Verifying DLMF with Maple and Mathematica: Difference between revisions

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This page presents the results of the publication ''Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems''.
This page presents the results of the publication ''Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems''.


== Bug Reports ==
= Bug Reports =


You can find a PDF with commands that illustrate the encountered errors in Mathematica here: [[File:Mathematica Bugs Overview.pdf|none|The overview of the bugs we reported to Mathematica]]
You can find a PDF with commands that illustrate the encountered errors in Mathematica here: [[File:Mathematica Bugs Overview.pdf|none|The overview of the bugs we reported to Mathematica]]
Line 8: Line 8:
[[File:Mathematica Bugs Notebook File.nb|The Wolfram notebook file of the reported bugs]]
[[File:Mathematica Bugs Notebook File.nb|The Wolfram notebook file of the reported bugs]]


== DLMF Translations and Results ==
= DLMF Translations and Results =


In the following, we present the translations of the DLMF equations to the CAS Maple and Mathematica.
In the following, we present the translations of the DLMF equations to the CAS Maple and Mathematica.
{| class="wikitable sortable"
|-
! DLMF !! Formula !! Translations<br>Maple !! Translations<br>Mathematica !! Symbolic Evaluation<br>Maple !! Symbolic Evaluation<br>Mathematica !! Numeric Evaluation<br>Maple !! Numeric Evaluation<br>Mathematica
|-
| [https://dlmf.nist.gov/ DLMF] || 6,623 || 4,114 (62.1%) || 4,713 (71.2%) || 1,084 (26.3%) || 1,235 (26.2%) || 698 (26.7%) || 784 (22.6%)
|-
|}
== Results of the Digital Library of Mathematical Functions ==
<div style="-moz-column-count:2; column-count:2;">
# [[Results of Algebraic and Analytic Methods|Algebraic and Analytic Methods]]
# [[Results of Asymptotic Approximations|Asymptotic Approximations]]
# [[Results of Numerical Methods|Numerical Methods]]
# [[Results of Elementary Functions|Elementary Functions]]
# [[Results of Gamma Function|Gamma Function]]
# [[Results of Exponential, Logarithmic, Sine, and Cosine Integrals|Exponential, Logarithmic, Sine, and Cosine Integrals]]
# [[Results of Error Functions, Dawson’s and Fresnel Integrals|Error Functions, Dawson’s and Fresnel Integrals]]
# [[Results of Incomplete Gamma and Related Functions|Incomplete Gamma and Related Functions]]
# [[Results of Airy and Related Functions|Airy and Related Functions]]
# [[Results of Bessel Functions|Bessel Functions]]
# [[Results of Struve and Related Functions|Struve and Related Functions]]
# [[Results of Parabolic Cylinder Functions|Parabolic Cylinder Functions]]
# [[Results of Confluent Hypergeometric Functions|Confluent Hypergeometric Functions]]
# [[Results of Legendre and Related Functions|Legendre and Related Functions]]
# [[Results of Hypergeometric Function|Hypergeometric Function]]
# [[Results of Generalized Hypergeometric Functions and Meijer G-Function|Generalized Hypergeometric Functions and Meijer ''G''-Function]]
# [[Results of q-Hypergeometric and Related Functions|''q''-Hypergeometric and Related Functions]]
# [[Results of Orthogonal Polynomials|Orthogonal Polynomials]]
# [[Results of Elliptic Integrals|Elliptic Integrals]]
# [[Results of Theta Functions|Theta Functions]]
# [[Results of Multidimensional Theta Functions|Multidimensional Theta Functions]]
# [[Results of Jacobian Elliptic Functions|Jacobian Elliptic Functions]]
# [[Results of Weierstrass Elliptic and Modular Functions|Weierstrass Elliptic and Modular Functions]]
# [[Results of Bernoulli and Euler Polynomials|Bernoulli and Euler Polynomials]]
# [[Results of Zeta and Related Functions|Zeta and Related Functions]]
# [[Results of Combinatorial Analysis|Combinatorial Analysis]]
# [[Results of Functions of Number Theory|Functions of Number Theory]]
# [[Results of Mathieu Functions and Hill’s Equation|Mathieu Functions and Hill’s Equation]]
# [[Results of Lamé Functions|Lamé Functions]]
# [[Results of Spheroidal Wave Functions|Spheroidal Wave Functions]]
# [[Results of Heun Functions|Heun Functions]]
# [[Results of Painlevé Transcendents|Painlevé Transcendents]]
# [[Results of Coulomb Functions|Coulomb Functions]]
# [[Results of 3j,6j,9j Symbols|''3j,6j,9j'' Symbols]]
# [[Results of Functions of Matrix Argument|Functions of Matrix Argument]]
# [[Results of Integrals with Coalescing Saddles|Integrals with Coalescing Saddles]]
</div>

Revision as of 16:21, 14 October 2020

This page presents the results of the publication Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems.

Bug Reports

You can find a PDF with commands that illustrate the encountered errors in Mathematica here: File:Mathematica Bugs Overview.pdf

We provide the same file as the Wolfram system notebook format (NB) here: File:Mathematica Bugs Notebook File.nb

DLMF Translations and Results

In the following, we present the translations of the DLMF equations to the CAS Maple and Mathematica.

DLMF Formula Translations
Maple		 Translations
Mathematica		 Symbolic Evaluation
Maple		 Symbolic Evaluation
Mathematica		 Numeric Evaluation
Maple		 Numeric Evaluation
Mathematica
DLMF 6,623 4,114 (62.1%) 4,713 (71.2%) 1,084 (26.3%) 1,235 (26.2%) 698 (26.7%) 784 (22.6%)

Results of the Digital Library of Mathematical Functions

  1. Algebraic and Analytic Methods
  2. Asymptotic Approximations
  3. Numerical Methods
  4. Elementary Functions
  5. Gamma Function
  6. Exponential, Logarithmic, Sine, and Cosine Integrals
  7. Error Functions, Dawson’s and Fresnel Integrals
  8. Incomplete Gamma and Related Functions
  9. Airy and Related Functions
  10. Bessel Functions
  11. Struve and Related Functions
  12. Parabolic Cylinder Functions
  13. Confluent Hypergeometric Functions
  14. Legendre and Related Functions
  15. Hypergeometric Function
  16. Generalized Hypergeometric Functions and Meijer G-Function
  17. q-Hypergeometric and Related Functions
  18. Orthogonal Polynomials
  19. Elliptic Integrals
  20. Theta Functions
  21. Multidimensional Theta Functions
  22. Jacobian Elliptic Functions
  23. Weierstrass Elliptic and Modular Functions
  24. Bernoulli and Euler Polynomials
  25. Zeta and Related Functions
  26. Combinatorial Analysis
  27. Functions of Number Theory
  28. Mathieu Functions and Hill’s Equation
  29. Lamé Functions
  30. Spheroidal Wave Functions
  31. Heun Functions
  32. Painlevé Transcendents
  33. Coulomb Functions
  34. 3j,6j,9j Symbols
  35. Functions of Matrix Argument
  36. Integrals with Coalescing Saddles
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