allow sympy algorithm in solve

[kcrisman]

What it says. See e.g. this post for why.

Depends on #23990
Depends on #24104
Depends on #24062

CC: @rwst @mforets @sagetrac-tmonteil @EmmanuelCharpentier

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 8e1e240

Reviewer: Emmanuel Charpentier

Issue created by migration from https://trac.sagemath.org/ticket/22322

[mforets]

comment:1

AFAIK, also useful for equations where the unkown appears as an exponent, cf. solve(4.94 * 1.062^x == 15, x)

[mforets]

comment:3

solve (from expression.pyx) passes a relational expression to Maxima's solve, but this doesn't seem to be available in sympy:

sage: (x==1)._maxima_()
_SAGE_VAR_x=1
sage: (x==1)._sympy_()
Traceback (most recent call last)
...
NotImplementedError: relation

do you have some idea on how to tackle this? otherwise, what about passing ex.lhs()-ex.rhs() to sympy's solve.

[rwst]

comment:4

Replying to @mforets:

solve (from expression.pyx) passes a relational expression to Maxima's solve, but this doesn't seem to be available in sympy:
...
do you have some idea on how to tackle this? otherwise, what about passing ex.lhs()-ex.rhs() to sympy's solve.

Yes, that would be it for the equalities. For inequalities SympyConverter.relation() is needed (atm the superclass's relation is called).

[rwst]

comment:5

Correction, doing ex.lhs()-ex.rhs() is not needed if the SympyConverter is fixed.

[rwst]

Dependencies: #23990

[EmmanuelCharpentier]

comment:8

Hmmm...

sage: var("a,b")
(a, b)
sage: sympy.sympify(a==b)._sage_()
a == b
sage: sympy.sympify(a==b).sage()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-14-25de6a4c8f0a> in <module>()
----> 1 sympy.sympify(a==b).sage()

AttributeError: 'Equality' object has no attribute 'sage'

Is that the expected behaviour ? Or do you plan to enhance the .sage() method for various objects ?

It is not obvious to me why (e. g.) mathematica objets can (sometimes...) be converted back to sage via the .sage() (exposed) method, whereas Sympy objects have to use the ._sage_() (unexposed method.

[rwst]

comment:9

As I explained in #23990 that is the SymPy convention.

[EmmanuelCharpentier]

comment:10

Replying to @rwst:

As I explained in #23990 that is the SymPy convention.

Wups, bad wrong ticket. I thought that my comment was cancelled ; it was not.

Apologies...

[rwst]

Changed dependencies from #23990 to #23990, #24078

[rwst]

comment:11

Now that (with #23990) relations are translated from/to SymPy there are still things needed. For example we need to translate any assumptions on variables (and maybe anon. functions?) that were made using assume and var('x', domain=...). This is not only relevant for this ticket, any SymPy operation may access the SymPy knowledge base any time. So I think this should be handled the same way as with Maxima, i.e. at the time the assume/var calls are made. This is #24078.