#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 malb):
I just tried it again with 3-1-1-3 which does have some new factorisation
code over GF(p)
{{{
sage: k.<a> = GF(9)sage: sage: R.<x,y> = PolynomialRing(k)
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: for i in range(10): h.factor(proof=False)
....:
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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)
(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:5>
Sage <http://www.sagemath.org>
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