On Wednesday, September 19, 2012 6:34:52 AM UTC+2, Georgi Guninski wrote: > > Hi, > > I may be missing something, but the resultant = 1 confuses me. > According to wikipedia [1] > the multivariate resultant or Macaulay's resultant of n homogeneous > polynomials in n variables is a polynomial in their coefficients that > vanishes when they have a common non-zero solution >
Note that this means n homogeneous polynomials in n variables, in your example you only have two polynomials in four variables, it is not the same case of Macaulay's resultant. > My pain is $1$ can't vanish while solutions exist. > > Here is homogeneous example: > sage: K.<x1,x2,x3,x4>=QQ[] > sage: p1,p2=(x2)*(x3-x4),x2*(x3-2*x4) > sage: p1.resultant(p2,x1) > 1 > > Certainly p1 and p2 have common solutions while the res. w.r.t. > x1 never vanishes (got this in a real world situation). > As said, in this case the resultant is computed in the ring QQ(x2,x3)[x1] and the resultant will vanish if the two (univariate) polynomials have a common root in the algebraic closure of QQ(x2,x3). This is the standard resultant of multivariate polynomials with respect to one variable. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
