pari disagrees with sage and maxima agrees with it. which way is it?
maxima session: (%i12) p1:(x2)*(x3-x4);p2:x2*(x3-2*x4); (%i14) resultant(p1,p2,x1); (%o14) 1 (%i15) resultant(p1,p2,x2); (%o15) 0 On Wed, Sep 19, 2012 at 07:34:46AM +0300, 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 > 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 > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
