#8499: partial_fraction_decomposition does not work over algebraic extensions
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Reporter: zimmerma | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by zimmerma):
I found out the solution by myself. If one wants say a decomposition over
Q[sqrt(2)] or Q[I], then simply use {{{QQ[sqrt(2)]}}} or
{{{QQ[sqrt(-1)]}}}:
{{{
sage: R.<x> = QQ[sqrt(2)][]
sage: r=1/(x^4+1)
sage: r.partial_fraction_decomposition()
(0,
[(-1/4*sqrt2*x + 1/2)/(x^2 - sqrt2*x + 1),
(1/4*sqrt2*x + 1/2)/(x^2 + sqrt2*x + 1)])
}}}
or:
{{{
sage: R.<x> = QQ[sqrt(-1)][]
sage: r=1/(x^4+1)
sage: r.partial_fraction_decomposition()
(0, [(-1/2*I)/(x^2 - I), 1/2*I/(x^2 + I)])
}}}
Now if you want Sage to automatically find the extension where the
denominator fully factors, use
{{{QQbar}}}:
{{{
sage: R.<x> = QQbar[]
sage: r=1/(x^4+1)
sage: r.partial_fraction_decomposition()
(0,
[([-0.17677669529663690 .. -0.17677669529663686] - [0.17677669529663686
.. 0.17677669529663690]*I)/(x + [-0.70710678118654758 ..
-0.70710678118654746] - [0.70710678118654746 .. 0.70710678118654758]*I),
([-0.17677669529663690 .. -0.17677669529663686] + [0.17677669529663686
.. 0.17677669529663690]*I)/(x + [-0.70710678118654758 ..
-0.70710678118654746] + [0.70710678118654746 .. 0.70710678118654758]*I),
([0.17677669529663686 .. 0.17677669529663690] - [0.17677669529663686 ..
0.17677669529663690]*I)/(x + [0.70710678118654746 .. 0.70710678118654758]
- [0.70710678118654746 .. 0.70710678118654758]*I),
([0.17677669529663686 .. 0.17677669529663690] + [0.17677669529663686 ..
0.17677669529663690]*I)/(x + [0.70710678118654746 .. 0.70710678118654758]
+ [0.70710678118654746 .. 0.70710678118654758]*I)])
}}}
I'll add some examples to the documentation and then we can close this
ticket.
Paul
--
Ticket URL: <http://trac.sagemath.org/ticket/8499#comment:2>
Sage <http://www.sagemath.org>
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