#10902: missing terms in factorization of multivariate polynomials
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Reporter: zimmerma | Owner: malb
Type: defect | Status: new
Priority: critical | Milestone: sage-4.7.2
Component: commutative algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by zimmerma):
and an example over GF(5):
{{{
sage: R.<x,y> = GF(5)[]
sage: p=x^27*y^9 + x^32*y^3 + 2*x^20*y^10 - x^4*y^24 - 2*x^17*y
sage: q=-2*x^10*y^24 + x^9*y^24 - 2*x^3*y^30
sage: f=p*q; f-f.factor(proof=False)
-2*x^37*y^33 - 2*x^42*y^27 + x^36*y^33 - 2*x^30*y^39 + x^41*y^27 -
2*x^35*y^33 + x^30*y^34 + 2*x^29*y^34 + x^23*y^40 + 2*x^14*y^48 -
x^13*y^48 + 2*x^7*y^54 + 2*x^37*y^18 + 2*x^42*y^12 - x^36*y^18 +
2*x^30*y^24 - x^41*y^12 + 2*x^35*y^18 - x^27*y^25 - 2*x^26*y^25 -
x^20*y^31 - x^30*y^19 - 2*x^29*y^19 - x^23*y^25 - 2*x^14*y^33 + x^13*y^33
- 2*x^7*y^39 + x^27*y^10 + 2*x^26*y^10 + x^20*y^16
}}}
and one over GF(7):
{{{
sage: R.<x,y> = GF(7)[]
sage: p=-3*x^47*y^24
sage: q=-3*x^47*y^37 - 3*x^24*y^49 + 2*x^56*y^8 + 3*x^29*y^15 - x^2*y^33
sage: f=p*q
sage: f-f.factor(proof=False)
2*x^94*y^61 + 2*x^71*y^73 + x^103*y^32 - 2*x^59*y^61 - 2*x^76*y^39 -
2*x^36*y^73 + 3*x^49*y^57 - x^68*y^32 + 2*x^41*y^39 - 3*x^14*y^57
}}}
Examples can be constructed at will with the following code (change GF(7)
by whatever you want):
{{{
R.<x,y> = GF(7)[]
nterms=2
for d in range(1,10^6):
print d
sys.stdout.flush()
p = R.random_element(degree=d,terms=nterms)
while p.degree()<=0:
p = R.random_element(degree=d,terms=nterms)
q = R.random_element(degree=d,terms=nterms)
while q.degree()<=0:
q = R.random_element(degree=d,terms=nterms)
f = p*q
lp = p.factor(proof=False)
lq = q.factor(proof=False)
lf = f.factor(proof=False)
if lp*lq <> lf:
print p, q
raise ValueError
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10902#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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