Allow giac algorithm in solve

[mforets]

To allow the giac interface as an optional keyword of the solve function.

CC: @slel @tscrim

Component: calculus

Keywords: solve, giac

Author: Frédéric Chapoton

Branch/Commit: 57c0ee7

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/23136

[mforets]

comment:1

Here are some tests:

involving the unknown as exponent:

sage: solve((2/3)^x-2, x)
[3^x == 2^(x - 1)] # not explicit x = ..
sage: giac('solve((2/3)^x-2, x)')
list[ln(2)/(ln(2)-ln(3))]  # ok

from #3745:

sage: sage: solve((sin(x) - 8*cos(x)*sin(x))*(sin(x)^2 + cos(x)) - (2*cos(x)*sin(x) - sin(x))*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x)), x) 
[x == pi, x == 1/2*pi, x == 0]  # wrong
sage: giac('solve((sin(x) - 8*cos(x)*sin(x))*(sin(x)^2 + cos(x)) - (2*cos(x)*sin(x) - sin(x))*(-2*sin(x)^2 + 2*cos(x)^2 - cos(x)), x)')
list[-2*atan(sqrt(2)),0,2*atan(sqrt(2)),pi]  # ok

[mforets]

comment:2

see also #22322 (allow sympy algorithm in solve)

[fchapoton]

comment:3

preliminary step in #23677

[fchapoton]

Author: Frédéric Chapoton

[fchapoton]

comment:4

just the basic setup, needs to be tested and improved

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New commits:

8c2e14c

allow_giac_for_solve

[fchapoton]

Commit: 8c2e14c

[fchapoton]

Branch: u/chapoton/23136

[sagetrac-git]

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

5b04bfa

work on giac solver