Give an `algorithm` keyword to (some?) `simplify` methods/functions

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

Case in point (many other examples exist...) :

sage: var("x", domain="positive")
x
sage: u = -1/2*I*x + 1/2*I*sqrt(x^2 - 1) + 1/2*I/(x - sqrt(x^2 - 1))
sage: u.simplify()
-1/2*I*x + 1/2*I*sqrt(x^2 - 1) + 1/2*I/(x - sqrt(x^2 - 1))
sage: u._giac_().simplify()._sage_()
I*sqrt(x^2 - 1)
sage: u._fricas_().simplify()._sage_()
-(I*x^2 - I*sqrt(x^2 - 1)*x - I)/(x - sqrt(x^2 - 1))
sage: u._sympy_().simplify()._sage_()
-I*(x^2 - sqrt(x^2 - 1)*x - 1)/(x - sqrt(x^2 - 1))
sage: mathematica.FullSimplify(u).sage()
I*sqrt(x^2 - 1)

Suggestion : give to the simplify method of symbolic expressions (and its wrapper function) an algorithm keyword selecting an alternative to our "default" (which is to send the expression to Maxima and accept whatever Maxima sends back to us...).

This might be also useful for the more specialized methods/functions (such as simplify_trig). Advice required...

Advice also required about adding it to simplify_full, which aims to be a useful helper in complicated cases, but often bites more than it can swallow...

CC: @slel

Component: symbolics

Author: Emmanuel Charpentier

Branch/Commit: u/charpent/give_analgorithmkeyword_tosome__simplify__methods_functions @ 6472588

Issue created by migration from https://trac.sagemath.org/ticket/32472

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

Branch: u/charpent/give_analgorithmkeyword_tosome__simplify__methods_functions

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

Commit: 5637286

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:2

Replying to @EmmanuelCharpentier:

This does the job excusively for the simplify method of symbolic expressions and the simplify() function.

Passes ptestlong without failure ==> needs_review.

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New commits:

5637286

Add an algorithm keyword to simplify.

[slel]

Author: Emmanuel Charpentier

[mezzarobba]

comment:4

Lgtm, except that the examples in sage.calculus.functional.simplify() should use simplify(foo), not foo.simplify().

(I am unable to help with deciding exactly what to do with other simplification methods, unfortunately, but I like the idea of having keywords to choose a backend there as well.)

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:5

Replying to @mezzarobba:

Lgtm, except that the examples in sage.calculus.functional.simplify() should use simplify(foo), not foo.simplify().

Right. I cut n' pasted the method examplen and forgot to modify it for the functional syntax. Shame on me.

Done, passes its doctest after rebasing on 9.5.beta7. Running ptestlong to be damn sure. Stay tuned...

(I am unable to help with deciding exactly what to do with other simplification methods, unfortunately, but I like the idea of having keywords to choose a backend there as well.)

Too bad. The specialized methods may (Maxima) or may not (giac, fricas) exost in the other backends... Advice still needed.

[7822f248-ba56-45f1-ab3d-4de7482bdf9f]

comment:6

Replying to @EmmanuelCharpentier:

...

Done, passes its doctest after rebasing on 9.5.beta7. Running ptestlong to be damn sure. Stay tuned...

ptestlong gives exactly the same failures as thos observed in 9.5.beta7 ==> probably worth positive_review.

Temporarily setting needs work , I'll set needs_review after pushing my edits.

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

Changed commit from 5637286 to 6472588

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

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

419aaa9	Add an algorithm keyword to simplify.
16c7733	Trac#39472 : fix example for the simplify function (rebased on 9.5.beta7)
6472588	Merge branch 'u/charpent/give_an__algorithm__keyword_to__some____simplify__methods_functions' of trac.sagemath.org:sage into t/32472/give_an__algorithm__keyword_to__some____simplify__methods_functions