#17251: Incomplete multivariate factorization
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Reporter: jdemeyer | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-6.4
Component: factorization | Resolution:
Keywords: singular | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old description:
> With sage-6.4.beta6, the following polynomial factorization gives a
> reducible factor `(-a^2 + b^2)`:
>
> {{{
> sage: R.<z,a,b> = PolynomialRing(QQ)
> sage: N = -a^4*z^8 + 2*a^2*b^2*z^8 - b^4*z^8 - 16*a^3*b*z^7 +
> 16*a*b^3*z^7 + 28*a^4*z^6 - 56*a^2*b^2*z^6 + 28*b^4*z^6 + 112*a^3*b*z^5 -
> 112*a*b^3*z^5 - 70*a^4*z^4 + 140*a^2*b^2*z^4 - 70*b^4*z^4 - 112*a^3*b*z^3
> + 112*a*b^3*z^3 + 28*a^4*z^2 - 56*a^2*b^2*z^2 + 28*b^4*z^2 + 16*a^3*b*z -
> 16*a*b^3*z - a^4 + 2*a^2*b^2 - b^4
> sage: N.factor()
> (-1) * (-a^2 + b^2) * (-z^4*a + z^4*b - 4*z^3*a - 4*z^3*b + 6*z^2*a -
> 6*z^2*b + 4*z*a + 4*z*b - a + b) * (z^4*a + z^4*b - 4*z^3*a + 4*z^3*b -
> 6*z^2*a - 6*z^2*b + 4*z*a - 4*z*b + a + b)
> }}}
New description:
With sage-6.4.beta6, the following polynomial factorization gives a
reducible factor `(-a^2 + b^2)`:
{{{
sage: R.<z,a,b> = PolynomialRing(QQ)
sage: N = -a^4*z^8 + 2*a^2*b^2*z^8 - b^4*z^8 - 16*a^3*b*z^7 + 16*a*b^3*z^7
+ 28*a^4*z^6 - 56*a^2*b^2*z^6 + 28*b^4*z^6 + 112*a^3*b*z^5 - 112*a*b^3*z^5
- 70*a^4*z^4 + 140*a^2*b^2*z^4 - 70*b^4*z^4 - 112*a^3*b*z^3 +
112*a*b^3*z^3 + 28*a^4*z^2 - 56*a^2*b^2*z^2 + 28*b^4*z^2 + 16*a^3*b*z -
16*a*b^3*z - a^4 + 2*a^2*b^2 - b^4
sage: N.factor()
(-1) * (-a^2 + b^2) * (-z^4*a + z^4*b - 4*z^3*a - 4*z^3*b + 6*z^2*a -
6*z^2*b + 4*z*a + 4*z*b - a + b) * (z^4*a + z^4*b - 4*z^3*a + 4*z^3*b -
6*z^2*a - 6*z^2*b + 4*z*a - 4*z*b + a + b)
}}}
This is ''not'' fixed by #17184.
--
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Ticket URL: <http://trac.sagemath.org/ticket/17251#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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