missing binding for SymPy's exp_polar()

[kalvotom]

The following integral cannot be evaluated by maxima:

sage: integrate(1/sqrt(1+x^3),x)
integrate(1/sqrt(x^3 + 1), x)

With 'sympy' algorithm the computation fails:

sage: integrate(1/sqrt(1+x^3),x,algorithm='sympy')
...
AttributeError: 'gamma' object has no attribute '_sage_'

However, SymPy? can compute the integral and gives the result in terms of gamma and hypergeometric functions:

sage: import sympy
sage: sympy.integrate(1/sqrt(1+x**3))
x*gamma(1/3)*hyper((1/3, 1/2), (4/3,), x**3*exp_polar(I*pi))/(3*gamma(4/3))

It can be seen that not only gamma is a problem (already fixed in sympy master) but also exp_polar which Sage does not know.

This ticket should track the status of the Sympy pull request fixing the exp_polar issue, and it should implement a skeleton exp_polar on the Sage side.

[vdelecroix]

The problem actually does occur in Sympy code...

sage: import sympy
sage: s = sympy.gamma(1/3)
sage: s._sage_()
Traceback (most recent call last):
...
AttributeError: 'gamma' object has no attribute '_sage_'

Would you like to make a bug report in Sympy? Either on

• the ​mailing list
• the ​issue tracker

Vincent

[kalvotom]

After some more digging it turned out the this is almost OK in the most recent git version of Sympy (not 0.7.6 which is shipped with Sage). Class Function ​has a _sage_ method and hypergeometric function hyper is also ​correctly dealt with.

However, the example mentioned above still fails because Sage does not know exp_polar function. I have created ​this pull request which adds _sage_ method to exp_polar and returns the usual exponential.

Tomáš

[rws]

I have commented on the pull request, ​https://github.com/sympy/sympy/pull/9224

[rws]

If you want to do try your hands at it, see ​http://trac.sagemath.org/wiki/symbolics/functions for symbolic function tickets, and ​https://github.com/sagemath/sage/compare/develop...rwst:special for a collection of most recent code examples.

[kalvotom]

New commits:

​0683dd3

add exp_polar function

[kalvotom]

I have doctested the function with git version of Sympy and all tests passed (especially the one with integration). I guess we have to wait for a new version of Sympy to arrive in Sage (probably Sympy 0.7.7).

Anyway, this is my first attempt to contribute to Sage, so feel free to knitpick.

I have one question. How complicated it would be to force Sage to perform simplifications like

sage: exp_polar(2 + 5*I)*exp_polar(5 - I)
exp_polar(7 + 4*I)

My current understanding is that such simplifications are taken care of by an external library ( Pynac ) and there is no way how to do this in Sage alone, am I right?

[rws]

Replying to kalvotom:

I have doctested the function with git version of Sympy and all tests passed (especially the one with integration). I guess we have to wait for a new version of Sympy to arrive in Sage (probably Sympy 0.7.7).

Yes, other tickets are waiting for that too.

Anyway, this is my first attempt to contribute to Sage, so feel free to knitpick.

Will get to it.

I have one question. How complicated it would be to force Sage to perform simplifications like

sage: exp_polar(2 + 5*I)*exp_polar(5 - I)
exp_polar(7 + 4*I)

My current understanding is that such simplifications are taken care of by an external library ( Pynac ) and there is no way how to do this in Sage alone, am I right?

I think so, but I'm not much into Pynac. Anyway, it could be part of Python Sage by including a function that does it in one of the Expression.simplify* methods.

[rws]

Thanks for your contribution. There were some minor problems requiring changes which I have added: removed the warning (because this ticket is pending Sympy-0.7.7 anyway), and adapted a bit to PEP 8. Documentation is fine, tests pass, so there is no reason to hold this back. If you agree with my changes you can set positive review.

---

New commits:

​ef4bdb7	Merge branch 'develop' into t/18085/missing_binding_for_sympy_s_exp_polar__
​6d3aeaa	18085: reviewer's patch: remove warnings, cosmetics

[kalvotom]

Replying to rws: Those changes are perfectly fine. Thanks.

[vbraun]

Why is this still sage-pending?

[vdelecroix]

"this ticket is pending Sympy-0.7.7" (see In comment:12) but

sage: import sympy
sage: sympy.__version__
'0.7.6.1'