#5074: singular factorization over GF(p) need not be a complete factorization
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Reporter: was | Owner: malb
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.5
Component: commutative algebra | Keywords:
Author: | Upstream: Not yet reported upstream;
Will do shortly.
Reviewer: | Merged:
Work_issues: |
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Comment(by was):
It's definitely still broken. Note that it isn't broken every single time
:-):
{{{
sage: sage: k.<a> = GF(9)sage: sage: R.<x,y> = PolynomialRing(k)
sage: sage: h = - (-x^2 - x*y + y^2 - 1)^2 * (x^2*y^2 + y^4 + x^2*y +
x*y^2 + y^3 - x^2 + x*y + y^2 - 1) * (-x^4 - x^3*y - x*y^3 + y^4 - x^3 +
x^2*y + x*y^2 - x^2 - x*y - y^2 + x + 1)
sage: h.factor()
(-1) * (-x^2 - x*y + y^2 - 1) * (x^2*y^2 + y^4 + x^2*y + x*y^2 + y^3 - x^2
+ x*y + y^2 - 1) * (x^6 - x^5*y + x*y^5 + y^6 + x^5 + x*y^4 - x^4 +
x^2*y^2 + x*y^3 + y^4 + x^2*y - y^2 - x - 1)
sage: h.factor()
(-1) * (-x^2 - x*y + y^2 - 1)^2 * (-x^6*y^2 - x^5*y^3 - x^4*y^4 + x^3*y^5
+ x^2*y^6 - x*y^7 + y^8 - x^6*y - x^4*y^3 + x^3*y^4 + x^2*y^5 + x*y^6 +
y^7 + x^6 - x^5*y + x^2*y^4 + x^5 + x^3*y^2 - x^2*y^3 - y^5 - x^4 - x^3*y
+ x^2*y^2 - y^4 + x^2*y + x*y^2 + y^3 - x*y - y^2 - x - 1)
sage: h.factor()
(-1) * (-x^2 - x*y + y^2 - 1) * (x^8*y^2 - x^7*y^3 + x^6*y^4 - x^5*y^5 +
x^3*y^7 + x^2*y^8 + x*y^9 + y^10 + x^8*y + x^7*y^2 - x^3*y^6 - x^2*y^7 +
y^9 - x^8 + x^3*y^5 + x*y^7 - y^8 - x^7 + x^4*y^3 + x^3*y^4 - x^2*y^5 +
y^7 - x^4*y^2 + x^3*y^3 + x^2*y^4 + x*y^5 - y^6 - x^5 - x^4*y - y^5 + x^4
- x^3*y + x^2*y^2 + x^3 + x*y^2 - y^3 + x^2 - x*y + x + 1)
sage: h.factor()
(-1) * (-x^2 - x*y + y^2 - 1)^2 * (x^2*y^2 + y^4 + x^2*y + x*y^2 + y^3 -
x^2 + x*y + y^2 - 1) * (-x^4 - x^3*y - x*y^3 + y^4 - x^3 + x^2*y + x*y^2 -
x^2 - x*y - y^2 + x + 1)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5074#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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