NA-MKM 2004 Phoenix MKM and the NIST DLMF Dan Lozier National Institute of Standards and Technology Gaithersburg, MD

KM and MKMNA-MKM 2004 Phoenix2 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

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KM and MKMNA-MKM 2004 Phoenix8 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

DLMFNA-MKM 2004 Phoenix9 NIST Digital Library of Mathematical Functions Project project conceived sample chapter & prototype web site NSF funding received 2000 – 2004 Math content development, editing, validation Web development, inc. search & graphics 2005 – book published, web site released

DLMFNA-MKM 2004 Phoenix10 Personnel 4 principal editors 10 associate editors 35 authors 25 validators 15 NIST staff

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DLMFNA-MKM 2004 Phoenix13 DLMF Web Site Features –Math content –Metadata –Interactive graphics –Math-aware search Demonstration

SearchNA-MKM 2004 Phoenix24 DLMF Equation Search System DLMF Database Query Input Query Processing Search Engine Query Output Presentation Module

SearchNA-MKM 2004 Phoenix25 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

SearchNA-MKM 2004 Phoenix26 Examples OpsEntryOpsEntry Arith ops+ - * /Power, super^ ±,  +-, -+Subscript_ ≤, ≥ =~, ≈~, ~~ ,  =~, =- , not < !=, !< Goes to-> ,  =>, ∫, ∑int, sum∞infinity  nebla√sqrt

SearchNA-MKM 2004 Phoenix27 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

SearchNA-MKM 2004 Phoenix28 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,,]

SearchNA-MKM 2004 Phoenix29 DLMF Search Demonstrations Mathematica and Maple Illustrations Equation Search Page

Legendre FunctionsNA-MKM 2004 Phoenix38 Legendre Functions

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Spheroidal Wave Functions NA-MKM 2004 Phoenix46 Spheroidal Wave Functions

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Spheroidal Wave Functions NA-MKM 2004 Phoenix48

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Spheroidal Wave Functions NA-MKM 2004 Phoenix53 SW.6 Functions of Complex Argument

NA-MKM 2004 Phoenix54 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

NA-MKM 2004 Phoenix55 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