na-mkm 2004 phoenix mkm and the nist dlmf dan lozier national institute of standards and technology...

NA-MKM 2004 Phoenix

MKM and the NIST DLMF

Dan Lozier

National Institute of Standards and Technology

Gaithersburg, MD 20899-8910

KM and MKM NA-MKM 2004 Phoenix 2

Traditional Methods of KM

• Handbooks, dictionaries, encyclopedias, atlases

• Springer-NY search:Keyword “handbook”: 1125 hits“Handbook” in title/subtitle: 802 hits

• CRC Press search:“Handbook” in title/subtitle, “mathematics” as

subject/discipline: 41 hits


New Methods of KM for Math• Stimulus:

– CD/DVD, web sites, “digital technology”– Interactive graphics (scientific visualization)– Computer algebra, theorem provers

• Key research areas– Math notation and definition– Presentation/representation of math– Math-aware search– Hardware/software standards– Formal methods

DLMF NA-MKM 2004 Phoenix 9

NIST Digital Library of Mathematical Functions Project

1997 - project conceived

1998 - sample chapter & prototype web site

1999 - NSF funding received

2000 – 2004

Math content development, editing, validation

Web development, inc. search & graphics

2005 – book published, web site released


Personnel

• 4 principal editors

• 10 associate editors

• 35 authors

• 25 validators

• 15 NIST staff


DLMF Web Site

• Features– Math content– Metadata– Interactive graphics– Math-aware search

• Demonstration

Search NA-MKM 2004 Phoenix 24

DLMF Equation Search System

DLMFDatabase

QueryInput

Query Processing

SearchEngine

QueryOutput

PresentationModule


Query Expression and Entry

• Simplified, Latex-like query language

• Operators & symbols that can be expressed with 1 or 2 keyboard strokes are so entered

• Otherwise, alphabetical names are used (both full-names and short-hand names)

• “\” not needed

• {} and () are equivalent


Examples

Ops Entry Ops Entry

Arith ops + - * / Power, super ^

± , +- , -+ Subscript _

≤ , ≥ <= , >= ~ , ≈ ~ , ~~

, =~ , =- , not < != , !<

Goes to -> , => , <=>

∫ , ∑ int, sum ∞ infinity

nebla √ sqrt


Query Results: 2 Choices

1. Document list– Links to DLMF sections– Matching equations highlighted

2. Equation list• Created on-the-fly• Links to containing document, positioned

with matching equation at top of window


Recent Developments• Mathematica and Maple nomenclature

function names order of arguments

• Wild cards $ matches any one token \* matches any alphanumeric string in a token Null in argument list, e.g. Euler’s generalized

beta integral Beta[z0,z1,,]


DLMF Search Demonstrations

Mathematica and Maple Illustrations

Equation Search Page

http://localhost/plweb-cgi/equationsearch.pl

Legendre Functions NA-MKM 2004 Phoenix 38

Legendre Functions

Spheroidal Wave Functions

NA-MKM 2004 Phoenix 46




SW.6 Functions of Complex Argument


Implications for MKM

• For a given “family” of SF there exist– many alternative notations– a wide variety of useful definitions– Increased complications when numerical

computation is considered

• We want to be able to move freely among them• Real variables are hard enough• Complex variables are much harder


Future Directions at NIST• (Complete development of basic content)• (Publish book, release initial web site)• Improve web site

– XML/MathML– Content MathML– Improved search (XQUERY)– Rudimentary, at least, equation equivalences– Tables & graphs “on demand”

• Possible second edition, possible new subject area

na-mkm 2004 phoenix mkm and the nist dlmf dan lozier national institute of standards and technology...

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