fyi, Elementary algebraic integrals added to CAS integration tests

[Nasser M. Abbasi]

Fyi,

A new CAS integration test, called the "Elementary algebraic" integrals
version is now available.

<https://www.12000.org/my_notes/CAS_integration_tests/index.htm>
<https://www.12000.org/my_notes/CAS_integration_tests/reports/sept_2021_algebraic_version/index.htm>

This uses a subset of the full CAS integration tests and includes
a new 9th CAS integrate program IntegrateAlgebraic.

This subset includes only Algebraic integrals with optimal
antiderivatives made only of elementary functions.

These integrals are filtered out of the following Rubi's test files
provided thanks to Albert Rich

Algebraic Binomial
Algebraic Trinomial
Miscellaneous Algebraic

And also integrals from IntegrateAlgebraic test suite provided thanks
to Sam Blake.

This test was done to be able to include IntegrateAlgebraic in the
CAS integration tests, as IntegrateAlgebraic is meant to use only
on algebraic type of integrals.

There are 22,622 integrals in this Elementary algebraic integrals version.

The Full test suite on the other hand contains 71,994 integrals.

CAS Systems used in the Elementary algebraic integrals version test are

1. Mathematica 12.3.1 (64 bit) on windows 10.
2. Rubi 4.16.1 in Mathematica 12 on windows 10. https://rulebasedintegration.org
3. Maple 2021.1 (64 bit) on windows 10.
4. Maxima 5.44 on Linux. (via sagemath 9.3)
5. Fricas 1.3.7 on Linux (via sagemath 9.3)
6. Sympy 1.8 under Python 3.8.8 using Anaconda distribution.
7. Giac/Xcas 1.7 on Linux. (via sagemath 9.3)
8. Mupad using Matlab 2021a with Symbolic Math Toolbox Version 8.7 under windows 10 (64 bit)
9. IntegrateAlgebraic under Mathematica 12.3.1 on windows 10.
https://github.com/stblake/algebraic_integration. This function can
also be used from Wolfram's resource function web site at

https://resources.wolframcloud.com/FunctionRepository/resources/IntegrateAlgebraic/

Also a blog on IntegrateAlgebraic is at

https://blog.wolfram.com/2021/08/18/new-methods-for-computing-algebraic-integrals/

This is the final result of percentage passed

system % passed
======== ===========
1. Mathematica 96.65
2. Rubi 96.16
3. Fricas 93.75
4. Maple 91.89
5. IntegrateAlgebraic 88.05
6. Giac 77.45
7. Mupad 70.46
8. Maxima 68.31
9. Sympy 54.15

This following the grading result (notice that Mupad is not currently
graded, a pass is given B grade automatically else an F grade is given).

System %A grade % B grade %C grade %F grade
======= ======== ========= ===== =======
1. Rubi 93.94 0.41 1.81 3.84
2. Mathematica 78.86 2.8 14.97 3.35
3. IntegrateAlgebraic 75.29 8.49 4.27 11.95
4. Fricas 69.12 24.12 0.5 6.25
5. Maple 63.41 20.09 8.4 8.11
6. Maxima 59.26 8.6 0.45 31.69
7. Giac 58.57 18.73 0.15 22.55
8. Sympy 39.29 10.82 4.04 45.85
9. Mupad N/A 70.46 0.0 29.54

Zip files that contains all integrals used in plain text format
in Mathematica, Maple, Sagemath, and Sympy format are also available
on the web page.

Any problems found in the above reports, please let me know.

--Nasser