#12752: resulant of two polynomials returns incorrect value
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Reporter: bhutz | Owner: tba
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: number theory | Keywords: polynomial resultant
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: todo |
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The resultant of two homogeneous polynomials can return an incorrect
value:
R.<x,y>=PolynomialRing(ZZ)[[BR]]
f=6*x^2^ + x*y + y^2^[[BR]]
g=y^2^
print f.resultant(g)[[BR]]
m=matrix([[6,1,1,0],[0,6,1,1],[0,0,1,0],[0,0,0,1]])[[BR]]
m.determinant()
notice that the coefficient of the f.resultant(g) does not match the
integer determinant (they should be the same). I believe this is because
the .resultant function is actually calling the pari library, which is
interpreting y^2^ as a single variable polynomial. Thus it builds the
wrong matrix. Probably the following:
m=matrix([[6,1,1,0],[0,6,1,1],[1,0,0,0],[0,1,0,0]])[[BR]]
m.determinant()
which is the value Sage is returning. The correct value is returned in
Sage from
m=f.sylvester_matrix(g,x)[[BR]]
m.determinant()
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12752>
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