#8972: Inversion and fraction fields for power series rings
-------------------------------------------------+--------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.4.2
Component: algebra | Keywords: power series
ring, fraction field
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: segfault of div of Laurent series |
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Changes (by SimonKing):
* status: new => needs_work
* work_issues: => segfault of div of Laurent series
Comment:
OK, here is a patch.
Idea:
* Introduce a fraction_field method to power series rings that returns the
Laurent series ring over the fraction field of the base ring. I hope that
the base_extend method for Laurent polynomials works stably enough,
otherwise it should be rewritten.
* In the division method of power serise, construct the fraction field of
the parent, move numerator and denominator into the fraction field, and
divide there. The original form of the method is preserved as a fail safe.
With the patch, I get:
{{{
sage: P.<t> = ZZ[]
sage: R.<x> = P[[]]
sage: FractionField(R)
Laurent Series Ring in x over Fraction Field of Univariate Polynomial Ring
in t over Integer Ring
}}}
O dear. I just realise that there will be more work. There is a
segmentation fault, as follows:
{{{
sage: R1.<x> = ZZ[[]]
sage: F = FractionField(R1)
sage: F
Laurent Series Ring in x over Rational Field
sage: F(x)
x
sage: ~F(x)
/home/king/SAGE/sage-4.3.1/local/bin/sage-sage: line 206: 4437
Segmentation fault sage-ipython "$@" -i
}}}
So, the division of elements of a Laurent series ring fails with a
segmentation fault. By consequence, division of power series segfaults as
well, with the patch. "Needs work", I presume.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8972#comment:1>
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