#13672: resultant over GF(q)[t][x] is plain wrong!!!
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Reporter: zimmerma | Owner: malb
Type: defect | Status: new
Priority: blocker | Milestone: sage-5.5
Component: commutative algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by malb):
This seems to be a bug in Pari or our conversion to Pari:
{{{
#!python
sage: R.<t> = GF(2)[]; S.<x> = R[]
sage: f=(t^2 + t)*x + t^2 + t; g=(t + 1)*x + t^2
sage: f.resultant(g)
t^3 + t
sage: f._pari_().polresultant(g._pari_(), x._pari_(), 0)
Mod(1, 2)*x^3 + Mod(1, 2)*x
sage: Q = PolynomialRing(GF(2), f.parent().variable_names_recursive())
sage: Q(f).resultant(Q(g),variable=Q(x))
t^4 + t
}}}
Note that {{{resultant()}}} has this logic:
{{{
#!python
variable = self.parent().gen()
if str(variable)<>'x' and
self.parent()._mpoly_base_ring()<>self.parent().base_ring():
# use multivariate instead
}}}
and this works:
{{{
#!python
sage: R.<t> = GF(2)[]; S.<y> = R[]
sage: f=(t^2 + t)*y + t^2 + t; g=(t + 1)*y + t^2
sage: f.resultant(g)
t^4 + t
}}}
I don't understand why this {{{str(variable)<>'x'}}} check is there.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13672#comment:3>
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