I think that is the correct answer. It agrees with one of the answers Magma gives, and someone else says Mathematica agrees.
My version of Sage is 'Sage Version 6.2, Release Date: 2014-05-06' Bill. On Thursday, 7 August 2014 16:10:52 UTC+2, Frédéric Chapoton wrote: > > Hello, > > it works for me on sage 6.3.beta8, giving: > > 2201*xbar^2 + 487324445*xbar + 487325602 > > which version of sage do you use ? type version() to know that. > > By the way, you should rather have asked that question on sage-support or > on ask.sagemath.org > > Le jeudi 7 août 2014 16:03:43 UTC+2, Bill Hart a écrit : >> >> I'm having difficulties with the polynomial resultant function in Sage. >> >> I'm trying to find the resultant of two polynomials. >> >> I compute the resultant of the polynomials below to be: >> >> 6768454*x^2+257200062*x+20305258 >> >> Pari/GP says the resultant is 1, which I don't believe, so I thought I'd >> try Sage 6.2: >> >> sage: R = Integers(487326487) >> sage: S.<x> = PolynomialRing(R) >> sage: T = QuotientRing(S, x^3 + 3*x + 1) >> sage: U.<y> = PolynomialRing(T) >> sage: f = x^4*y^2 + (x^3 + 1)*y + (x - 2) >> sage: g = (x^3 + 2*x + 1)*y^2 + (x + 1)*y + (x^4 + x^3 + x^2 + 1) >> sage: f.resultant(g) >> >> --------------------------------------------------------------------------- >> PariError Traceback (most recent call >> last) >> <ipython-input-9-14f40f55d982> in <module>() >> ----> 1 f.resultant(g) >> >> /usr/local/sage/sage-current/local/lib/python2.7/site-packages/sage/structure/element.so >> >> in sage.structure.element.NamedBinopMethod.__call__ >> (sage/structure/element.c:25475)() >> >> /usr/local/sage/sage-current/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.so >> >> in sage.rings.polynomial.polynomial_element.Polynomial.resultant >> (sage/rings/polynomial/polynomial_element.c:33908)() >> >> /usr/local/sage/sage-current/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.so >> >> in sage.rings.polynomial.polynomial_element.Polynomial._pari_with_name >> (sage/rings/polynomial/polynomial_element.c:33119)() >> >> /usr/local/sage/sage-current/local/lib/python2.7/site-packages/sage/libs/pari/gen.so >> >> in sage.libs.pari.gen.gen.Polrev (sage/libs/pari/gen.c:12936)() >> >> /usr/local/sage/sage-current/local/lib/python2.7/site-packages/sage/libs/pari/handle_error.so >> >> in sage.libs.pari.handle_error._pari_handle_exception >> (sage/libs/pari/handle_error.c:1178)() >> >> PariError: variable must have higher priority in gtopoly >> >> ------------------- >> >> Magma gives two different answers, depending on whether you coerce the >> coefficients of f and g into T or not (I don't see why). Neither agree with >> the Pari/GP answer, or the answer I compute myself (which is very likely >> wrong). >> >> Coercing the coefficients into T makes no difference to the resulting >> error in Sage. >> >> Can someone tell me what I am doing wrong here. I obviously don't know >> what I'm doing. I've never really tried to do any genuine computer algebra >> before. >> >> Bill. >> >> >> >> >> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
