#16240: regression in partial_fraction_decomposition()
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: commutative algebra | Resolution:
Keywords: partial fractions, polynomials | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> Note the sign of the denominator:
> {{{
> sage: R.<x> = ZZ['x']
> sage: p=(6*x^2 - 9*x + 5)/(-x^3 + 3*x^2 - 3*x + 1)
> sage: p.partial_fraction_decomposition()
> (0, [6/(x - 1), 3/(x^2 - 2*x + 1), 2/(x^3 - 3*x^2 + 3*x - 1)])
> sage: 6/(x - 1) + 3/(x^2 - 2*x + 1) + 2/(x^3 - 3*x^2 + 3*x - 1)
> (6*x^2 - 9*x + 5)/(x^3 - 3*x^2 + 3*x - 1)
> }}}
> while in SR:
> {{{
> sage: var('x')
> x
> sage: p=(6*x^2 - 9*x + 5)/(-x^3 + 3*x^2 - 3*x + 1)
> sage: p.partial_fraction()
> -6/(x - 1) - 3/(x - 1)^2 - 2/(x - 1)^3
> }}}
> The minimal case, showing with odd exponents:
> {{{
> sage: R.<x> = ZZ['x']
> sage: p=1/(-x + 1)
> sage: p.partial_fraction_decomposition()
> (0, [1/(x - 1)])
> }}}
New description:
This worked in 6.1.1. Maybe triggered in #15306.
Note the sign of the denominator:
{{{
sage: R.<x> = ZZ['x']
sage: p=(6*x^2 - 9*x + 5)/(-x^3 + 3*x^2 - 3*x + 1)
sage: p.partial_fraction_decomposition()
(0, [6/(x - 1), 3/(x^2 - 2*x + 1), 2/(x^3 - 3*x^2 + 3*x - 1)])
sage: 6/(x - 1) + 3/(x^2 - 2*x + 1) + 2/(x^3 - 3*x^2 + 3*x - 1)
(6*x^2 - 9*x + 5)/(x^3 - 3*x^2 + 3*x - 1)
}}}
while in SR:
{{{
sage: var('x')
x
sage: p=(6*x^2 - 9*x + 5)/(-x^3 + 3*x^2 - 3*x + 1)
sage: p.partial_fraction()
-6/(x - 1) - 3/(x - 1)^2 - 2/(x - 1)^3
}}}
The minimal case, showing with odd exponents:
{{{
sage: R.<x> = ZZ['x']
sage: p=1/(-x + 1)
sage: p.partial_fraction_decomposition()
(0, [1/(x - 1)])
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16240#comment:2>
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