more fricas conversions

[fchapoton]

just a few more missing conversions, for Jacobi functions, orthogonal polynomials, etc

CC: @mantepse

Component: interfaces: optional

Keywords: FriCAS

Author: Frédéric Chapoton

Branch/Commit: 46d0501

Reviewer: Martin Rubey, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/33204

[fchapoton]

New commits:

f1cdb5e

adding some conversions to/from Fricas functions

[fchapoton]

Branch: u/chapoton/33204

[fchapoton]

Commit: f1cdb5e

[mantepse]

comment:2

Wouldn't it be good to have some doctests? I know very little about these functions, but at the very least it appears that the function names do not quite match up. Possibly, fricas is missing some. For example, at https://fricas.github.io/api/SpecialFunctionCategory.html I cannot find jacobiCs.

One place for such tests might be fricas.py, line 1510.

I guess one could systematically compare some numerical values, to make sure that the definitions agree. For example

sage: jacobi_cn(0.9,2.1) - fricas("jacobiCn")(0.9,2.1).sage()
-7.04818555476145e-20*I

but I have absolutely no idea which values would make sense.

[fchapoton]

Changed keywords from none to FriCAS

[tscrim]

comment:4

Would you be willing to add a doctest for each of these to show the conversions are working correctly?

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from f1cdb5e to b61836d

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

3a2d32b	Merge branch 'u/chapoton/33204' in 9.6.b7
b61836d	more doctests for fricas conversions

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

772487a

more doctests for fricas conversions of orthogonal polynomials

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from b61836d to 772487a

[fchapoton]

comment:7

now with doctests

[tscrim]

comment:8

Thank you.

Martin, if there is something else you would want to see, you can revert the positive review.

[tscrim]

Reviewer: Martin Rubey, Travis Scrimshaw

[mantepse]

comment:9

I'm sorry to be pedantic, but I find doctests like

sage: fricas(gen_legendre_P(2,1/2,x))  # optional - fricas
            1
legendreP(2,-,x)
            2

not very informative. All this tests is that there is a trivariate fricas function legendreP. It does not test, for example, that the ordering of the variables is as suggested.

I admit that it is a bit of work to find out how much information fricas actually has about these functions. I did some digging:

• for the univariate elliptic, fricas can evaluate numerically
• for the bivariate legendre, hermite fricas knows the polynomial, e.g.:

sage: fricas.legendreP(4,x)
35  4   15  2   3
-- x  - -- x  + -
 8       4      8

• for the bivariate jacobiCn, jacobiSn, jacobiDn, ellipticE, ellipticF fricas knows the taylor series:

sage: fricas.series(fricas.jacobiCn(x,4), x=0)
    1  2   17  4   433  6   2903  8   226327  10      11
1 - - x  + -- x  - --- x  + ---- x  - ------ x   + O(x  )
    2      24      720      5760      518400

sage: fricas.series(fricas.ellipticF(x,2), x=0)
    1  3   19  5    9  7   289  9   279  11      12
x + - x  + -- x  + -- x  + --- x  + --- x   + O(x  )
    2      40      16      384      256

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

46d0501

doctest fricas conversions, comment out some dubious ones

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 772487a to 46d0501

[fchapoton]

comment:12

here are some refined doctests. I will not add more, but feel free to do so.

[mantepse]

comment:13

Great, thank you!

[fchapoton]

comment:14

bump to 9.7

[vbraun]

Changed branch from u/chapoton/33204 to 46d0501