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]

Description changed:

--- 
+++ 
@@ -21,3 +21,5 @@
 
 ```
 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.

[rwst]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-This shows an equivalent to SymPy's `ExprCondPair` is missing in Sage:
+This shows an equivalent to SymPy's `Piecewise` is missing in Sage:
 
 ```
         sage: _ = var('y, z')
@@ -20,6 +20,8 @@
        ⎝⎩                      ⎠
 
 ```
+`Piecewise` in SymPy is a held function of `ExprCondPair` arguments. It would be a superset of our `piecewise`.
+
 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.

[rwst]

Description changed:

--- 
+++ 
@@ -14,13 +14,13 @@
        ⎛⎧  y     for log(x) = 0⎞
        ⎜⎪                      ⎟
        ⎜⎪   y                  ⎟
--y⋅z + ⎜⎨  x                   ⎟
+ -y⋅z + ⎜⎨  x                   ⎟
        ⎜⎪──────    otherwise   ⎟
        ⎜⎪log(x)                ⎟
        ⎝⎩                      ⎠
 
 ```
-`Piecewise` in SymPy is a held function of `ExprCondPair` arguments. It would be a superset of our `piecewise`.
+`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.
 

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Branch: u/rws/implement_sympy_piecewise_equivalent

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Commit: 1929337

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New commits:

1929337

20191: cases() function

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Dependencies: pynac-0.7.11

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Changed dependencies from pynac-0.7.11 to #23820