Peter-Lawrence . Montgomery on Fri, 26 Feb 1999 01:17:22 +0100 (MET) |
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Re: Strange polresultant behavior |
Roland Dreier <droland@mail.math.okstate.edu> reports > I'm getting the following strange behavior from gp version 2.0.13. I have > two polynomials in two variables, x and y (over the field with 5 > elements). I take their resultant with respect to x to get a big > polynomial in y. I then take a root of this polynomial and plug it in for > y in the original two polynomials to get two polynomials in x. Unless I'm > confused, the resultant of these two new polynomials should be zero -- it > doesn't matter whether I plug the root in after taking the resultant or > before. But for certain polynomials, I don't get zero. > I didn't try Roland's example, but the problem may be a double projective root in x, if the two leading coefficints vanish for the same value of y. When we substitute a numerical value for y before taking the resultant, the degrees change. GP/PARI CALCULATOR Version 2.0.11 (beta) unknown 32-bit version (readline disabled, extended help not available) Copyright (C) 1989-1998 by C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier. Send bug reports, suggestions and patches to pari@math.u-bordeaux.fr Type ? for help. realprecision = 38 significant digits seriesprecision = 16 significant terms format = g0.38 parisize = 10000000, primelimit = 500000, buffersize = 30000 echo = 1 (on) ? f1=x*y-1 %1 = y*x - 1 ? f2=x*y-2 %2 = y*x - 2 ? polresultant(f1,f2,x) %3 = -y ? quit Good bye! By the way, why are blanks removed in echo mode? My input to this example was \e f1 = x*y - 1 f2 = x*y - 2 polresultant(f1, f2, x) quit