There is a different answer from Maxima, at least different from what is posted.
algebraic:true; tellrat(x^3+3*x+1); resultant(f,g,y) gives 2201*x^2-2042*x-885 Note that Maxima can also compute the resultant wrt x without renaming variables. On Thursday, August 7, 2014 10:25:19 AM UTC-7, Bill Hart wrote: > > 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. >> > To post to this group, send email to sage-...@googlegroups.com. >> > 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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