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

▶
dlmf content dictionaries
SMART_READER_LITE
LIVE PREVIEW

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

Jan 09, 2024 41 likes •243 views

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

slide-1
SLIDE 1

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

DLMF Content Dictionaries The Next Iteration

Bruce R. Miller NIST August 10, 2018

slide-2
SLIDE 2

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

DLMF Project

https://dlmf.nist.gov/

slide-3
SLIDE 3

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

Goals

◮ Up-to-date source of Properties of Mathematical

Special Functions and Applications

◮ Preserve the character of a Handbook

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.

slide-4
SLIDE 4

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

Technical Goals

◮ Maintainable, ◮ Current with web-technologies ◮ Presentation MathML. ◮ Permalinks for reference data

slide-5
SLIDE 5

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

Future Technical Goals

◮ Machine-readable data/metadata ◮ Interoperability with other systems

Mathematica, Maple, Sage, . . .

◮ System Agnostic:

Content MathML, OpenMath

◮ (semi-)formalize representation of Math in DLMF.

(path to doing similar in general L

AT

EX)

slide-6
SLIDE 6

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

L

AT

EX

◮ We use L AT

EX.

◮ Depending on the markup you adopt

◮ purely presentation, ambiguous, ◮ clear semantics ◮ anywhere inbetween!

slide-7
SLIDE 7

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

Semantic Macros

◮ We’ve adopted a system of semantic macros ◮ Most egregious offenders: Special Functions, first. ◮ Many ambiguities resolved; many remain.

slide-8
SLIDE 8

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

Semantic Macros; Examples

\BesselJ{\mu} Jµ \BesselJ{\mu}@{z} Jµ(z) \BesselJ{\mu}’’@{z} J′′

µ(z)

\BesselJ{\mu}^2@{z} J2

µ(z)

slide-9
SLIDE 9

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

Disambiguation Project

◮ Begun intense effort with Deyan Ginev ◮ Resolve ambiguities — by hook-or-crook:

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.

slide-10
SLIDE 10

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

Back to Special Functions

◮ We have Semantic Markup. ◮ We have clear notion of each function is,

mathematically.

slide-11
SLIDE 11

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

But

◮ How do they relate to Wolfram’s? Maplesoft’s? NAG’s? ◮ Not always clear!

Sometimes same, Sometimes different!

◮ Arguments, ◮ Branch cuts, ◮ Generalizations. ◮ . . .

◮ GDML’s Special Function Concordance

Need a basis from which to start discussions

slide-12
SLIDE 12

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

Caveats

◮ I’m not a Special Functions expert,

  • r even a Mathematician.

◮ Concordance can be tricky and subtle (to me).

slide-13
SLIDE 13

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

Approach

◮ Publish OpenMath Content Dictionaries for DLMF’s

Special Functions

◮ In case of doubt, err on side of

◮ Define DLMF versions of (almost) everything ◮ Assume Alignments established by others.

slide-14
SLIDE 14

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

Plausible organization

◮ Based on DLMF Chapters ◮ Subdivided according to

zeros, magnitudes, q-analogs, . . .

◮ DLMF AI ◮ DLMF AI gen ◮ DLMF AI mag ◮ DLMF AI z

slide-15
SLIDE 15

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

Plausbile Naming

◮ Based on DLMF Macro set (to be published) ◮ Limitations/Abbreviations subject to L AT

EX requirements

◮ But avoid multiple naming conventions.

slide-16
SLIDE 16

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

Defining URL’s

◮ See https://math.nist.gov/∼BMiller/DLMF-CDS/

slide-17
SLIDE 17

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

JSON Encoding

◮ Virtual CDs ◮ Currently simplistic

slide-18
SLIDE 18

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

What we’re working on

◮ OpenMath CD, DefMP’s, MP’s

(or Content MathML)

◮ Refine defining URL’s

◮ Smallest containing unit, ◮ permalink ◮ Ultimately more formal

  • eg. DE + boundary conditions
slide-19
SLIDE 19

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

Debating points

◮ Currying ◮ Derivatives

slide-20
SLIDE 20

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

Please Comment

◮ See https://math.nist.gov/∼BMiller/DLMF-CDS/