Add .is_square() function for symbolic expression

[vinklein]

Fix the following behaviour :

sage: f(n)=n^2
sage: f(2).is_square()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-2-07de71372bf0> in <module>()
----> 1 f(Integer(2)).is_square()

/home/vklein/odk/sage/local/lib/python2.7/site-packages/sage/structure/element.pyx in sage.structure.element.CommutativeRingElement.is_square (build/cythonized/sage/structure/element.c:20900)()
   3020             framework.
   3021         """
-> 3022         raise NotImplementedError("is_square() not implemented for elements of %s" % self.parent())
   3023 
   3024     def sqrt(self, extend=True, all=False, name=None):

NotImplementedError: is_square() not implemented for elements of Symbolic Ring

CC: @videlec

Component: symbolics

Author: Vincent Klein

Branch/Commit: 88a1145

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/25460

[vinklein]

Branch: u/vklein/add__is_square___function_for_symbolic_expression

[vinklein]

Author: Vincent Klein

[vinklein]

Commit: ac0dc8e

[vinklein]

New commits:

ac0dc8e

Trac #25460: Add is_square method to symbolic expression

[vinklein]

comment:4

Currently is_square((x-1)^2) return True the last commit don't do that.

[sagetrac-git]

Changed commit from ac0dc8e to d3fdcae

[sagetrac-git]

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

d3fdcae

Trac #25460: enable is_square to manage non numeric ...

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

c1c77e7

Trac #25460: enable is_square to manage non numeric ...

[sagetrac-git]

Changed commit from d3fdcae to c1c77e7

[vinklein]

comment:7

Enable is_square to manage non numeric expression.

[videlec]

comment:8

Note that is_square is completely broken for symbolic expression. Moving it as a method is not helping in any way.

sage: x = SR.var('x')
sage: is_square((cos(x) + 1)^2)
True
sage: is_square((cos(x) + 1)^2, True)   # WTF?
Traceback (most recetn call last):
...
TypeError: unable to convert 2 - 1/2*x^2 + 1/24*x^4 - 1/720*x^6 + 1/40320*x^8 - 1/3628800*x^10 + 1/479001600*x^12 - 1/87178291200*x^14 + 1/20922789888000*x^16 + O(x^18) to a symbolic expression

And for example, the following should be False

sage: is_square(cos(x) - cos(x).taylor(x, 0, 20))
True

I would suggest to let this method raise NotImplementedError whenever it is not possible to call is_square on the underlying pyobject.

[vinklein]

comment:9

This mean is_square((x-1)^2) (with #24677) will have a different behaviour, are you ok with that ?

[videlec]

comment:10

Replying to @vinklein:

This mean is_square((x-1)^2) (with #24677) will have a different behaviour, are you ok with that ?

yes

[sagetrac-git]

Changed commit from c1c77e7 to db90194

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

db90194

Trac #25460: Raise NotImplementedError when is_square ...

[vinklein]

comment:12

Done

[videlec]

comment:13

try:
    obj = self.pyobject()
except TypeError:
    raise NotImplementedError("is_square() not implemented for non numeric elements of Symbolic Ring")

return obj.is_square()

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

88a1145

Trac #25460: Raise NotImplementedError when is_square ...

[sagetrac-git]

Changed commit from db90194 to 88a1145

[vinklein]

comment:15

Ok

[videlec]

Reviewer: Vincent Delecroix

[vbraun]

Changed branch from u/vklein/add__is_square___function_for_symbolic_expression to 88a1145