DLMF Content Dictionaries Special Function Catalog The Next - PowerPoint PPT Presentation

DLMF Content Dictionaries The Next Iteration Bruce R. Miller NIST Background DLMF Content Dictionaries Special Function Catalog The Next Iteration DLMF Content Dictionaries Conclusion Bruce R. Miller NIST August 10, 2018

DLMF Content DLMF Project Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries Conclusion https://dlmf.nist.gov/

DLMF Content Goals Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function ◮ Up-to-date source of Properties of Mathematical Catalog Special Functions and Applications DLMF Content Dictionaries ◮ Preserve the character of a Handbook Conclusion Primarily for Physicists, Engineers, ◮ More than Book on the Web But not a CAS or ATP on the Web. ◮ Quarterly releases Errata; Clarifications; Additions; . . . Hear more from Adri Olde Daalhuis, Thursday morning.

DLMF Content Technical Goals Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries ◮ Maintainable, Conclusion ◮ Current with web-technologies ◮ Presentation MathML. ◮ Permalinks for reference data

DLMF Content Future Technical Goals Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog ◮ Machine-readable data/metadata DLMF Content Dictionaries ◮ Interoperability with other systems Conclusion Mathematica, Maple, Sage, . . . ◮ System Agnostic: Content MathML, OpenMath ◮ (semi-)formalize representation of Math in DLMF. (path to doing similar in general L A T EX)

DLMF Content L A T EX Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content ◮ We use L Dictionaries A T EX. Conclusion ◮ Depending on the markup you adopt ◮ purely presentation, ambiguous, ◮ clear semantics ◮ anywhere inbetween!

DLMF Content Semantic Macros Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries ◮ We’ve adopted a system of semantic macros Conclusion ◮ Most egregious offenders: Special Functions, first. ◮ Many ambiguities resolved; many remain.

DLMF Content Semantic Macros; Examples Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries \BesselJ{\mu} J µ Conclusion J µ ( z ) \BesselJ{\mu}@{z} J ′′ \BesselJ{\mu}’’@{z} µ ( z ) J 2 µ ( z ) \BesselJ{\mu}^2@{z}

DLMF Content Disambiguation Project Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog ◮ Begun intense effort with Deyan Ginev DLMF Content ◮ Resolve ambiguities — by hook-or-crook: Dictionaries Conclusion Declarations, richer markup, inference whatever it takes for DLMF. ◮ Why? ◮ It’s time! ◮ Provide (small) annotated data set for machine-learning See Abdou Youssef’s talk, Tuesday afternoon.

DLMF Content Back to Special Functions Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries ◮ We have Semantic Markup. Conclusion ◮ We have clear notion of each function is, mathematically.

DLMF Content But Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function ◮ How do they relate to Wolfram’s? Maplesoft’s? NAG’s? Catalog DLMF Content ◮ Not always clear! Dictionaries Sometimes same, Sometimes different! Conclusion ◮ Arguments, ◮ Branch cuts, ◮ Generalizations. ◮ . . . ◮ GDML’s Special Function Concordance Need a basis from which to start discussions

DLMF Content Caveats Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries ◮ I’m not a Special Functions expert, Conclusion or even a Mathematician. ◮ Concordance can be tricky and subtle (to me).

DLMF Content Approach Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content ◮ Publish OpenMath Content Dictionaries for DLMF’s Dictionaries Conclusion Special Functions ◮ In case of doubt, err on side of ◮ Define DLMF versions of (almost) everything ◮ Assume Alignments established by others.

DLMF Content Plausible organization Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog ◮ Based on DLMF Chapters DLMF Content Dictionaries ◮ Subdivided according to Conclusion zeros, magnitudes, q -analogs, . . . ◮ DLMF AI ◮ DLMF AI gen ◮ DLMF AI mag ◮ DLMF AI z

DLMF Content Plausbile Naming Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries ◮ Based on DLMF Macro set (to be published) Conclusion ◮ Limitations/Abbreviations subject to L A T EX requirements ◮ But avoid multiple naming conventions.

DLMF Content Defining URL’s Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries Conclusion ◮ See https://math.nist.gov/ ∼ BMiller/DLMF-CDS/

DLMF Content JSON Encoding Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries Conclusion ◮ Virtual CDs ◮ Currently simplistic

DLMF Content What we’re working on Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog ◮ OpenMath CD, DefMP’s, MP’s DLMF Content Dictionaries (or Content MathML) Conclusion ◮ Refine defining URL’s ◮ Smallest containing unit, ◮ permalink ◮ Ultimately more formal eg. DE + boundary conditions

DLMF Content Debating points Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries Conclusion ◮ Currying ◮ Derivatives

DLMF Content Please Comment Dictionaries The Next Iteration Bruce R. Miller NIST Background Special Function Catalog DLMF Content Dictionaries Conclusion ◮ See https://math.nist.gov/ ∼ BMiller/DLMF-CDS/