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.
