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 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). On the same example pari/gp returns 0: ? p1=(x2)*(x3-x4);p2=x2*(x3-2*x4);polresultant(p1,p2,x1) %5 = 0 [1]: http://en.wikipedia.org/w/index.php?title=Resultant&oldid=511538674 On Tue, Sep 18, 2012 at 05:22:59PM +0200, Julian Rüth wrote: > Hi, > > I'm not sure if I understand what is counterintuitive about the results. > > * Georgi Guninski <gunin...@guninski.com> [2012-09-18 16:55:37 +0300]: > > sage: K.<x1,x2,x3>=PolynomialRing(QQ) > > sage: p1=(x2-1)*(x3+2) > > sage: p2=(x2-1)*(x3+3) > > sage: p1.resultant(p2) > > 1 > This is the resultant of p1 and p2 w.r.t. x1 (the first variable of K). > > > sage: K_.<x2,x3>=PolynomialRing(QQ) > > sage: p1_=K_(p1) > > sage: p2_=K_(p2) > > sage: p1_.resultant(p2_) > > 0 > The resultant of p1 and p2 w.r.t. x2 (the first variable of K_). > > > sage: gp.polresultant(gp(p1),gp(p2)) > > 0 > I'm not entirely sure what gp.polresultant() does, but it seems it > computes the resultant w.r.t. variable() > > sage: gp(p1).variable() > x2 > > The following is strange though: > > sage: gp.polresultant(p1,p2,x1) > 0 # this should be 1? > sage: gp.polresultant(p1,p2,x2) > 0 > sage: gp.polresultant(p1,p2,x3) > x2^2 - 2*x2 + 1 > > Am I missing something here? > > julian > > -- > 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. -- 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.
