Symbolic elliptic integrals

[eviatarbach]

This ticket is for making the elliptic integrals symbolic, including arbitrary-precision numeric evaluation.

Defect because elliptic_e(2.5,2.5).n() throwing an ECL error is fixed with it.

CC: @burcin @paulmasson

Component: symbolics

Keywords: special, functions

Author: Eviatar Bach, Ralf Stephan

Branch/Commit: fc1ac57

Reviewer: Karl-Dieter Crisman, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/15046

[eviatarbach]

Attachment: trac15046.patch.gz

[eviatarbach]

comment:2

Need to get full doctest coverage.

[rwst]

Branch: u/rws/symbolic_elliptic_integrals

[rwst]

Commit: a922acc

[rwst]

Author: Eviatar Bach

[rwst]

comment:6

Updated to 6.3beta6:

3 items had failures:
   1 of   4 in sage.functions.special.elliptic_j.EllipticEC
   1 of   2 in sage.functions.special.elliptic_j.EllipticEC._derivative_
   1 of   4 in sage.functions.special.elliptic_j.EllipticPi

---

New commits:

a922acc

15046: Making elliptic integrals symbolic

[sagetrac-git]

Changed commit from a922acc to e950c33

[sagetrac-git]

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

67d51c9	15046: corrections to previous patch to pass doctests
1b33207	15046: accept algorithm param for all evalf functions
e950c33	15046: add all doctests; fix latex; augment documentation

[rwst]

Changed keywords from none to special, functions

[rwst]

comment:8

This is now ready for review.

BTW, is Maxima not able to solve the resp. integrals?

sage: integrate(sqrt(1 - m*sin(x)^2), x, 0, phi)
sage: integrate(sqrt(1 - m*sin(x)^2), x, 0, pi/2)
sage: integrate(1/sqrt(1 - m*sin(x)^2), x, 0, phi)

[rwst]

Changed author from Eviatar Bach to Eviatar Bach, Ralf Stephan

[sagetrac-git]

Changed commit from e950c33 to 5547215

[sagetrac-git]

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

5547215

Merge branch 'develop' into t/15046/symbolic_elliptic_integrals

[sagetrac-git]

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

829da64

Merge branch 'develop' into t/15046/symbolic_elliptic_integrals

[sagetrac-git]

Changed commit from 5547215 to 829da64

[kcrisman]

comment:23

I'd like to look at this - can you confirm that you are giving positive review to Eviatar's original changes? If so, I think I only need to give this one more good look and try out some more numerical things to confirm it's ready to go.

By the way, I note some inconsistency (probably due to my relative unfamiliarity with elliptic integrals). I see

This returns the value of the "incomplete elliptic integral of the
    second kind"

in two places, EllipticE and EllipticEU. Since the Maxima manual clarifies the relationship, we should too. Indeed, there is a bunch of stuff in here which assumes familiarity with syntax for the Jacobi functions dn or sn or the rest which should be clarified. Maybe a link in internal documentation to that file, or perhaps some Wikipedia refs would also not be amiss? Just throwing out doc ideas, as long as we implement a little more it will be fine.

[kcrisman]

Changed dependencies from #14996 to none

[sagetrac-git]

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

9a62ed2	Merge branch 'develop' into t/15046/symbolic_elliptic_integrals
27278e3	15046: add refs

[sagetrac-git]

Changed commit from b3b2e8c to 27278e3

[sagetrac-git]

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

6138b32	Merge branch 'develop' into t/15046/symbolic_elliptic_integrals
fa4fd69	fix doctest

[sagetrac-git]

Changed commit from 27278e3 to fa4fd69

[rwst]

comment:29

Sage startup time increased by 0.3%, why?

[tscrim]

comment:30

I am pretty sure that is from a bad startup time test batch. Also, could you break the longer lines to ~80 characters?

[sagetrac-git]

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

bebff6c	Merge branch 'develop' into t/15046/symbolic_elliptic_integrals
e4b089a	15046: cosmetics

[sagetrac-git]

Changed commit from fa4fd69 to e4b089a

[rwst]

comment:32

I didn't break all the lines. If you insist I'll try again. Anything else?

[tscrim]

comment:33

I would prefer if the doctest output lines were split, probably 1 term per line should be good (or more if they are shorter). Once you do that, you can set a positive review on my behalf

[tscrim]

Reviewer: Karl-Dieter Crisman, Travis Scrimshaw

[sagetrac-git]

Changed commit from e4b089a to fc1ac57

[sagetrac-git]

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

fc1ac57

15046: break doctest output lines

[rwst]

comment:35

I couldn't break lines at abc*xyz (bug?) but it worked at abc - xyz and abc + xyz so I succeeded in most of the cases.

[tscrim]

comment:36

Thanks. What you did is exactly what I was looking for and plenty good. The reason why abc*xyz cannot split is because there is no whitespace around the operator (and newlines get counted as whitespace, which the doctest framework ignores all after one whitespace char).

[vbraun]

Changed branch from u/rws/symbolic_elliptic_integrals to fc1ac57