#18085: missing binding for SymPy's exp_polar()
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Reporter: kalvotom | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.6
Component: symbolics | Resolution:
Keywords: sd66 | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. No | Work issues:
feedback yet. | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by rws):
* cc: kcrisman (added)
Old description:
> The following integral cannot be evalueated 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:
>
> {{{
> >>> from sympy import *
> >>> x = Symbol('x')
> >>> integrate(1/sqrt(1+x**3), x)
> x*gamma(1/3)*hyper((1/3, 1/2), (4/3,),
> x**3*exp_polar(I*pi))/(3*gamma(4/3))
> }}}
New description:
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.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/18085#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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