On 2014-08-08, John Cremona <john.crem...@gmail.com> wrote: > On 8 August 2014 03:21, rjf <fate...@gmail.com> wrote: >> 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 > > This certainly the correct answer, as one can check by going back to > first principles: the resultant of 2 quadratics is a homogenous > polynomial in the 6 coefficients, actually bihomogeneous of bidegree > (2,2), given by a 4x4 determinant. It makes no difference when one > reduces modulo the modulus: > > sage: x = polygen(QQ) > sage: a,b,c,d,e,f = [x^4, x^3+1, x-2, x^3+2*x+1, x+1, x^4+x^3+x^2+1] > sage: M = Matrix(4,4,[a,0,d,0,b,a,e,d,c,b,f,e,0,c,0,f]); M > [ x^4 0 x^3 + 2*x + 1 > 0] > [ x^3 + 1 x^4 x + 1 x^3 > + 2*x + 1] > [ x - 2 x^3 + 1 x^4 + x^3 + x^2 + 1 > x + 1] > [ 0 x - 2 0 x^4 + x^3 > + x^2 + 1] > sage: M.det() % (x^3+3*x+1) > 2201*x^2 - 2042*x - 885
and this is in agreement with the direct computation in GF(487326487) done on Sage 6.3.rc0, as -2042 % 487326487 == 487324445 and -885 % 487326487 == 487325602. -- 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.
