implement SymPy Piecewise equivalent

[rwst]

This shows an equivalent to SymPy's Piecewise is missing in Sage:

        sage: _ = var('y, z')
        sage: (x^y - z).integrate(y)
        -y*z + x^y/log(x)
        sage: (x^y - z).integrate(y, algorithm="sympy")  # see Trac #14694
        Traceback (most recent call last):
        ...
        AttributeError: 'ExprCondPair' object has no attribute '_sage_'

SymPy-1.0:
>>> integrate(x**y-z,y)
       ⎛⎧  y     for log(x) = 0⎞
       ⎜⎪                      ⎟
       ⎜⎪   y                  ⎟
 -y⋅z + ⎜⎨  x                   ⎟
       ⎜⎪──────    otherwise   ⎟
       ⎜⎪log(x)                ⎟
       ⎝⎩                      ⎠

Piecewise in SymPy is a held function of ExprCondPair arguments. It would be a superset of our piecewise. The name should not be confusable, a suggestion is if_then([(log(x)==0, y), (x^y/log(x), 1)]).

When it is implemented a SymPy patch should be done for the _sage_ method.

EDIT: Maxima 5.38.1 returns a similar function for some integrals.

Depends on #23820

CC: @mforets

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 1929337

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/20191

[rwst]

Branch: u/rws/implement_sympy_piecewise_equivalent

[rwst]

Commit: 1929337

[rwst]

New commits:

1929337

20191: cases() function

[rwst]

Dependencies: pynac-0.7.11

[rwst]

Changed dependencies from pynac-0.7.11 to #23820

[rwst]

Author: Ralf Stephan

[tscrim]

comment:9

Does this solve the issue in the ticket description? If so, I feel like we should add that as a doctest. If not, then you can set a positive review and post in a comment here which ticket will actually address it.

[tscrim]

Reviewer: Travis Scrimshaw

[rwst]

comment:10

Right. #23923 depends on this.

[vbraun]

Changed branch from u/rws/implement_sympy_piecewise_equivalent to 1929337