The resultant of two homogeneous polynomials can return an incorrect value: R.<x,y>=PolynomialRing(ZZ) f=6*x^2 + x*y + y^2 g=y^2 print f.resultant(g) m=matrix([[6,1,1,0],[0,6,1,1],[0,0,1,0],[0,0,0,1]]) 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 m=matrix([[6,1,1,0],[0,6,1,1],[1,0,0,0],[0,1,0,0]]) m.determinant() which is the value Sage is returning. The correct value is returned in Sage from m=f.sylvester_matrix(g,x) m.determinant() Ben -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
