Giac mixes variables and constants of the same name such as I, e, π

[gh-mwageringel]

The Giac interface needs to be more careful when handling symbolic variables that are also mathematical constants:

sage: var('I')._giac_()._sage_()^2  # should be I^2
-1
sage: var('e')._giac_()._sage_().n()  # should not evaluate
2.71828182845905
sage: var('π')._giac_()._sage_().n()  # should not evaluate
3.14159265358979

sage: e, x = var('e,x')
sage: integrate(e^x, x, algorithm='maxima')  # correct
e^x/log(e)
sage: integrate(e^x, x, algorithm='giac')  # wrong
e^x

sage: y = var('π')
sage: integrate(cos(y), y, algorithm='maxima')  # correct (after ticket 30112)
sin(π)
sage: integrate(cos(y), y, algorithm='giac')  # wrong
-pi

This also came up in this ​ask-sage question.

To avoid this conflict, this ticket changes the names of the internal variables in the Giac interface, which mirrors the behavior of the Maxima interface.

sage: giac(SR.var('e'))
sageVARe
sage: _.sage()
e

[mkoeppe]

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[gh-mwageringel]

Here is a basic fix which follows the implementation of the Maxima interface by changing the names of variables in the interface.

---

New commits:

​6df1160	30133: rename internal variables in Giac interface to avoid clashes with constants
​a7e211e	30133: fix conversion of polynomials to Giac

[tscrim]

LGTM overall. One little thing is adding # -*- coding: utf-8 -*- to the first line of src/sage/symbolic/integration/external.py. A while-we-are-at-it thing that you can ignore is fixing the pyflakes warnings in src/sage/symbolic/expression_conversions.py. Once done, you can set a positive review on my behalf.

[git]

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

​aaf26b9

30133: fix pyflakes warning

[gh-mwageringel]

Thanks for the review.

Replying to tscrim:

LGTM overall. One little thing is adding # -*- coding: utf-8 -*- to the first line of src/sage/symbolic/integration/external.py.

In Python 3, utf-8 encoding is ​the default, so this line is not needed.

I have fixed the pyflakes warning, though.

[tscrim]

I am not fully convinced and would rather be safe, but it's not a hill I am willing to die on as I don't know of something that definitely breaks right now that we support.