Thanks Peter. That clears it up well. I actually thought that you could specify which variable Pari/GP took the resultant with respect to. But this obviously doesn't get you around the variable ordering issue.
I was vaguely aware of that problem, but had no idea I wasn't working around it already. I'm glad to hear this is also fixed in Sage. I tend to use the latest stable release of Sage, but not usually the beta, so I missed that this had been fixed. Thanks again for the help. Bill. On Thursday, 7 August 2014 17:02:56 UTC+2, Peter Bruin wrote: > > Hi Bill, > > This bug was only fixed two weeks ago (Trac tickets #15061 and #16360), > so it only works in the most recent beta versions of Sage. > > The reason why PARI gives the wrong answer has to do with variable > ordering; for example, f is translated to > > f = Mod(-3*y^2*x^2 + (-y^2 - 3*y + 1)*x - 2, x^3 + 3*x + 1) > > which is not a polynomial at all. If you want to do this computation in > PARI, you have to replace x by a variable with lower priority than y: > > gp > y; z; > gp > f = (z^4*y^2 + (z^3 + 1)*y + (z - 2)) * Mod(1, z^3 + 3*z + 1) * > Mod(1, 487326487); > gp > g = ((z^3 + 2*z + 1)*y^2 + (z + 1)*y + (z^4 + z^3 + z^2 + 1)) * > Mod(1, z^3 + 3*z + 1) * Mod(1, 487326487); > gp > polresultant(f, g) > %4 = Mod(Mod(2201, 487326487)*z^2 + Mod(487324445, 487326487)*z + > Mod(487325602, 487326487), z^3 + 3*z + 1) > > Peter > > > Bill Hart wrote: > > > 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+...@googlegroups.com <javascript:>. > > To post to this group, send email to sage-...@googlegroups.com > <javascript:>. > > Visit this group at http://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/d/optout. > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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