator itr)• native void drop disjuncts (Pointset Powerset C Polyhedron Iterator itr1, Pointset Powerset C ←↩

Polyhedron Iterator itr2)• native void BHZ03 BHRZ03 BHRZ03 widening assign (Pointset Powerset C Polyhedron y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset C Polyhedron y)• native void BGP99 BHRZ03 extrapolation assign (Pointset Powerset C Polyhedron y, Integer d)• native void BGP99 H79 extrapolation assign (Pointset Powerset C Polyhedron y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>The documentation for this class was generated from the following file:

• Pointset Powerset C Polyhedron.java

10.99 parma polyhedra library.Pointset Powerset C Polyhedron Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset C Polyhedron Iterator (Pointset Powerset C Polyhedron Iterator y)• native boolean equals (Pointset Powerset C Polyhedron Iterator itr)• native void next ()• native void prev ()• native C Polyhedron get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<C Polyhedron>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset C Polyhedron Iterator.java

10.100 parma polyhedra library.Pointset Powerset Double Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>


223


• Pointset Powerset Double Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Double Box (Pointset Powerset Double Box y)• Pointset Powerset Double Box (Double Box y)• Pointset Powerset Double Box (Pointset Powerset Double Box y, Complexity Class complexity)• Pointset Powerset Double Box (Double Box y, Complexity Class complexity)• Pointset Powerset Double Box (Constraint System cs)• Pointset Powerset Double Box (Congruence System cs)• native void swap (Pointset Powerset Double Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Double Box y)• native boolean strictly contains (Pointset Powerset Double Box y)• native boolean is disjoint from (Pointset Powerset Double Box y)• native boolean geometrically covers (Pointset Powerset Double Box y)• native boolean geometrically equals (Pointset Powerset Double Box y)• native boolean equals (Pointset Powerset Double Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Double Box p)

224

• native void upper bound assign (Pointset Powerset Double Box p)• native void difference assign (Pointset Powerset Double Box p)• native void concatenate assign (Pointset Powerset Double Box p)• native void time elapse assign (Pointset Powerset Double Box p)• native boolean upper bound assign if exact (Pointset Powerset Double Box y)• native boolean simplify using context assign (Pointset Powerset Double Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Double Box Iterator begin iterator ()• native Pointset Powerset Double Box Iterator end iterator ()• native void add disjunct (Double Box j disj)• native void drop disjunct (Pointset Powerset Double Box Iterator itr)• native void drop disjuncts (Pointset Powerset Double Box Iterator itr1, Pointset Powerset Double←↩

Box Iterator itr2)• native void free ()• native int hashCode ()• native String toString ()



225


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>The documentation for this class was generated from the following file:

• Pointset Powerset Double Box.java

10.101 parma polyhedra library.Pointset Powerset Double Box Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Double Box Iterator (Pointset Powerset Double Box Iterator y)• native boolean equals (Pointset Powerset Double Box Iterator itr)• native void next ()• native void prev ()• native Double Box get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Double Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Double Box Iterator.java

10.102 parma polyhedra library.Pointset Powerset Float Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>



• Pointset Powerset Float Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Float Box (Pointset Powerset Float Box y)• Pointset Powerset Float Box (Float Box y)• Pointset Powerset Float Box (Pointset Powerset Float Box y, Complexity Class complexity)• Pointset Powerset Float Box (Float Box y, Complexity Class complexity)• Pointset Powerset Float Box (Constraint System cs)• Pointset Powerset Float Box (Congruence System cs)• native void swap (Pointset Powerset Float Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()

226

• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Float Box y)• native boolean strictly contains (Pointset Powerset Float Box y)• native boolean is disjoint from (Pointset Powerset Float Box y)• native boolean geometrically covers (Pointset Powerset Float Box y)• native boolean geometrically equals (Pointset Powerset Float Box y)• native boolean equals (Pointset Powerset Float Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Float Box p)• native void upper bound assign (Pointset Powerset Float Box p)• native void difference assign (Pointset Powerset Float Box p)• native void concatenate assign (Pointset Powerset Float Box p)• native void time elapse assign (Pointset Powerset Float Box p)• native boolean upper bound assign if exact (Pointset Powerset Float Box y)• native boolean simplify using context assign (Pointset Powerset Float Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



227





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Float Box Iterator begin iterator ()• native Pointset Powerset Float Box Iterator end iterator ()• native void add disjunct (Float Box j disj)• native void drop disjunct (Pointset Powerset Float Box Iterator itr)• native void drop disjuncts (Pointset Powerset Float Box Iterator itr1, Pointset Powerset Float ←↩





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>The documentation for this class was generated from the following file:

• Pointset Powerset Float Box.java

10.103 parma polyhedra library.Pointset Powerset Float Box Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>:: iterator.Inherits parma polyhedra library.PPL Object.

228


• Pointset Powerset Float Box Iterator (Pointset Powerset Float Box Iterator y)• native boolean equals (Pointset Powerset Float Box Iterator itr)• native void next ()• native void prev ()• native Float Box get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Float Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Float Box Iterator.java

10.104 parma polyhedra library.Pointset Powerset Grid Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>



• Pointset Powerset Grid (long num dimensions, Degenerate Element kind)• Pointset Powerset Grid (Pointset Powerset Grid y)• Pointset Powerset Grid (Grid y)• Pointset Powerset Grid (Pointset Powerset Grid y, Complexity Class complexity)• Pointset Powerset Grid (Grid y, Complexity Class complexity)• Pointset Powerset Grid (Constraint System cs)• Pointset Powerset Grid (Congruence System cs)• native void swap (Pointset Powerset Grid y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<

Boolean > maximum)

229




• native boolean contains (Pointset Powerset Grid y)• native boolean strictly contains (Pointset Powerset Grid y)• native boolean is disjoint from (Pointset Powerset Grid y)• native boolean geometrically covers (Pointset Powerset Grid y)• native boolean geometrically equals (Pointset Powerset Grid y)• native boolean equals (Pointset Powerset Grid p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Grid p)• native void upper bound assign (Pointset Powerset Grid p)• native void difference assign (Pointset Powerset Grid p)• native void concatenate assign (Pointset Powerset Grid p)• native void time elapse assign (Pointset Powerset Grid p)• native boolean upper bound assign if exact (Pointset Powerset Grid y)• native boolean simplify using context assign (Pointset Powerset Grid p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







230

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Grid Iterator begin iterator ()• native Pointset Powerset Grid Iterator end iterator ()• native void add disjunct (Grid j disj)• native void drop disjunct (Pointset Powerset Grid Iterator itr)• native void drop disjuncts (Pointset Powerset Grid Iterator itr1, Pointset Powerset Grid Iterator

itr2)• native void BHZ03 Grid congruence widening assign (Pointset Powerset Grid y)• native void BHZ03 Grid generator widening assign (Pointset Powerset Grid y)• native void BGP99 congruence extrapolation assign (Pointset Powerset Grid y, Integer d)• native void BGP99 generator extrapolation assign (Pointset Powerset Grid y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>The documentation for this class was generated from the following file:

• Pointset Powerset Grid.java

10.105 parma polyhedra library.Pointset Powerset Grid Iterator Class Reference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Grid Iterator (Pointset Powerset Grid Iterator y)• native boolean equals (Pointset Powerset Grid Iterator itr)• native void next ()• native void prev ()• native Grid get disjunct ()• native void free ()



231


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Grid>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Grid Iterator.java

10.106 parma polyhedra library.Pointset Powerset Int16 Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>



• Pointset Powerset Int16 Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Int16 Box (Pointset Powerset Int16 Box y)• Pointset Powerset Int16 Box (Int16 Box y)• Pointset Powerset Int16 Box (Pointset Powerset Int16 Box y, Complexity Class complexity)• Pointset Powerset Int16 Box (Int16 Box y, Complexity Class complexity)• Pointset Powerset Int16 Box (Constraint System cs)• Pointset Powerset Int16 Box (Congruence System cs)• native void swap (Pointset Powerset Int16 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Int16 Box y)• native boolean strictly contains (Pointset Powerset Int16 Box y)• native boolean is disjoint from (Pointset Powerset Int16 Box y)• native boolean geometrically covers (Pointset Powerset Int16 Box y)• native boolean geometrically equals (Pointset Powerset Int16 Box y)• native boolean equals (Pointset Powerset Int16 Box p)

232

• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Int16 Box p)• native void upper bound assign (Pointset Powerset Int16 Box p)• native void difference assign (Pointset Powerset Int16 Box p)• native void concatenate assign (Pointset Powerset Int16 Box p)• native void time elapse assign (Pointset Powerset Int16 Box p)• native boolean upper bound assign if exact (Pointset Powerset Int16 Box y)• native boolean simplify using context assign (Pointset Powerset Int16 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Int16 Box Iterator begin iterator ()• native Pointset Powerset Int16 Box Iterator end iterator ()• native void add disjunct (Int16 Box j disj)

233

• native void drop disjunct (Pointset Powerset Int16 Box Iterator itr)

• native void drop disjuncts (Pointset Powerset Int16 Box Iterator itr1, Pointset Powerset Int16 ←↩

Box Iterator itr2)


• native int hashCode ()





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>The documentation for this class was generated from the following file:

• Pointset Powerset Int16 Box.java

10.107 parma polyhedra library.Pointset Powerset Int16 Box Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Int16 Box Iterator (Pointset Powerset Int16 Box Iterator y)

• native boolean equals (Pointset Powerset Int16 Box Iterator itr)

• native void next ()

• native void prev ()

• native Int16 Box get disjunct ()





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int16 Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Int16 Box Iterator.java

10.108 parma polyhedra library.Pointset Powerset Int32 Box Class Reference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Int32 Box>Inherits parma polyhedra library.PPL Object.

234






Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Int32 Box y)• native boolean strictly contains (Pointset Powerset Int32 Box y)• native boolean is disjoint from (Pointset Powerset Int32 Box y)• native boolean geometrically covers (Pointset Powerset Int32 Box y)• native boolean geometrically equals (Pointset Powerset Int32 Box y)• native boolean equals (Pointset Powerset Int32 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Int32 Box p)

235

• native void upper bound assign (Pointset Powerset Int32 Box p)• native void difference assign (Pointset Powerset Int32 Box p)• native void concatenate assign (Pointset Powerset Int32 Box p)• native void time elapse assign (Pointset Powerset Int32 Box p)• native boolean upper bound assign if exact (Pointset Powerset Int32 Box y)• native boolean simplify using context assign (Pointset Powerset Int32 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Int32 Box Iterator begin iterator ()• native Pointset Powerset Int32 Box Iterator end iterator ()• native void add disjunct (Int32 Box j disj)• native void drop disjunct (Pointset Powerset Int32 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Int32 Box Iterator itr1, Pointset Powerset Int32 ←↩




236







• Pointset Powerset Int32 Box Iterator (Pointset Powerset Int32 Box Iterator y)• native boolean equals (Pointset Powerset Int32 Box Iterator itr)• native void next ()• native void prev ()• native Int32 Box get disjunct ()• native void free ()









• Pointset Powerset Int64 Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Int64 Box (Pointset Powerset Int64 Box y)• Pointset Powerset Int64 Box (Int64 Box y)• Pointset Powerset Int64 Box (Pointset Powerset Int64 Box y, Complexity Class complexity)• Pointset Powerset Int64 Box (Int64 Box y, Complexity Class complexity)• Pointset Powerset Int64 Box (Constraint System cs)• Pointset Powerset Int64 Box (Congruence System cs)• native void swap (Pointset Powerset Int64 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()

237





Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Int64 Box y)• native boolean strictly contains (Pointset Powerset Int64 Box y)• native boolean is disjoint from (Pointset Powerset Int64 Box y)• native boolean geometrically covers (Pointset Powerset Int64 Box y)• native boolean geometrically equals (Pointset Powerset Int64 Box y)• native boolean equals (Pointset Powerset Int64 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Int64 Box p)• native void upper bound assign (Pointset Powerset Int64 Box p)• native void difference assign (Pointset Powerset Int64 Box p)• native void concatenate assign (Pointset Powerset Int64 Box p)• native void time elapse assign (Pointset Powerset Int64 Box p)• native boolean upper bound assign if exact (Pointset Powerset Int64 Box y)• native boolean simplify using context assign (Pointset Powerset Int64 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



238





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Int64 Box Iterator begin iterator ()• native Pointset Powerset Int64 Box Iterator end iterator ()• native void add disjunct (Int64 Box j disj)• native void drop disjunct (Pointset Powerset Int64 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Int64 Box Iterator itr1, Pointset Powerset Int64 ←↩









239












Boolean > maximum)

240




• native boolean contains (Pointset Powerset Int8 Box y)• native boolean strictly contains (Pointset Powerset Int8 Box y)• native boolean is disjoint from (Pointset Powerset Int8 Box y)• native boolean geometrically covers (Pointset Powerset Int8 Box y)• native boolean geometrically equals (Pointset Powerset Int8 Box y)• native boolean equals (Pointset Powerset Int8 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Int8 Box p)• native void upper bound assign (Pointset Powerset Int8 Box p)• native void difference assign (Pointset Powerset Int8 Box p)• native void concatenate assign (Pointset Powerset Int8 Box p)• native void time elapse assign (Pointset Powerset Int8 Box p)• native boolean upper bound assign if exact (Pointset Powerset Int8 Box y)• native boolean simplify using context assign (Pointset Powerset Int8 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







241

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Int8 Box Iterator begin iterator ()• native Pointset Powerset Int8 Box Iterator end iterator ()• native void add disjunct (Int8 Box j disj)• native void drop disjunct (Pointset Powerset Int8 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Int8 Box Iterator itr1, Pointset Powerset Int8 Box←↩

Iterator itr2)• native void free ()• native int hashCode ()• native String toString ()






10.113 parma polyhedra library.Pointset Powerset Int8 Box Iterator Class Refer-ence









242

10.114 parma polyhedra library.Pointset Powerset Long Double Box Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Long Double Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Long Double Box (Pointset Powerset Long Double Box y)• Pointset Powerset Long Double Box (Long Double Box y)• Pointset Powerset Long Double Box (Pointset Powerset Long Double Box y, Complexity Class

complexity)• Pointset Powerset Long Double Box (Long Double Box y, Complexity Class complexity)• Pointset Powerset Long Double Box (Constraint System cs)• Pointset Powerset Long Double Box (Congruence System cs)• native void swap (Pointset Powerset Long Double Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Long Double Box y)• native boolean strictly contains (Pointset Powerset Long Double Box y)• native boolean is disjoint from (Pointset Powerset Long Double Box y)• native boolean geometrically covers (Pointset Powerset Long Double Box y)• native boolean geometrically equals (Pointset Powerset Long Double Box y)• native boolean equals (Pointset Powerset Long Double Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)

243

• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Long Double Box p)• native void upper bound assign (Pointset Powerset Long Double Box p)• native void difference assign (Pointset Powerset Long Double Box p)• native void concatenate assign (Pointset Powerset Long Double Box p)• native void time elapse assign (Pointset Powerset Long Double Box p)• native boolean upper bound assign if exact (Pointset Powerset Long Double Box y)• native boolean simplify using context assign (Pointset Powerset Long Double Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Long Double Box Iterator begin iterator ()• native Pointset Powerset Long Double Box Iterator end iterator ()• native void add disjunct (Long Double Box j disj)• native void drop disjunct (Pointset Powerset Long Double Box Iterator itr)• native void drop disjuncts (Pointset Powerset Long Double Box Iterator itr1, Pointset Powerset←↩

Long Double Box Iterator itr2)• native void free ()• native int hashCode ()• native String toString ()

244




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>The documentation for this class was generated from the following file:

• Pointset Powerset Long Double Box.java

10.115 parma polyhedra library.Pointset Powerset Long Double Box Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Long Double Box Iterator (Pointset Powerset Long Double Box Iterator y)• native boolean equals (Pointset Powerset Long Double Box Iterator itr)• native void next ()• native void prev ()• native Long Double Box get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Long Double Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Long Double Box Iterator.java

10.116 parma polyhedra library.Pointset Powerset NNC Polyhedron Class Refer-ence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>Inherits parma polyhedra library.PPL Object.


• Pointset Powerset NNC Polyhedron (long num dimensions, Degenerate Element kind)• Pointset Powerset NNC Polyhedron (Pointset Powerset NNC Polyhedron y)• Pointset Powerset NNC Polyhedron (NNC Polyhedron y)• Pointset Powerset NNC Polyhedron (Pointset Powerset NNC Polyhedron y, Complexity Class com-

plexity)• Pointset Powerset NNC Polyhedron (NNC Polyhedron y, Complexity Class complexity)• Pointset Powerset NNC Polyhedron (Constraint System cs)• Pointset Powerset NNC Polyhedron (Congruence System cs)• native void swap (Pointset Powerset NNC Polyhedron y)• native long space dimension ()

245

• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset NNC Polyhedron y)• native boolean strictly contains (Pointset Powerset NNC Polyhedron y)• native boolean is disjoint from (Pointset Powerset NNC Polyhedron y)• native boolean geometrically covers (Pointset Powerset NNC Polyhedron y)• native boolean geometrically equals (Pointset Powerset NNC Polyhedron y)• native boolean equals (Pointset Powerset NNC Polyhedron p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset NNC Polyhedron p)• native void upper bound assign (Pointset Powerset NNC Polyhedron p)• native void difference assign (Pointset Powerset NNC Polyhedron p)• native void concatenate assign (Pointset Powerset NNC Polyhedron p)• native void time elapse assign (Pointset Powerset NNC Polyhedron p)• native boolean upper bound assign if exact (Pointset Powerset NNC Polyhedron y)• native boolean simplify using context assign (Pointset Powerset NNC Polyhedron p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)

246

• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset NNC Polyhedron Iterator begin iterator ()• native Pointset Powerset NNC Polyhedron Iterator end iterator ()• native void add disjunct (NNC Polyhedron j disj)• native void drop disjunct (Pointset Powerset NNC Polyhedron Iterator itr)• native void drop disjuncts (Pointset Powerset NNC Polyhedron Iterator itr1, Pointset Powerset←↩

NNC Polyhedron Iterator itr2)• native void BHZ03 BHRZ03 BHRZ03 widening assign (Pointset Powerset NNC Polyhedron y)• native void BHZ03 H79 H79 widening assign (Pointset Powerset NNC Polyhedron y)• native void BGP99 BHRZ03 extrapolation assign (Pointset Powerset NNC Polyhedron y, Integer

d)• native void BGP99 H79 extrapolation assign (Pointset Powerset NNC Polyhedron y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>The documentation for this class was generated from the following file:

• Pointset Powerset NNC Polyhedron.java

247

10.117 parma polyhedra library.Pointset Powerset NNC Polyhedron Iterator ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset NNC Polyhedron Iterator (Pointset Powerset NNC Polyhedron Iterator y)• native boolean equals (Pointset Powerset NNC Polyhedron Iterator itr)• native void next ()• native void prev ()• native NNC Polyhedron get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<NNC Polyhedron>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset NNC Polyhedron Iterator.java

10.118 parma polyhedra library.Pointset Powerset Octagonal Shape double ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<double> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Octagonal Shape double (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape double (Pointset Powerset Octagonal Shape double y)• Pointset Powerset Octagonal Shape double (Octagonal Shape double y)• Pointset Powerset Octagonal Shape double (Pointset Powerset Octagonal Shape double y, Complexity←↩

Class complexity)• Pointset Powerset Octagonal Shape double (Octagonal Shape double y, Complexity Class com-

plexity)• Pointset Powerset Octagonal Shape double (Constraint System cs)• Pointset Powerset Octagonal Shape double (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()

248

• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape double y)• native boolean strictly contains (Pointset Powerset Octagonal Shape double y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape double y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape double y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape double y)• native boolean equals (Pointset Powerset Octagonal Shape double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape double p)• native void upper bound assign (Pointset Powerset Octagonal Shape double p)• native void difference assign (Pointset Powerset Octagonal Shape double p)• native void concatenate assign (Pointset Powerset Octagonal Shape double p)• native void time elapse assign (Pointset Powerset Octagonal Shape double p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape double y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





249



Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape double Iterator begin iterator ()• native Pointset Powerset Octagonal Shape double Iterator end iterator ()• native void add disjunct (Octagonal Shape double j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape double Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape double Iterator itr1, Pointset ←↩

Powerset Octagonal Shape double Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape double

y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape double y,

Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<double> >


• Pointset Powerset Octagonal Shape double.java

10.119 parma polyhedra library.Pointset Powerset Octagonal Shape double IteratorClass Reference


:: iterator.Inherits parma polyhedra library.PPL Object.

250


• Pointset Powerset Octagonal Shape double Iterator (Pointset Powerset Octagonal Shape double←↩

Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape double Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape double get disjunct ()• native void free ()





:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Octagonal Shape double Iterator.java

10.120 parma polyhedra library.Pointset Powerset Octagonal Shape float Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Octagonal Shape float (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape float (Pointset Powerset Octagonal Shape float y)• Pointset Powerset Octagonal Shape float (Octagonal Shape float y)• Pointset Powerset Octagonal Shape float (Pointset Powerset Octagonal Shape float y, Complexity←↩

Class complexity)• Pointset Powerset Octagonal Shape float (Octagonal Shape float y, Complexity Class complex-

ity)• Pointset Powerset Octagonal Shape float (Constraint System cs)• Pointset Powerset Octagonal Shape float (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape float y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()

251

• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape float y)• native boolean strictly contains (Pointset Powerset Octagonal Shape float y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape float y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape float y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape float y)• native boolean equals (Pointset Powerset Octagonal Shape float p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape float p)• native void upper bound assign (Pointset Powerset Octagonal Shape float p)• native void difference assign (Pointset Powerset Octagonal Shape float p)• native void concatenate assign (Pointset Powerset Octagonal Shape float p)• native void time elapse assign (Pointset Powerset Octagonal Shape float p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape float y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape float p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)

252

• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape float Iterator begin iterator ()• native Pointset Powerset Octagonal Shape float Iterator end iterator ()• native void add disjunct (Octagonal Shape float j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape float Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape float Iterator itr1, Pointset Powerset←↩

Octagonal Shape float Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape float y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape float y,





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >The documentation for this class was generated from the following file:

• Pointset Powerset Octagonal Shape float.java

10.121 parma polyhedra library.Pointset Powerset Octagonal Shape float IteratorClass Reference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >:←↩

: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Octagonal Shape float Iterator (Pointset Powerset Octagonal Shape float ←↩

Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape float Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape float get disjunct ()• native void free ()

253




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<float> >:←↩

: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Octagonal Shape float Iterator.java

10.122 parma polyhedra library.Pointset Powerset Octagonal Shape int16 t ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int16 t> >Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Octagonal Shape int16 t (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape int16 t (Pointset Powerset Octagonal Shape int16 t y)• Pointset Powerset Octagonal Shape int16 t (Octagonal Shape int16 t y)• Pointset Powerset Octagonal Shape int16 t (Pointset Powerset Octagonal Shape int16 t y, Complexity←↩

Class complexity)• Pointset Powerset Octagonal Shape int16 t (Octagonal Shape int16 t y, Complexity Class com-

plexity)• Pointset Powerset Octagonal Shape int16 t (Constraint System cs)• Pointset Powerset Octagonal Shape int16 t (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape int16 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




254


• native boolean contains (Pointset Powerset Octagonal Shape int16 t y)• native boolean strictly contains (Pointset Powerset Octagonal Shape int16 t y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape int16 t y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape int16 t y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape int16 t y)• native boolean equals (Pointset Powerset Octagonal Shape int16 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape int16 t p)• native void upper bound assign (Pointset Powerset Octagonal Shape int16 t p)• native void difference assign (Pointset Powerset Octagonal Shape int16 t p)• native void concatenate assign (Pointset Powerset Octagonal Shape int16 t p)• native void time elapse assign (Pointset Powerset Octagonal Shape int16 t p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape int16 t y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape int16 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)

255

• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape int16 t Iterator begin iterator ()• native Pointset Powerset Octagonal Shape int16 t Iterator end iterator ()• native void add disjunct (Octagonal Shape int16 t j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape int16 t Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape int16 t Iterator itr1, Pointset Powerset←↩

Octagonal Shape int16 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape int16←↩

t y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape int16 ←↩

t y, Integer d)• native void free ()• native int hashCode ()• native String toString ()






• Pointset Powerset Octagonal Shape int16 t.java

10.123 parma polyhedra library.Pointset Powerset Octagonal Shape int16 t IteratorClass Reference




• Pointset Powerset Octagonal Shape int16 t Iterator (Pointset Powerset Octagonal Shape int16←↩

t Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape int16 t Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape int16 t get disjunct ()• native void free ()



256




• Pointset Powerset Octagonal Shape int16 t Iterator.java










Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape int32 t y)• native boolean strictly contains (Pointset Powerset Octagonal Shape int32 t y)

257

• native boolean is disjoint from (Pointset Powerset Octagonal Shape int32 t y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape int32 t y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape int32 t y)• native boolean equals (Pointset Powerset Octagonal Shape int32 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape int32 t p)• native void upper bound assign (Pointset Powerset Octagonal Shape int32 t p)• native void difference assign (Pointset Powerset Octagonal Shape int32 t p)• native void concatenate assign (Pointset Powerset Octagonal Shape int32 t p)• native void time elapse assign (Pointset Powerset Octagonal Shape int32 t p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape int32 t y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape int32 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()

258

• native long size ()• native Pointset Powerset Octagonal Shape int32 t Iterator begin iterator ()• native Pointset Powerset Octagonal Shape int32 t Iterator end iterator ()• native void add disjunct (Octagonal Shape int32 t j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape int32 t Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape int32 t Iterator itr1, Pointset Powerset←↩

Octagonal Shape int32 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape int32←↩






Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int32 t> >The documentation for this class was generated from the following file:














259










Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape int64 t y)• native boolean strictly contains (Pointset Powerset Octagonal Shape int64 t y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape int64 t y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape int64 t y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape int64 t y)• native boolean equals (Pointset Powerset Octagonal Shape int64 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)

260

• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape int64 t p)• native void upper bound assign (Pointset Powerset Octagonal Shape int64 t p)• native void difference assign (Pointset Powerset Octagonal Shape int64 t p)• native void concatenate assign (Pointset Powerset Octagonal Shape int64 t p)• native void time elapse assign (Pointset Powerset Octagonal Shape int64 t p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape int64 t y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape int64 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape int64 t Iterator begin iterator ()• native Pointset Powerset Octagonal Shape int64 t Iterator end iterator ()• native void add disjunct (Octagonal Shape int64 t j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape int64 t Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape int64 t Iterator itr1, Pointset Powerset←↩

Octagonal Shape int64 t Iterator itr2)

261

• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape int64←↩






















262



Class complexity)• Pointset Powerset Octagonal Shape int8 t (Octagonal Shape int8 t y, Complexity Class complex-

ity)• Pointset Powerset Octagonal Shape int8 t (Constraint System cs)• Pointset Powerset Octagonal Shape int8 t (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape int8 t y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape int8 t y)• native boolean strictly contains (Pointset Powerset Octagonal Shape int8 t y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape int8 t y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape int8 t y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape int8 t y)• native boolean equals (Pointset Powerset Octagonal Shape int8 t p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)

263

• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape int8 t p)• native void upper bound assign (Pointset Powerset Octagonal Shape int8 t p)• native void difference assign (Pointset Powerset Octagonal Shape int8 t p)• native void concatenate assign (Pointset Powerset Octagonal Shape int8 t p)• native void time elapse assign (Pointset Powerset Octagonal Shape int8 t p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape int8 t y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape int8 t p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape int8 t Iterator begin iterator ()• native Pointset Powerset Octagonal Shape int8 t Iterator end iterator ()• native void add disjunct (Octagonal Shape int8 t j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape int8 t Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape int8 t Iterator itr1, Pointset Powerset←↩

Octagonal Shape int8 t Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape int8 ←↩

t y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape int8 t y,


264







Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int8 t> >::iterator.



• Pointset Powerset Octagonal Shape int8 t Iterator (Pointset Powerset Octagonal Shape int8 ←↩





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<int8 t> >::iterator.



10.130 parma polyhedra library.Pointset Powerset Octagonal Shape long doubleClass Reference




• Pointset Powerset Octagonal Shape long double (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape long double (Pointset Powerset Octagonal Shape long double

y)• Pointset Powerset Octagonal Shape long double (Octagonal Shape long double y)• Pointset Powerset Octagonal Shape long double (Pointset Powerset Octagonal Shape long double

y, Complexity Class complexity)

265

• Pointset Powerset Octagonal Shape long double (Octagonal Shape long double y, Complexity←↩

Class complexity)• Pointset Powerset Octagonal Shape long double (Constraint System cs)• Pointset Powerset Octagonal Shape long double (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape long double y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape long double y)• native boolean strictly contains (Pointset Powerset Octagonal Shape long double y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape long double y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape long double y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape long double y)• native boolean equals (Pointset Powerset Octagonal Shape long double p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape long double p)• native void upper bound assign (Pointset Powerset Octagonal Shape long double p)• native void difference assign (Pointset Powerset Octagonal Shape long double p)• native void concatenate assign (Pointset Powerset Octagonal Shape long double p)• native void time elapse assign (Pointset Powerset Octagonal Shape long double p)

266

• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape long double y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape long double p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape long double Iterator begin iterator ()• native Pointset Powerset Octagonal Shape long double Iterator end iterator ()• native void add disjunct (Octagonal Shape long double j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape long double Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape long double Iterator itr1, Pointset←↩

Powerset Octagonal Shape long double Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape long ←↩

double y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape long ←↩

double y, Integer d)• native void free ()• native int hashCode ()• native String toString ()



267




• Pointset Powerset Octagonal Shape long double.java

10.131 parma polyhedra library.Pointset Powerset Octagonal Shape long double←↩

Iterator Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<long double>>:: iterator.



• Pointset Powerset Octagonal Shape long double Iterator (Pointset Powerset Octagonal Shape←↩

long double Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape long double Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape long double get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<long double>>:: iterator.


• Pointset Powerset Octagonal Shape long double Iterator.java

10.132 parma polyhedra library.Pointset Powerset Octagonal Shape mpq class ClassReference




• Pointset Powerset Octagonal Shape mpq class (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape mpq class (Pointset Powerset Octagonal Shape mpq class y)• Pointset Powerset Octagonal Shape mpq class (Octagonal Shape mpq class y)• Pointset Powerset Octagonal Shape mpq class (Pointset Powerset Octagonal Shape mpq class y,

Complexity Class complexity)• Pointset Powerset Octagonal Shape mpq class (Octagonal Shape mpq class y, Complexity Class

complexity)• Pointset Powerset Octagonal Shape mpq class (Constraint System cs)• Pointset Powerset Octagonal Shape mpq class (Congruence System cs)

268

• native void swap (Pointset Powerset Octagonal Shape mpq class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape mpq class y)• native boolean strictly contains (Pointset Powerset Octagonal Shape mpq class y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape mpq class y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape mpq class y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape mpq class y)• native boolean equals (Pointset Powerset Octagonal Shape mpq class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape mpq class p)• native void upper bound assign (Pointset Powerset Octagonal Shape mpq class p)• native void difference assign (Pointset Powerset Octagonal Shape mpq class p)• native void concatenate assign (Pointset Powerset Octagonal Shape mpq class p)• native void time elapse assign (Pointset Powerset Octagonal Shape mpq class p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape mpq class y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape mpq class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)

269

• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape mpq class Iterator begin iterator ()• native Pointset Powerset Octagonal Shape mpq class Iterator end iterator ()• native void add disjunct (Octagonal Shape mpq class j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape mpq class Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape mpq class Iterator itr1, Pointset←↩

Powerset Octagonal Shape mpq class Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape mpq ←↩

class y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape mpq ←↩

class y, Integer d)• native void free ()• native int hashCode ()• native String toString ()






• Pointset Powerset Octagonal Shape mpq class.java

270

10.133 parma polyhedra library.Pointset Powerset Octagonal Shape mpq class←↩

Iterator Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpq class>>:: iterator.



• Pointset Powerset Octagonal Shape mpq class Iterator (Pointset Powerset Octagonal Shape ←↩

mpq class Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape mpq class Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape mpq class get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpq class>>:: iterator.


• Pointset Powerset Octagonal Shape mpq class Iterator.java

10.134 parma polyhedra library.Pointset Powerset Octagonal Shape mpz class ClassReference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>



• Pointset Powerset Octagonal Shape mpz class (long num dimensions, Degenerate Element kind)• Pointset Powerset Octagonal Shape mpz class (Pointset Powerset Octagonal Shape mpz class y)• Pointset Powerset Octagonal Shape mpz class (Octagonal Shape mpz class y)• Pointset Powerset Octagonal Shape mpz class (Pointset Powerset Octagonal Shape mpz class y,

Complexity Class complexity)• Pointset Powerset Octagonal Shape mpz class (Octagonal Shape mpz class y, Complexity Class

complexity)• Pointset Powerset Octagonal Shape mpz class (Constraint System cs)• Pointset Powerset Octagonal Shape mpz class (Congruence System cs)• native void swap (Pointset Powerset Octagonal Shape mpz class y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()

271





Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Octagonal Shape mpz class y)• native boolean strictly contains (Pointset Powerset Octagonal Shape mpz class y)• native boolean is disjoint from (Pointset Powerset Octagonal Shape mpz class y)• native boolean geometrically covers (Pointset Powerset Octagonal Shape mpz class y)• native boolean geometrically equals (Pointset Powerset Octagonal Shape mpz class y)• native boolean equals (Pointset Powerset Octagonal Shape mpz class p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Octagonal Shape mpz class p)• native void upper bound assign (Pointset Powerset Octagonal Shape mpz class p)• native void difference assign (Pointset Powerset Octagonal Shape mpz class p)• native void concatenate assign (Pointset Powerset Octagonal Shape mpz class p)• native void time elapse assign (Pointset Powerset Octagonal Shape mpz class p)• native boolean upper bound assign if exact (Pointset Powerset Octagonal Shape mpz class y)• native boolean simplify using context assign (Pointset Powerset Octagonal Shape mpz class p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



272





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Octagonal Shape mpz class Iterator begin iterator ()• native Pointset Powerset Octagonal Shape mpz class Iterator end iterator ()• native void add disjunct (Octagonal Shape mpz class j disj)• native void drop disjunct (Pointset Powerset Octagonal Shape mpz class Iterator itr)• native void drop disjuncts (Pointset Powerset Octagonal Shape mpz class Iterator itr1, Pointset←↩

Powerset Octagonal Shape mpz class Iterator itr2)• native void BHZ03 H79 BHMZ05 widening assign (Pointset Powerset Octagonal Shape mpz ←↩

class y)• native void BGP99 BHMZ05 extrapolation assign (Pointset Powerset Octagonal Shape mpz ←↩

class y, Integer d)• native void free ()• native int hashCode ()• native String toString ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>


• Pointset Powerset Octagonal Shape mpz class.java

10.135 parma polyhedra library.Pointset Powerset Octagonal Shape mpz class←↩

Iterator Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>:: iterator.


273


• Pointset Powerset Octagonal Shape mpz class Iterator (Pointset Powerset Octagonal Shape ←↩

mpz class Iterator y)• native boolean equals (Pointset Powerset Octagonal Shape mpz class Iterator itr)• native void next ()• native void prev ()• native Octagonal Shape mpz class get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Octagonal Shape<mpz class>>:: iterator.


• Pointset Powerset Octagonal Shape mpz class Iterator.java

10.136 parma polyhedra library.Pointset Powerset Rational Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>



• Pointset Powerset Rational Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Rational Box (Pointset Powerset Rational Box y)• Pointset Powerset Rational Box (Rational Box y)• Pointset Powerset Rational Box (Pointset Powerset Rational Box y, Complexity Class complex-

ity)• Pointset Powerset Rational Box (Rational Box y, Complexity Class complexity)• Pointset Powerset Rational Box (Constraint System cs)• Pointset Powerset Rational Box (Congruence System cs)• native void swap (Pointset Powerset Rational Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)

274

• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Rational Box y)• native boolean strictly contains (Pointset Powerset Rational Box y)• native boolean is disjoint from (Pointset Powerset Rational Box y)• native boolean geometrically covers (Pointset Powerset Rational Box y)• native boolean geometrically equals (Pointset Powerset Rational Box y)• native boolean equals (Pointset Powerset Rational Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Rational Box p)• native void upper bound assign (Pointset Powerset Rational Box p)• native void difference assign (Pointset Powerset Rational Box p)• native void concatenate assign (Pointset Powerset Rational Box p)• native void time elapse assign (Pointset Powerset Rational Box p)• native boolean upper bound assign if exact (Pointset Powerset Rational Box y)• native boolean simplify using context assign (Pointset Powerset Rational Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)

275

• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Rational Box Iterator begin iterator ()• native Pointset Powerset Rational Box Iterator end iterator ()• native void add disjunct (Rational Box j disj)• native void drop disjunct (Pointset Powerset Rational Box Iterator itr)• native void drop disjuncts (Pointset Powerset Rational Box Iterator itr1, Pointset Powerset Rational←↩





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>The documentation for this class was generated from the following file:

• Pointset Powerset Rational Box.java

10.137 parma polyhedra library.Pointset Powerset Rational Box Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Rational Box Iterator (Pointset Powerset Rational Box Iterator y)• native boolean equals (Pointset Powerset Rational Box Iterator itr)• native void next ()• native void prev ()• native Rational Box get disjunct ()• native void free ()



276


Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Rational Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Rational Box Iterator.java

10.138 parma polyhedra library.Pointset Powerset Uint16 Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>



• Pointset Powerset Uint16 Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Uint16 Box (Pointset Powerset Uint16 Box y)• Pointset Powerset Uint16 Box (Uint16 Box y)• Pointset Powerset Uint16 Box (Pointset Powerset Uint16 Box y, Complexity Class complexity)• Pointset Powerset Uint16 Box (Uint16 Box y, Complexity Class complexity)• Pointset Powerset Uint16 Box (Constraint System cs)• Pointset Powerset Uint16 Box (Congruence System cs)• native void swap (Pointset Powerset Uint16 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Uint16 Box y)• native boolean strictly contains (Pointset Powerset Uint16 Box y)• native boolean is disjoint from (Pointset Powerset Uint16 Box y)• native boolean geometrically covers (Pointset Powerset Uint16 Box y)• native boolean geometrically equals (Pointset Powerset Uint16 Box y)• native boolean equals (Pointset Powerset Uint16 Box p)

277

• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Uint16 Box p)• native void upper bound assign (Pointset Powerset Uint16 Box p)• native void difference assign (Pointset Powerset Uint16 Box p)• native void concatenate assign (Pointset Powerset Uint16 Box p)• native void time elapse assign (Pointset Powerset Uint16 Box p)• native boolean upper bound assign if exact (Pointset Powerset Uint16 Box y)• native boolean simplify using context assign (Pointset Powerset Uint16 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Uint16 Box Iterator begin iterator ()• native Pointset Powerset Uint16 Box Iterator end iterator ()• native void add disjunct (Uint16 Box j disj)

278

• native void drop disjunct (Pointset Powerset Uint16 Box Iterator itr)

• native void drop disjuncts (Pointset Powerset Uint16 Box Iterator itr1, Pointset Powerset Uint16←↩

Box Iterator itr2)


• native int hashCode ()





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>The documentation for this class was generated from the following file:

• Pointset Powerset Uint16 Box.java

10.139 parma polyhedra library.Pointset Powerset Uint16 Box Iterator Class Ref-erence

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>:: iterator.Inherits parma polyhedra library.PPL Object.


• Pointset Powerset Uint16 Box Iterator (Pointset Powerset Uint16 Box Iterator y)

• native boolean equals (Pointset Powerset Uint16 Box Iterator itr)

• native void next ()

• native void prev ()

• native Uint16 Box get disjunct ()





Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint16 Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Uint16 Box Iterator.java

10.140 parma polyhedra library.Pointset Powerset Uint32 Box Class Reference

Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Uint32 Box>Inherits parma polyhedra library.PPL Object.

279






Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Uint32 Box y)• native boolean strictly contains (Pointset Powerset Uint32 Box y)• native boolean is disjoint from (Pointset Powerset Uint32 Box y)• native boolean geometrically covers (Pointset Powerset Uint32 Box y)• native boolean geometrically equals (Pointset Powerset Uint32 Box y)• native boolean equals (Pointset Powerset Uint32 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Uint32 Box p)

280

• native void upper bound assign (Pointset Powerset Uint32 Box p)• native void difference assign (Pointset Powerset Uint32 Box p)• native void concatenate assign (Pointset Powerset Uint32 Box p)• native void time elapse assign (Pointset Powerset Uint32 Box p)• native boolean upper bound assign if exact (Pointset Powerset Uint32 Box y)• native boolean simplify using context assign (Pointset Powerset Uint32 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Uint32 Box Iterator begin iterator ()• native Pointset Powerset Uint32 Box Iterator end iterator ()• native void add disjunct (Uint32 Box j disj)• native void drop disjunct (Pointset Powerset Uint32 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Uint32 Box Iterator itr1, Pointset Powerset Uint32←↩




281







• Pointset Powerset Uint32 Box Iterator (Pointset Powerset Uint32 Box Iterator y)• native boolean equals (Pointset Powerset Uint32 Box Iterator itr)• native void next ()• native void prev ()• native Uint32 Box get disjunct ()• native void free ()









• Pointset Powerset Uint64 Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Uint64 Box (Pointset Powerset Uint64 Box y)• Pointset Powerset Uint64 Box (Uint64 Box y)• Pointset Powerset Uint64 Box (Pointset Powerset Uint64 Box y, Complexity Class complexity)• Pointset Powerset Uint64 Box (Uint64 Box y, Complexity Class complexity)• Pointset Powerset Uint64 Box (Constraint System cs)• Pointset Powerset Uint64 Box (Congruence System cs)• native void swap (Pointset Powerset Uint64 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()

282





Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Uint64 Box y)• native boolean strictly contains (Pointset Powerset Uint64 Box y)• native boolean is disjoint from (Pointset Powerset Uint64 Box y)• native boolean geometrically covers (Pointset Powerset Uint64 Box y)• native boolean geometrically equals (Pointset Powerset Uint64 Box y)• native boolean equals (Pointset Powerset Uint64 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Uint64 Box p)• native void upper bound assign (Pointset Powerset Uint64 Box p)• native void difference assign (Pointset Powerset Uint64 Box p)• native void concatenate assign (Pointset Powerset Uint64 Box p)• native void time elapse assign (Pointset Powerset Uint64 Box p)• native boolean upper bound assign if exact (Pointset Powerset Uint64 Box y)• native boolean simplify using context assign (Pointset Powerset Uint64 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩



283





Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Uint64 Box Iterator begin iterator ()• native Pointset Powerset Uint64 Box Iterator end iterator ()• native void add disjunct (Uint64 Box j disj)• native void drop disjunct (Pointset Powerset Uint64 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Uint64 Box Iterator itr1, Pointset Powerset Uint64←↩









284












Boolean > maximum)

285




• native boolean contains (Pointset Powerset Uint8 Box y)• native boolean strictly contains (Pointset Powerset Uint8 Box y)• native boolean is disjoint from (Pointset Powerset Uint8 Box y)• native boolean geometrically covers (Pointset Powerset Uint8 Box y)• native boolean geometrically equals (Pointset Powerset Uint8 Box y)• native boolean equals (Pointset Powerset Uint8 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Uint8 Box p)• native void upper bound assign (Pointset Powerset Uint8 Box p)• native void difference assign (Pointset Powerset Uint8 Box p)• native void concatenate assign (Pointset Powerset Uint8 Box p)• native void time elapse assign (Pointset Powerset Uint8 Box p)• native boolean upper bound assign if exact (Pointset Powerset Uint8 Box y)• native boolean simplify using context assign (Pointset Powerset Uint8 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩







286

• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Uint8 Box Iterator begin iterator ()• native Pointset Powerset Uint8 Box Iterator end iterator ()• native void add disjunct (Uint8 Box j disj)• native void drop disjunct (Pointset Powerset Uint8 Box Iterator itr)• native void drop disjuncts (Pointset Powerset Uint8 Box Iterator itr1, Pointset Powerset Uint8 ←↩
















287

10.146 parma polyhedra library.Pointset Powerset Z Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>



• Pointset Powerset Z Box (long num dimensions, Degenerate Element kind)• Pointset Powerset Z Box (Pointset Powerset Z Box y)• Pointset Powerset Z Box (Z Box y)• Pointset Powerset Z Box (Pointset Powerset Z Box y, Complexity Class complexity)• Pointset Powerset Z Box (Z Box y, Complexity Class complexity)• Pointset Powerset Z Box (Constraint System cs)• Pointset Powerset Z Box (Congruence System cs)• native void swap (Pointset Powerset Z Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native void pairwise reduce ()• native void omega reduce ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<




Boolean > maximum, Generator point)• native boolean contains (Pointset Powerset Z Box y)• native boolean strictly contains (Pointset Powerset Z Box y)• native boolean is disjoint from (Pointset Powerset Z Box y)• native boolean geometrically covers (Pointset Powerset Z Box y)• native boolean geometrically equals (Pointset Powerset Z Box y)• native boolean equals (Pointset Powerset Z Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)

288

• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Pointset Powerset Z Box p)• native void upper bound assign (Pointset Powerset Z Box p)• native void difference assign (Pointset Powerset Z Box p)• native void concatenate assign (Pointset Powerset Z Box p)• native void time elapse assign (Pointset Powerset Z Box p)• native boolean upper bound assign if exact (Pointset Powerset Z Box y)• native boolean simplify using context assign (Pointset Powerset Z Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native long size ()• native Pointset Powerset Z Box Iterator begin iterator ()• native Pointset Powerset Z Box Iterator end iterator ()• native void add disjunct (Z Box j disj)• native void drop disjunct (Pointset Powerset Z Box Iterator itr)• native void drop disjuncts (Pointset Powerset Z Box Iterator itr1, Pointset Powerset Z Box Iterator

itr2)• native void free ()• native int hashCode ()• native String toString ()

289




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>The documentation for this class was generated from the following file:

• Pointset Powerset Z Box.java

10.147 parma polyhedra library.Pointset Powerset Z Box Iterator Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>:: iterator.



• Pointset Powerset Z Box Iterator (Pointset Powerset Z Box Iterator y)• native boolean equals (Pointset Powerset Z Box Iterator itr)• native void next ()• native void prev ()• native Z Box get disjunct ()• native void free ()




Java class interfacing C++ Parma Polyhedra Library::Pointset Powerset<Z Box>:: iterator.The documentation for this class was generated from the following file:

• Pointset Powerset Z Box Iterator.java

10.148 parma polyhedra library.Poly Con Relation Class ReferenceThe relation between a polyhedron and a constraint.


• Poly Con Relation (int val)Constructs from a integer value.

• boolean implies (Poly Con Relation y)True if and only if this implies y.


• static Poly Con Relation nothing ()The assertion that says nothing.

• static Poly Con Relation is disjoint ()The polyhedron and the set of points satisfying the constraint are disjoint.

• static Poly Con Relation strictly intersects ()The polyhedron intersects the set of points satisfying the constraint, but it is not included in it.

290

• static Poly Con Relation is included ()

The polyhedron is included in the set of points satisfying the constraint.

• static Poly Con Relation saturates ()

The polyhedron is included in the set of points saturating the constraint.

Static Public Attributes

• static final int NOTHING = 0• static final int IS DISJOINT = 1• static final int STRICTLY INTERSECTS = 2• static final int IS INCLUDED = 4• static final int SATURATES = 8


The relation between a polyhedron and a constraint.This class implements conjunctions of assertions on the relation between a polyhedron and a constraint.The documentation for this class was generated from the following file:

• Poly Con Relation.java

10.149 parma polyhedra library.Poly Gen Relation Class ReferenceThe relation between a polyhedron and a generator.


• Poly Gen Relation (int val)

Constructs from a integer value.

• boolean implies (Poly Gen Relation y)

True if and only if this implies y.


• static Poly Gen Relation nothing ()

The assertion that says nothing.

• static Poly Gen Relation subsumes ()

Adding the generator would not change the polyhedron.

Static Public Attributes

• static final int NOTHING = 0• static final int SUBSUMES = 1


The relation between a polyhedron and a generator.This class implements conjunctions of assertions on the relation between a polyhedron and a generator.The documentation for this class was generated from the following file:

• Poly Gen Relation.java

291

10.150 parma polyhedra library.Polyhedron Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Polyhedron.

Inheritance diagram for parma polyhedra library.Polyhedron:


parma_polyhedra_library.C_Polyhedron

parma_polyhedra_library.NNC_Polyhedron


• native void swap (Polyhedron y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Generator System generators ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native Generator System minimized generators ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean maximize (Linear Expression expr, Coefficient sup n, Coefficient sup d, By Reference<





292


• native boolean contains (Polyhedron y)• native boolean strictly contains (Polyhedron y)• native boolean is disjoint from (Polyhedron y)• native boolean equals (Polyhedron p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add generator (Generator c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void add generators (Generator System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Polyhedron p)• native void upper bound assign (Polyhedron p)• native void difference assign (Polyhedron p)• native void concatenate assign (Polyhedron p)• native void time elapse assign (Polyhedron p)• native void poly hull assign (Polyhedron p)• native void poly difference assign (Polyhedron p)• native boolean simplify using context assign (Polyhedron p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)

293

• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void BHRZ03 widening assign (Polyhedron y, By Reference< Integer > tp)• native void H79 widening assign (Polyhedron y, By Reference< Integer > tp)• native void widening assign (Polyhedron y, By Reference< Integer > tp)• native void limited BHRZ03 extrapolation assign (Polyhedron y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void bounded BHRZ03 extrapolation assign (Polyhedron y, Constraint System cs, By ←↩

Reference< Integer > tp)• native void limited H79 extrapolation assign (Polyhedron y, Constraint System cs, By Reference<

Integer > tp)• native void bounded H79 extrapolation assign (Polyhedron y, Constraint System cs, By Reference<

Integer > tp)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩


threshold, boolean wrap individually)• native int hashCode ()• native String toString ()


Java class interfacing C++ Parma Polyhedra Library::Polyhedron.The documentation for this class was generated from the following file:

• Polyhedron.java

10.151 parma polyhedra library.Rational Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Rational Box.



• Rational Box (long num dimensions, Degenerate Element kind)• Rational Box (Int8 Box y)• Rational Box (Int16 Box y)• Rational Box (Int32 Box y)• Rational Box (Int64 Box y)• Rational Box (Uint8 Box y)• Rational Box (Uint16 Box y)• Rational Box (Uint32 Box y)• Rational Box (Uint64 Box y)• Rational Box (Z Box y)• Rational Box (Rational Box y)• Rational Box (BD Shape int8 t y)• Rational Box (BD Shape int16 t y)• Rational Box (BD Shape int32 t y)• Rational Box (BD Shape int64 t y)• Rational Box (BD Shape mpz class y)• Rational Box (BD Shape mpq class y)

294

• Rational Box (Octagonal Shape int8 t y)• Rational Box (Octagonal Shape int16 t y)• Rational Box (Octagonal Shape int32 t y)• Rational Box (Octagonal Shape int64 t y)• Rational Box (Octagonal Shape mpz class y)• Rational Box (Octagonal Shape mpq class y)• Rational Box (C Polyhedron y)• Rational Box (NNC Polyhedron y)• Rational Box (Grid y)• Rational Box (Float Box y)• Rational Box (BD Shape float y)• Rational Box (Octagonal Shape float y)• Rational Box (Double Box y)• Rational Box (BD Shape double y)• Rational Box (Octagonal Shape double y)• Rational Box (Long Double Box y)• Rational Box (BD Shape long double y)• Rational Box (Octagonal Shape long double y)• Rational Box (Int8 Box y, Complexity Class complexity)• Rational Box (Int16 Box y, Complexity Class complexity)• Rational Box (Int32 Box y, Complexity Class complexity)• Rational Box (Int64 Box y, Complexity Class complexity)• Rational Box (Uint8 Box y, Complexity Class complexity)• Rational Box (Uint16 Box y, Complexity Class complexity)• Rational Box (Uint32 Box y, Complexity Class complexity)• Rational Box (Uint64 Box y, Complexity Class complexity)• Rational Box (Z Box y, Complexity Class complexity)• Rational Box (Rational Box y, Complexity Class complexity)• Rational Box (BD Shape int8 t y, Complexity Class complexity)• Rational Box (BD Shape int16 t y, Complexity Class complexity)• Rational Box (BD Shape int32 t y, Complexity Class complexity)• Rational Box (BD Shape int64 t y, Complexity Class complexity)• Rational Box (BD Shape mpz class y, Complexity Class complexity)• Rational Box (BD Shape mpq class y, Complexity Class complexity)• Rational Box (Octagonal Shape int8 t y, Complexity Class complexity)• Rational Box (Octagonal Shape int16 t y, Complexity Class complexity)• Rational Box (Octagonal Shape int32 t y, Complexity Class complexity)• Rational Box (Octagonal Shape int64 t y, Complexity Class complexity)• Rational Box (Octagonal Shape mpz class y, Complexity Class complexity)• Rational Box (Octagonal Shape mpq class y, Complexity Class complexity)• Rational Box (C Polyhedron y, Complexity Class complexity)• Rational Box (NNC Polyhedron y, Complexity Class complexity)• Rational Box (Grid y, Complexity Class complexity)• Rational Box (Float Box y, Complexity Class complexity)• Rational Box (BD Shape float y, Complexity Class complexity)• Rational Box (Octagonal Shape float y, Complexity Class complexity)• Rational Box (Double Box y, Complexity Class complexity)• Rational Box (BD Shape double y, Complexity Class complexity)• Rational Box (Octagonal Shape double y, Complexity Class complexity)• Rational Box (Long Double Box y, Complexity Class complexity)

295

• Rational Box (BD Shape long double y, Complexity Class complexity)• Rational Box (Octagonal Shape long double y, Complexity Class complexity)• Rational Box (Constraint System cs)• Rational Box (Congruence System cs)• Rational Box (Generator System cs)• native void swap (Rational Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Rational Box y)• native boolean strictly contains (Rational Box y)• native boolean is disjoint from (Rational Box y)• native boolean equals (Rational Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)

296

• native void refine with congruences (Congruence System c)• native void intersection assign (Rational Box p)• native void upper bound assign (Rational Box p)• native void difference assign (Rational Box p)• native void concatenate assign (Rational Box p)• native void time elapse assign (Rational Box p)• native boolean upper bound assign if exact (Rational Box y)• native boolean simplify using context assign (Rational Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Rational Box y, By Reference< Integer > tp)• native void widening assign (Rational Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Rational Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Rational Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩



297


• static native Pair< Rational Box, Pointset Powerset NNC Polyhedron > linear partition (Rational←↩

Box p, Rational Box q)




Java class interfacing C++ Parma Polyhedra Library::Rational Box.The documentation for this class was generated from the following file:

• Rational Box.java

10.152 parma polyhedra library.Relation Symbol Enum ReferenceRelation symbols.



Public Attributes

• LESS THAN

Less than.

• LESS OR EQUAL

Less than or equal to.

• EQUAL

Equal to.

• GREATER OR EQUAL

Greater than or equal to.

• GREATER THAN

Greater than.


Relation symbols.The documentation for this enum was generated from the following file:

• Relation Symbol.java

10.153 parma polyhedra library.Timeout Exception Class ReferenceExceptions caused by timeout expiring.



• Timeout Exception (String s)

Constructor.

298


Exceptions caused by timeout expiring.The documentation for this class was generated from the following file:

• Timeout Exception.java

10.154 parma polyhedra library.Uint16 Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Uint16 Box.



• Uint16 Box (long num dimensions, Degenerate Element kind)• Uint16 Box (Int8 Box y)• Uint16 Box (Int16 Box y)• Uint16 Box (Int32 Box y)• Uint16 Box (Int64 Box y)• Uint16 Box (Uint8 Box y)• Uint16 Box (Uint16 Box y)• Uint16 Box (Uint32 Box y)• Uint16 Box (Uint64 Box y)• Uint16 Box (Z Box y)• Uint16 Box (Rational Box y)• Uint16 Box (BD Shape int8 t y)• Uint16 Box (BD Shape int16 t y)• Uint16 Box (BD Shape int32 t y)• Uint16 Box (BD Shape int64 t y)• Uint16 Box (BD Shape mpz class y)• Uint16 Box (BD Shape mpq class y)• Uint16 Box (Octagonal Shape int8 t y)• Uint16 Box (Octagonal Shape int16 t y)• Uint16 Box (Octagonal Shape int32 t y)• Uint16 Box (Octagonal Shape int64 t y)• Uint16 Box (Octagonal Shape mpz class y)• Uint16 Box (Octagonal Shape mpq class y)• Uint16 Box (C Polyhedron y)• Uint16 Box (NNC Polyhedron y)• Uint16 Box (Grid y)• Uint16 Box (Float Box y)• Uint16 Box (BD Shape float y)• Uint16 Box (Octagonal Shape float y)• Uint16 Box (Double Box y)• Uint16 Box (BD Shape double y)• Uint16 Box (Octagonal Shape double y)• Uint16 Box (Long Double Box y)• Uint16 Box (BD Shape long double y)• Uint16 Box (Octagonal Shape long double y)• Uint16 Box (Int8 Box y, Complexity Class complexity)• Uint16 Box (Int16 Box y, Complexity Class complexity)• Uint16 Box (Int32 Box y, Complexity Class complexity)

299

• Uint16 Box (Int64 Box y, Complexity Class complexity)• Uint16 Box (Uint8 Box y, Complexity Class complexity)• Uint16 Box (Uint16 Box y, Complexity Class complexity)• Uint16 Box (Uint32 Box y, Complexity Class complexity)• Uint16 Box (Uint64 Box y, Complexity Class complexity)• Uint16 Box (Z Box y, Complexity Class complexity)• Uint16 Box (Rational Box y, Complexity Class complexity)• Uint16 Box (BD Shape int8 t y, Complexity Class complexity)• Uint16 Box (BD Shape int16 t y, Complexity Class complexity)• Uint16 Box (BD Shape int32 t y, Complexity Class complexity)• Uint16 Box (BD Shape int64 t y, Complexity Class complexity)• Uint16 Box (BD Shape mpz class y, Complexity Class complexity)• Uint16 Box (BD Shape mpq class y, Complexity Class complexity)• Uint16 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Uint16 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Uint16 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Uint16 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Uint16 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Uint16 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Uint16 Box (C Polyhedron y, Complexity Class complexity)• Uint16 Box (NNC Polyhedron y, Complexity Class complexity)• Uint16 Box (Grid y, Complexity Class complexity)• Uint16 Box (Float Box y, Complexity Class complexity)• Uint16 Box (BD Shape float y, Complexity Class complexity)• Uint16 Box (Octagonal Shape float y, Complexity Class complexity)• Uint16 Box (Double Box y, Complexity Class complexity)• Uint16 Box (BD Shape double y, Complexity Class complexity)• Uint16 Box (Octagonal Shape double y, Complexity Class complexity)• Uint16 Box (Long Double Box y, Complexity Class complexity)• Uint16 Box (BD Shape long double y, Complexity Class complexity)• Uint16 Box (Octagonal Shape long double y, Complexity Class complexity)• Uint16 Box (Constraint System cs)• Uint16 Box (Congruence System cs)• Uint16 Box (Generator System cs)• native void swap (Uint16 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()

300

• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Uint16 Box y)• native boolean strictly contains (Uint16 Box y)• native boolean is disjoint from (Uint16 Box y)• native boolean equals (Uint16 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Uint16 Box p)• native void upper bound assign (Uint16 Box p)• native void difference assign (Uint16 Box p)• native void concatenate assign (Uint16 Box p)• native void time elapse assign (Uint16 Box p)• native boolean upper bound assign if exact (Uint16 Box y)• native boolean simplify using context assign (Uint16 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩





301



Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Uint16 Box y, By Reference< Integer > tp)• native void widening assign (Uint16 Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Uint16 Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Uint16 Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Uint16 Box, Pointset Powerset NNC Polyhedron > linear partition (Uint16←↩

Box p, Uint16 Box q)




Java class interfacing C++ Parma Polyhedra Library::Uint16 Box.The documentation for this class was generated from the following file:

• Uint16 Box.java

10.155 parma polyhedra library.Uint32 Box Class Reference

Java class interfacing C++ Parma Polyhedra Library::Uint32 Box.Inherits parma polyhedra library.PPL Object.

302


• Uint32 Box (long num dimensions, Degenerate Element kind)• Uint32 Box (Int8 Box y)• Uint32 Box (Int16 Box y)• Uint32 Box (Int32 Box y)• Uint32 Box (Int64 Box y)• Uint32 Box (Uint8 Box y)• Uint32 Box (Uint16 Box y)• Uint32 Box (Uint32 Box y)• Uint32 Box (Uint64 Box y)• Uint32 Box (Z Box y)• Uint32 Box (Rational Box y)• Uint32 Box (BD Shape int8 t y)• Uint32 Box (BD Shape int16 t y)• Uint32 Box (BD Shape int32 t y)• Uint32 Box (BD Shape int64 t y)• Uint32 Box (BD Shape mpz class y)• Uint32 Box (BD Shape mpq class y)• Uint32 Box (Octagonal Shape int8 t y)• Uint32 Box (Octagonal Shape int16 t y)• Uint32 Box (Octagonal Shape int32 t y)• Uint32 Box (Octagonal Shape int64 t y)• Uint32 Box (Octagonal Shape mpz class y)• Uint32 Box (Octagonal Shape mpq class y)• Uint32 Box (C Polyhedron y)• Uint32 Box (NNC Polyhedron y)• Uint32 Box (Grid y)• Uint32 Box (Float Box y)• Uint32 Box (BD Shape float y)• Uint32 Box (Octagonal Shape float y)• Uint32 Box (Double Box y)• Uint32 Box (BD Shape double y)• Uint32 Box (Octagonal Shape double y)• Uint32 Box (Long Double Box y)• Uint32 Box (BD Shape long double y)• Uint32 Box (Octagonal Shape long double y)• Uint32 Box (Int8 Box y, Complexity Class complexity)• Uint32 Box (Int16 Box y, Complexity Class complexity)• Uint32 Box (Int32 Box y, Complexity Class complexity)• Uint32 Box (Int64 Box y, Complexity Class complexity)• Uint32 Box (Uint8 Box y, Complexity Class complexity)• Uint32 Box (Uint16 Box y, Complexity Class complexity)• Uint32 Box (Uint32 Box y, Complexity Class complexity)• Uint32 Box (Uint64 Box y, Complexity Class complexity)• Uint32 Box (Z Box y, Complexity Class complexity)• Uint32 Box (Rational Box y, Complexity Class complexity)• Uint32 Box (BD Shape int8 t y, Complexity Class complexity)• Uint32 Box (BD Shape int16 t y, Complexity Class complexity)• Uint32 Box (BD Shape int32 t y, Complexity Class complexity)• Uint32 Box (BD Shape int64 t y, Complexity Class complexity)

303

• Uint32 Box (BD Shape mpz class y, Complexity Class complexity)• Uint32 Box (BD Shape mpq class y, Complexity Class complexity)• Uint32 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Uint32 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Uint32 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Uint32 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Uint32 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Uint32 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Uint32 Box (C Polyhedron y, Complexity Class complexity)• Uint32 Box (NNC Polyhedron y, Complexity Class complexity)• Uint32 Box (Grid y, Complexity Class complexity)• Uint32 Box (Float Box y, Complexity Class complexity)• Uint32 Box (BD Shape float y, Complexity Class complexity)• Uint32 Box (Octagonal Shape float y, Complexity Class complexity)• Uint32 Box (Double Box y, Complexity Class complexity)• Uint32 Box (BD Shape double y, Complexity Class complexity)• Uint32 Box (Octagonal Shape double y, Complexity Class complexity)• Uint32 Box (Long Double Box y, Complexity Class complexity)• Uint32 Box (BD Shape long double y, Complexity Class complexity)• Uint32 Box (Octagonal Shape long double y, Complexity Class complexity)• Uint32 Box (Constraint System cs)• Uint32 Box (Congruence System cs)• Uint32 Box (Generator System cs)• native void swap (Uint32 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩




Boolean > maximum)

304




• native boolean contains (Uint32 Box y)• native boolean strictly contains (Uint32 Box y)• native boolean is disjoint from (Uint32 Box y)• native boolean equals (Uint32 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Uint32 Box p)• native void upper bound assign (Uint32 Box p)• native void difference assign (Uint32 Box p)• native void concatenate assign (Uint32 Box p)• native void time elapse assign (Uint32 Box p)• native boolean upper bound assign if exact (Uint32 Box y)• native boolean simplify using context assign (Uint32 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)

305

• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Uint32 Box y, By Reference< Integer > tp)• native void widening assign (Uint32 Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Uint32 Box y, Constraint System cs, By Reference<











• Uint32 Box.java




• Uint64 Box (long num dimensions, Degenerate Element kind)• Uint64 Box (Int8 Box y)• Uint64 Box (Int16 Box y)• Uint64 Box (Int32 Box y)• Uint64 Box (Int64 Box y)• Uint64 Box (Uint8 Box y)• Uint64 Box (Uint16 Box y)• Uint64 Box (Uint32 Box y)• Uint64 Box (Uint64 Box y)• Uint64 Box (Z Box y)• Uint64 Box (Rational Box y)• Uint64 Box (BD Shape int8 t y)• Uint64 Box (BD Shape int16 t y)

306

• Uint64 Box (BD Shape int32 t y)• Uint64 Box (BD Shape int64 t y)• Uint64 Box (BD Shape mpz class y)• Uint64 Box (BD Shape mpq class y)• Uint64 Box (Octagonal Shape int8 t y)• Uint64 Box (Octagonal Shape int16 t y)• Uint64 Box (Octagonal Shape int32 t y)• Uint64 Box (Octagonal Shape int64 t y)• Uint64 Box (Octagonal Shape mpz class y)• Uint64 Box (Octagonal Shape mpq class y)• Uint64 Box (C Polyhedron y)• Uint64 Box (NNC Polyhedron y)• Uint64 Box (Grid y)• Uint64 Box (Float Box y)• Uint64 Box (BD Shape float y)• Uint64 Box (Octagonal Shape float y)• Uint64 Box (Double Box y)• Uint64 Box (BD Shape double y)• Uint64 Box (Octagonal Shape double y)• Uint64 Box (Long Double Box y)• Uint64 Box (BD Shape long double y)• Uint64 Box (Octagonal Shape long double y)• Uint64 Box (Int8 Box y, Complexity Class complexity)• Uint64 Box (Int16 Box y, Complexity Class complexity)• Uint64 Box (Int32 Box y, Complexity Class complexity)• Uint64 Box (Int64 Box y, Complexity Class complexity)• Uint64 Box (Uint8 Box y, Complexity Class complexity)• Uint64 Box (Uint16 Box y, Complexity Class complexity)• Uint64 Box (Uint32 Box y, Complexity Class complexity)• Uint64 Box (Uint64 Box y, Complexity Class complexity)• Uint64 Box (Z Box y, Complexity Class complexity)• Uint64 Box (Rational Box y, Complexity Class complexity)• Uint64 Box (BD Shape int8 t y, Complexity Class complexity)• Uint64 Box (BD Shape int16 t y, Complexity Class complexity)• Uint64 Box (BD Shape int32 t y, Complexity Class complexity)• Uint64 Box (BD Shape int64 t y, Complexity Class complexity)• Uint64 Box (BD Shape mpz class y, Complexity Class complexity)• Uint64 Box (BD Shape mpq class y, Complexity Class complexity)• Uint64 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Uint64 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Uint64 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Uint64 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Uint64 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Uint64 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Uint64 Box (C Polyhedron y, Complexity Class complexity)• Uint64 Box (NNC Polyhedron y, Complexity Class complexity)• Uint64 Box (Grid y, Complexity Class complexity)• Uint64 Box (Float Box y, Complexity Class complexity)• Uint64 Box (BD Shape float y, Complexity Class complexity)• Uint64 Box (Octagonal Shape float y, Complexity Class complexity)

307

• Uint64 Box (Double Box y, Complexity Class complexity)• Uint64 Box (BD Shape double y, Complexity Class complexity)• Uint64 Box (Octagonal Shape double y, Complexity Class complexity)• Uint64 Box (Long Double Box y, Complexity Class complexity)• Uint64 Box (BD Shape long double y, Complexity Class complexity)• Uint64 Box (Octagonal Shape long double y, Complexity Class complexity)• Uint64 Box (Constraint System cs)• Uint64 Box (Congruence System cs)• Uint64 Box (Generator System cs)• native void swap (Uint64 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Uint64 Box y)• native boolean strictly contains (Uint64 Box y)• native boolean is disjoint from (Uint64 Box y)• native boolean equals (Uint64 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)

308

• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Uint64 Box p)• native void upper bound assign (Uint64 Box p)• native void difference assign (Uint64 Box p)• native void concatenate assign (Uint64 Box p)• native void time elapse assign (Uint64 Box p)• native boolean upper bound assign if exact (Uint64 Box y)• native boolean simplify using context assign (Uint64 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩










309








• Uint64 Box.java




• Uint8 Box (long num dimensions, Degenerate Element kind)• Uint8 Box (Int8 Box y)• Uint8 Box (Int16 Box y)• Uint8 Box (Int32 Box y)• Uint8 Box (Int64 Box y)• Uint8 Box (Uint8 Box y)• Uint8 Box (Uint16 Box y)• Uint8 Box (Uint32 Box y)• Uint8 Box (Uint64 Box y)• Uint8 Box (Z Box y)• Uint8 Box (Rational Box y)• Uint8 Box (BD Shape int8 t y)• Uint8 Box (BD Shape int16 t y)• Uint8 Box (BD Shape int32 t y)• Uint8 Box (BD Shape int64 t y)• Uint8 Box (BD Shape mpz class y)• Uint8 Box (BD Shape mpq class y)• Uint8 Box (Octagonal Shape int8 t y)• Uint8 Box (Octagonal Shape int16 t y)• Uint8 Box (Octagonal Shape int32 t y)• Uint8 Box (Octagonal Shape int64 t y)• Uint8 Box (Octagonal Shape mpz class y)• Uint8 Box (Octagonal Shape mpq class y)• Uint8 Box (C Polyhedron y)• Uint8 Box (NNC Polyhedron y)• Uint8 Box (Grid y)• Uint8 Box (Float Box y)• Uint8 Box (BD Shape float y)• Uint8 Box (Octagonal Shape float y)• Uint8 Box (Double Box y)

310

• Uint8 Box (BD Shape double y)• Uint8 Box (Octagonal Shape double y)• Uint8 Box (Long Double Box y)• Uint8 Box (BD Shape long double y)• Uint8 Box (Octagonal Shape long double y)• Uint8 Box (Int8 Box y, Complexity Class complexity)• Uint8 Box (Int16 Box y, Complexity Class complexity)• Uint8 Box (Int32 Box y, Complexity Class complexity)• Uint8 Box (Int64 Box y, Complexity Class complexity)• Uint8 Box (Uint8 Box y, Complexity Class complexity)• Uint8 Box (Uint16 Box y, Complexity Class complexity)• Uint8 Box (Uint32 Box y, Complexity Class complexity)• Uint8 Box (Uint64 Box y, Complexity Class complexity)• Uint8 Box (Z Box y, Complexity Class complexity)• Uint8 Box (Rational Box y, Complexity Class complexity)• Uint8 Box (BD Shape int8 t y, Complexity Class complexity)• Uint8 Box (BD Shape int16 t y, Complexity Class complexity)• Uint8 Box (BD Shape int32 t y, Complexity Class complexity)• Uint8 Box (BD Shape int64 t y, Complexity Class complexity)• Uint8 Box (BD Shape mpz class y, Complexity Class complexity)• Uint8 Box (BD Shape mpq class y, Complexity Class complexity)• Uint8 Box (Octagonal Shape int8 t y, Complexity Class complexity)• Uint8 Box (Octagonal Shape int16 t y, Complexity Class complexity)• Uint8 Box (Octagonal Shape int32 t y, Complexity Class complexity)• Uint8 Box (Octagonal Shape int64 t y, Complexity Class complexity)• Uint8 Box (Octagonal Shape mpz class y, Complexity Class complexity)• Uint8 Box (Octagonal Shape mpq class y, Complexity Class complexity)• Uint8 Box (C Polyhedron y, Complexity Class complexity)• Uint8 Box (NNC Polyhedron y, Complexity Class complexity)• Uint8 Box (Grid y, Complexity Class complexity)• Uint8 Box (Float Box y, Complexity Class complexity)• Uint8 Box (BD Shape float y, Complexity Class complexity)• Uint8 Box (Octagonal Shape float y, Complexity Class complexity)• Uint8 Box (Double Box y, Complexity Class complexity)• Uint8 Box (BD Shape double y, Complexity Class complexity)• Uint8 Box (Octagonal Shape double y, Complexity Class complexity)• Uint8 Box (Long Double Box y, Complexity Class complexity)• Uint8 Box (BD Shape long double y, Complexity Class complexity)• Uint8 Box (Octagonal Shape long double y, Complexity Class complexity)• Uint8 Box (Constraint System cs)• Uint8 Box (Congruence System cs)• Uint8 Box (Generator System cs)• native void swap (Uint8 Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()

311

• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Uint8 Box y)• native boolean strictly contains (Uint8 Box y)• native boolean is disjoint from (Uint8 Box y)• native boolean equals (Uint8 Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Uint8 Box p)• native void upper bound assign (Uint8 Box p)• native void difference assign (Uint8 Box p)• native void concatenate assign (Uint8 Box p)• native void time elapse assign (Uint8 Box p)• native boolean upper bound assign if exact (Uint8 Box y)• native boolean simplify using context assign (Uint8 Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)

312

• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩











• static native Pair< Uint8 Box, Pointset Powerset NNC Polyhedron > linear partition (Uint8 Boxp, Uint8 Box q)





• Uint8 Box.java

313

10.158 parma polyhedra library.Variable Class ReferenceA dimension of the vector space.

Inherits Comparable< Variable >.


• Variable (long i)

Builds the variable corresponding to the Cartesian axis of index i.• long id ()

Returns the index of the Cartesian axis associated to this.• int compareTo (Variable v)

Returns a negative number if this is smaller than v, a zero if this equals v, a positive number if v isgreater than v.



• static native void setStringifier (Variable Stringifier vs)

Sets the variable stringifier object.


A dimension of the vector space.An object of the class Variable represents a dimension of the space, that is one of the Cartesian axes.

Variables are used as basic blocks in order to build more complex linear expressions. Each variable isidentified by a non-negative integer, representing the index of the corresponding Cartesian axis (the firstaxis has index 0).


parma polyhedra library.Variable.Variable ( long i ) [inline] Builds the variable correspond-ing to the Cartesian axis of index i.Exceptions

RuntimeErrorException Thrown if i is has negative value.


static native void parma polyhedra library.Variable.setStringifier ( Variable Stringifier vs ) [static]Sets the variable stringifier object.

A variable stringifier object provides customization for the toStringmethod; if no variable stringifierobject is set (or if it is set to a null refeerence value), the PPL default variable output function will be used.


• Variable.java

10.159 parma polyhedra library.Variable Stringifier Interface ReferenceAn interface for objects converting a Variable id to a string.


• String stringify (long var id)

314


An interface for objects converting a Variable id to a string.If customized variable output is required, the user should implement this interface and pass a corre-

sponding instance to Variable's static method setStringifier.The documentation for this interface was generated from the following file:

• Variable Stringifier.java

10.160 parma polyhedra library.Variables Set Class ReferenceA java.util.TreeSet of variables' indexes.

Inherits TreeSet< Variable >.


• Variables Set ()Builds the empty set of variable indexes.


A java.util.TreeSet of variables' indexes.The documentation for this class was generated from the following file:

• Variables Set.java

10.161 parma polyhedra library.Z Box Class ReferenceJava class interfacing C++ Parma Polyhedra Library::Z Box.



• Z Box (long num dimensions, Degenerate Element kind)• Z Box (Int8 Box y)• Z Box (Int16 Box y)• Z Box (Int32 Box y)• Z Box (Int64 Box y)• Z Box (Uint8 Box y)• Z Box (Uint16 Box y)• Z Box (Uint32 Box y)• Z Box (Uint64 Box y)• Z Box (Z Box y)• Z Box (Rational Box y)• Z Box (BD Shape int8 t y)• Z Box (BD Shape int16 t y)• Z Box (BD Shape int32 t y)• Z Box (BD Shape int64 t y)• Z Box (BD Shape mpz class y)• Z Box (BD Shape mpq class y)• Z Box (Octagonal Shape int8 t y)• Z Box (Octagonal Shape int16 t y)• Z Box (Octagonal Shape int32 t y)• Z Box (Octagonal Shape int64 t y)

315

• Z Box (Octagonal Shape mpz class y)• Z Box (Octagonal Shape mpq class y)• Z Box (C Polyhedron y)• Z Box (NNC Polyhedron y)• Z Box (Grid y)• Z Box (Float Box y)• Z Box (BD Shape float y)• Z Box (Octagonal Shape float y)• Z Box (Double Box y)• Z Box (BD Shape double y)• Z Box (Octagonal Shape double y)• Z Box (Long Double Box y)• Z Box (BD Shape long double y)• Z Box (Octagonal Shape long double y)• Z Box (Int8 Box y, Complexity Class complexity)• Z Box (Int16 Box y, Complexity Class complexity)• Z Box (Int32 Box y, Complexity Class complexity)• Z Box (Int64 Box y, Complexity Class complexity)• Z Box (Uint8 Box y, Complexity Class complexity)• Z Box (Uint16 Box y, Complexity Class complexity)• Z Box (Uint32 Box y, Complexity Class complexity)• Z Box (Uint64 Box y, Complexity Class complexity)• Z Box (Z Box y, Complexity Class complexity)• Z Box (Rational Box y, Complexity Class complexity)• Z Box (BD Shape int8 t y, Complexity Class complexity)• Z Box (BD Shape int16 t y, Complexity Class complexity)• Z Box (BD Shape int32 t y, Complexity Class complexity)• Z Box (BD Shape int64 t y, Complexity Class complexity)• Z Box (BD Shape mpz class y, Complexity Class complexity)• Z Box (BD Shape mpq class y, Complexity Class complexity)• Z Box (Octagonal Shape int8 t y, Complexity Class complexity)• Z Box (Octagonal Shape int16 t y, Complexity Class complexity)• Z Box (Octagonal Shape int32 t y, Complexity Class complexity)• Z Box (Octagonal Shape int64 t y, Complexity Class complexity)• Z Box (Octagonal Shape mpz class y, Complexity Class complexity)• Z Box (Octagonal Shape mpq class y, Complexity Class complexity)• Z Box (C Polyhedron y, Complexity Class complexity)• Z Box (NNC Polyhedron y, Complexity Class complexity)• Z Box (Grid y, Complexity Class complexity)• Z Box (Float Box y, Complexity Class complexity)• Z Box (BD Shape float y, Complexity Class complexity)• Z Box (Octagonal Shape float y, Complexity Class complexity)• Z Box (Double Box y, Complexity Class complexity)• Z Box (BD Shape double y, Complexity Class complexity)• Z Box (Octagonal Shape double y, Complexity Class complexity)• Z Box (Long Double Box y, Complexity Class complexity)• Z Box (BD Shape long double y, Complexity Class complexity)• Z Box (Octagonal Shape long double y, Complexity Class complexity)• Z Box (Constraint System cs)• Z Box (Congruence System cs)

316

• Z Box (Generator System cs)• native void swap (Z Box y)• native long space dimension ()• native long affine dimension ()• native Poly Con Relation relation with (Constraint c)• native Poly Gen Relation relation with (Generator c)• native Poly Con Relation relation with (Congruence c)• native Constraint System constraints ()• native Congruence System congruences ()• native Constraint System minimized constraints ()• native Congruence System minimized congruences ()• native boolean is empty ()• native boolean is universe ()• native boolean is bounded ()• native boolean contains integer point ()• native boolean is topologically closed ()• native boolean is discrete ()• native void topological closure assign ()• native boolean bounds from above (Linear Expression expr)• native boolean bounds from below (Linear Expression expr)• native boolean has upper bound (Variable var, Coefficient bound n, Coefficient bound d, By ←↩







cient val n, Coefficient val d)• native boolean contains (Z Box y)• native boolean strictly contains (Z Box y)• native boolean is disjoint from (Z Box y)• native boolean equals (Z Box p)• boolean equals (Object y)• native boolean OK ()• native void add constraint (Constraint c)• native void add congruence (Congruence c)• native void add constraints (Constraint System c)• native void add congruences (Congruence System c)• native void refine with constraint (Constraint c)• native void refine with congruence (Congruence c)• native void refine with constraints (Constraint System c)• native void refine with congruences (Congruence System c)• native void intersection assign (Z Box p)• native void upper bound assign (Z Box p)• native void difference assign (Z Box p)

317

• native void concatenate assign (Z Box p)• native void time elapse assign (Z Box p)• native boolean upper bound assign if exact (Z Box y)• native boolean simplify using context assign (Z Box p)• native boolean constrains (Variable var)• native void unconstrain space dimension (Variable var)• native void unconstrain space dimensions (Variables Set vars)• native void affine image (Variable var, Linear Expression expr, Coefficient denominator)• native void affine preimage (Variable var, Linear Expression expr, Coefficient denominator)• native void bounded affine image (Variable var, Linear Expression lb expr, Linear Expression ub←↩






Expression rhs)• native void add space dimensions and embed (long m)• native void add space dimensions and project (long m)• native void remove space dimensions (Variables Set vars)• native void remove higher space dimensions (long new dimension)• native void expand space dimension (Variable var, long m)• native void fold space dimensions (Variables Set vars, Variable dest)• native void map space dimensions (Partial Function pfunc)• native void drop some non integer points (Complexity Class complexity)• native void drop some non integer points (Variables Set vars, Complexity Class complexity)• native String ascii dump ()• native long external memory in bytes ()• native long total memory in bytes ()• native void CC76 widening assign (Z Box y, By Reference< Integer > tp)• native void widening assign (Z Box y, By Reference< Integer > tp)• native void limited CC76 extrapolation assign (Z Box y, Constraint System cs, By Reference<

Integer > tp)• native void CC76 narrowing assign (Z Box arg)• native void wrap assign (Variables Set vars, Bounded Integer Type Width w, Bounded Integer ←↩




• static native Pair< Z Box, Pointset Powerset NNC Polyhedron > linear partition (Z Box p, Z ←↩

Box q)

318




Java class interfacing C++ Parma Polyhedra Library::Z Box.The documentation for this class was generated from the following file:

• Z Box.java

319

Indexadd constraint

parma polyhedra library::MIP Problem, 145parma polyhedra library::PIP Problem, 191

add constraintsparma polyhedra library::MIP Problem, 146parma polyhedra library::PIP Problem, 191

add space dimensions and embedparma polyhedra library::MIP Problem, 145parma polyhedra library::PIP Problem, 191

add to integer space dimensionsparma polyhedra library::MIP Problem, 145

bannerparma polyhedra library::Parma Polyhedra Library,

185

clearparma polyhedra library::MIP Problem, 145parma polyhedra library::PIP Problem, 191

closure pointparma polyhedra library::Generator, 107

Coefficientparma polyhedra library::Coefficient, 80

constraintsparma polyhedra library::PIP Tree Node, 195

divisorparma polyhedra library::Generator, 108parma polyhedra library::Grid Generator, 114

evaluate objective functionparma polyhedra library::MIP Problem, 146

feasible pointparma polyhedra library::MIP Problem, 146

finalize libraryparma polyhedra library::Parma Polyhedra Library,

185

grid lineparma polyhedra library::Grid Generator, 113

grid pointparma polyhedra library::Grid Generator, 114

has empty codomainparma polyhedra library::Partial Function, 187

initialize libraryparma polyhedra library::Parma Polyhedra Library,

185is satisfiable

parma polyhedra library::MIP Problem, 146

parma polyhedra library::PIP Problem, 192

Java Language Interface, 31

lineparma polyhedra library::Generator, 107

MIP Problemparma polyhedra library::MIP Problem, 144, 145

mapsparma polyhedra library::Partial Function, 187

optimal valueparma polyhedra library::MIP Problem, 147

optimizing pointparma polyhedra library::MIP Problem, 147

PIP Problemparma polyhedra library::PIP Problem, 191

parameterparma polyhedra library::Grid Generator, 114

parametric valuesparma polyhedra library::PIP Solution Node, 194

parma polyhedra library, 33parma polyhedra library.Artificial Parameter, 41parma polyhedra library.Artificial Parameter Sequence,

42parma polyhedra library.BD Shape double, 42parma polyhedra library.BD Shape float, 46parma polyhedra library.BD Shape int16 t, 50parma polyhedra library.BD Shape int32 t, 53parma polyhedra library.BD Shape int64 t, 57parma polyhedra library.BD Shape int8 t, 61parma polyhedra library.BD Shape long double, 65parma polyhedra library.BD Shape mpq class, 68parma polyhedra library.BD Shape mpz class, 72parma polyhedra library.Bounded Integer Type Overflow,

76parma polyhedra library.Bounded Integer Type Representation,

76parma polyhedra library.Bounded Integer Type Width,

77parma polyhedra library.By Reference< T >, 77parma polyhedra library.C Polyhedron, 78parma polyhedra library.Coefficient, 80parma polyhedra library.Complexity Class, 81parma polyhedra library.Congruence, 81parma polyhedra library.Congruence System, 82parma polyhedra library.Constraint, 82parma polyhedra library.Constraint System, 83parma polyhedra library.Constraints Product C Polyhedron←↩

Grid, 83

321

parma polyhedra library.Constraints Product Grid←↩

C Polyhedron, 87parma polyhedra library.Constraints Product Grid←↩

NNC Polyhedron, 90parma polyhedra library.Constraints Product NN←↩

C Polyhedron Grid, 94parma polyhedra library.Control Parameter Name, 98parma polyhedra library.Control Parameter Value, 98parma polyhedra library.Degenerate Element, 98parma polyhedra library.Domain Error Exception, 99parma polyhedra library.Double Box, 99parma polyhedra library.Float Box, 103parma polyhedra library.Generator, 106parma polyhedra library.Generator System, 108parma polyhedra library.Generator Type, 108parma polyhedra library.Grid, 109parma polyhedra library.Grid Generator, 113parma polyhedra library.Grid Generator System, 114parma polyhedra library.Grid Generator Type, 114parma polyhedra library.IO, 130parma polyhedra library.Int16 Box, 115parma polyhedra library.Int32 Box, 119parma polyhedra library.Int64 Box, 122parma polyhedra library.Int8 Box, 126parma polyhedra library.Invalid Argument Exception,

130parma polyhedra library.Length Error Exception, 131parma polyhedra library.Linear Expression, 131parma polyhedra library.Linear Expression Coefficient,

132parma polyhedra library.Linear Expression Difference,

133parma polyhedra library.Linear Expression Sum, 134parma polyhedra library.Linear Expression Times, 135parma polyhedra library.Linear Expression Unary←↩

Minus, 136parma polyhedra library.Linear Expression Variable,

137parma polyhedra library.Logic Error Exception, 137parma polyhedra library.Long Double Box, 138parma polyhedra library.MIP Problem, 141parma polyhedra library.MIP Problem Status, 147parma polyhedra library.NNC Polyhedron, 147parma polyhedra library.Octagonal Shape double, 150parma polyhedra library.Octagonal Shape float, 153parma polyhedra library.Octagonal Shape int16 t, 157parma polyhedra library.Octagonal Shape int32 t, 161parma polyhedra library.Octagonal Shape int64 t, 165parma polyhedra library.Octagonal Shape int8 t, 168parma polyhedra library.Octagonal Shape long double,

172parma polyhedra library.Octagonal Shape mpq class,

176

parma polyhedra library.Octagonal Shape mpz class,179

parma polyhedra library.Optimization Mode, 183parma polyhedra library.Overflow Error Exception,

184parma polyhedra library.PIP Decision Node, 188parma polyhedra library.PIP Problem, 188parma polyhedra library.PIP Problem Control Parameter←↩

Name, 192parma polyhedra library.PIP Problem Control Parameter←↩

Value, 192parma polyhedra library.PIP Problem Status, 193parma polyhedra library.PIP Solution Node, 193parma polyhedra library.PIP Tree Node, 194parma polyhedra library.Pair< K, V >, 184parma polyhedra library.Parma Polyhedra Library, 184parma polyhedra library.Partial Function, 187parma polyhedra library.Pointset Powerset BD Shape←↩

double, 195parma polyhedra library.Pointset Powerset BD Shape←↩

double Iterator, 197parma polyhedra library.Pointset Powerset BD Shape←↩

float, 198parma polyhedra library.Pointset Powerset BD Shape←↩

float Iterator, 200parma polyhedra library.Pointset Powerset BD Shape←↩

int16 t, 201parma polyhedra library.Pointset Powerset BD Shape←↩

int16 t Iterator, 203parma polyhedra library.Pointset Powerset BD Shape←↩







long double, 212parma polyhedra library.Pointset Powerset BD Shape←↩

long double Iterator, 214parma polyhedra library.Pointset Powerset BD Shape←↩

mpq class, 215parma polyhedra library.Pointset Powerset BD Shape←↩

mpq class Iterator, 217parma polyhedra library.Pointset Powerset BD Shape←↩

mpz class, 218parma polyhedra library.Pointset Powerset BD Shape←↩

mpz class Iterator, 220

322

parma polyhedra library.Pointset Powerset C Polyhedron,221

parma polyhedra library.Pointset Powerset C Polyhedron←↩

Iterator, 223parma polyhedra library.Pointset Powerset Double←↩

Box, 223parma polyhedra library.Pointset Powerset Double←↩

Box Iterator, 226parma polyhedra library.Pointset Powerset Float ←↩

Box, 226parma polyhedra library.Pointset Powerset Float ←↩

Box Iterator, 228parma polyhedra library.Pointset Powerset Grid, 229parma polyhedra library.Pointset Powerset Grid ←↩

Iterator, 231parma polyhedra library.Pointset Powerset Int16 ←↩

Box, 232parma polyhedra library.Pointset Powerset Int16 ←↩

Box Iterator, 234parma polyhedra library.Pointset Powerset Int32 ←↩


Box Iterator, 237parma polyhedra library.Pointset Powerset Int64 ←↩


Box Iterator, 239parma polyhedra library.Pointset Powerset Int8 Box,

240parma polyhedra library.Pointset Powerset Int8 Box←↩

Iterator, 242parma polyhedra library.Pointset Powerset Long ←↩

Double Box, 243parma polyhedra library.Pointset Powerset Long ←↩

Double Box Iterator, 245parma polyhedra library.Pointset Powerset NNC ←↩

Polyhedron, 245parma polyhedra library.Pointset Powerset NNC ←↩

Polyhedron Iterator, 248parma polyhedra library.Pointset Powerset Octagonal←↩

Shape double, 248parma polyhedra library.Pointset Powerset Octagonal←↩

Shape double Iterator, 250parma polyhedra library.Pointset Powerset Octagonal←↩

Shape float, 251parma polyhedra library.Pointset Powerset Octagonal←↩

Shape float Iterator, 253parma polyhedra library.Pointset Powerset Octagonal←↩

Shape int16 t, 254parma polyhedra library.Pointset Powerset Octagonal←↩

Shape int16 t Iterator, 256parma polyhedra library.Pointset Powerset Octagonal←↩

Shape int32 t, 257

parma polyhedra library.Pointset Powerset Octagonal←↩






Shape long double, 265parma polyhedra library.Pointset Powerset Octagonal←↩

Shape long double Iterator, 268parma polyhedra library.Pointset Powerset Octagonal←↩

Shape mpq class, 268parma polyhedra library.Pointset Powerset Octagonal←↩

Shape mpq class Iterator, 271parma polyhedra library.Pointset Powerset Octagonal←↩

Shape mpz class, 271parma polyhedra library.Pointset Powerset Octagonal←↩

Shape mpz class Iterator, 273parma polyhedra library.Pointset Powerset Rational←↩

Box, 274parma polyhedra library.Pointset Powerset Rational←↩

Box Iterator, 276parma polyhedra library.Pointset Powerset Uint16←↩

Box, 277parma polyhedra library.Pointset Powerset Uint16←↩







Box Iterator, 287parma polyhedra library.Pointset Powerset Z Box, 288parma polyhedra library.Pointset Powerset Z Box←↩

Iterator, 290parma polyhedra library.Poly Con Relation, 290parma polyhedra library.Poly Gen Relation, 291parma polyhedra library.Polyhedron, 292parma polyhedra library.Rational Box, 294parma polyhedra library.Relation Symbol, 298parma polyhedra library.Timeout Exception, 298parma polyhedra library.Uint16 Box, 299parma polyhedra library.Uint32 Box, 302parma polyhedra library.Uint64 Box, 306

323

parma polyhedra library.Uint8 Box, 310parma polyhedra library.Variable, 314parma polyhedra library.Variable Stringifier, 314parma polyhedra library.Variables Set, 315parma polyhedra library.Z Box, 315parma polyhedra library::Coefficient

Coefficient, 80parma polyhedra library::Generator

closure point, 107divisor, 108line, 107point, 107ray, 107

parma polyhedra library::Grid Generatordivisor, 114grid line, 113grid point, 114parameter, 114

parma polyhedra library::IOwrap string, 130

parma polyhedra library::MIP Problemadd constraint, 145add constraints, 146add space dimensions and embed, 145add to integer space dimensions, 145clear, 145evaluate objective function, 146feasible point, 146is satisfiable, 146MIP Problem, 144, 145optimal value, 147optimizing point, 147set objective function, 146solve, 146

parma polyhedra library::PIP Problemadd constraint, 191add constraints, 191add space dimensions and embed, 191clear, 191is satisfiable, 192PIP Problem, 191solve, 192

parma polyhedra library::PIP Solution Nodeparametric values, 194

parma polyhedra library::PIP Tree Nodeconstraints, 195

parma polyhedra library::Parma Polyhedra Librarybanner, 185finalize library, 185initialize library, 185restore pre PPL rounding, 186set deterministic timeout, 186set irrational precision, 186set rounding for PPL, 185

set timeout, 186parma polyhedra library::Partial Function

has empty codomain, 187maps, 187

parma polyhedra library::VariablesetStringifier, 314Variable, 314

pointparma polyhedra library::Generator, 107

rayparma polyhedra library::Generator, 107

restore pre PPL roundingparma polyhedra library::Parma Polyhedra Library,

186

set deterministic timeoutparma polyhedra library::Parma Polyhedra Library,

186set irrational precision

parma polyhedra library::Parma Polyhedra Library,186

set objective functionparma polyhedra library::MIP Problem, 146

set rounding for PPLparma polyhedra library::Parma Polyhedra Library,

185set timeout

parma polyhedra library::Parma Polyhedra Library,186

setStringifierparma polyhedra library::Variable, 314

solveparma polyhedra library::MIP Problem, 146parma polyhedra library::PIP Problem, 192

Variableparma polyhedra library::Variable, 314

wrap stringparma polyhedra library::IO, 130

324

· the parma polyhedra library conﬁgured java language interface user’s manual (version 1.2)...

Documents