MKM and the NIST DLMF

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MKM and the NIST DLMF

• Dan Lozier
• National Institute of Standards and Technology
• Gaithersburg, MD 20899-8910

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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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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

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NIST Digital Library of Mathematical Functions
Project

• - 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

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Personnel

• 4 principal editors
• 10 associate editors
• 35 authors
• 25 validators
• 15 NIST staff

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DLMF Web Site

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

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DLMF Equation Search System
DLMF Database
Query Input
Query Processing
Search Engine
Query Output
Presentation Module
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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

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Examples
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Query Results 2 Choices

• Document list
• Links to DLMF sections
• Matching equations highlighted
• Equation list
• Created on-the-fly
• Links to containing document, positioned with
  matching equation at top of window

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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. Eulers generalized
  beta integral Betaz0,z1,,

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DLMF Search Demonstrations

• Mathematica and Maple Illustrations
• Equation Search Page

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Legendre Functions
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Spheroidal Wave Functions
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SW.6 Functions of Complex Argument
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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

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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