#13672: resultant over GF(2)[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 | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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Consider the following:
{{{
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
}}}
This is wrong: the resultant of {{{f}}} and {{{g}}} is {{{t^4+t}}}.
Plenty of failures can be found with the following code which computes the
resultant as the determinant of the Sylvester matrix:
{{{
def Resultant(f,g):
df = f.degree()
dg = g.degree()
K = f.base_ring()
M = matrix(K,df+dg,df+dg)
for i in range(dg):
for j in range(df+1):
M[i,i+j] = f.coeffs()[df-j]
for i in range(df):
for j in range(dg+1):
M[dg+i,i+j] = g.coeffs()[dg-j]
return M.det()
def check(df,dg):
f = S.random_element(degree=df)
g = S.random_element(degree=dg)
r1 = f.resultant(g)
r2 = Resultant(f,g)
if r1 <> r2:
print f, g, r1, r2
raise ValueError
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13672>
Sage <http://www.sagemath.org>
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