Karim Belabas on Fri, 03 Aug 2012 11:04:20 +0200 |
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Re: Polynomial division with imprecise types |
* SÃren Lennart Berg [2012-08-03 04:30]: > Hello, > using the PARI library I'm having the following issue: > Let p1,p2 be two (multivariate) polynomials. From the mathematical context I know that p2 divides p1. > However, both may contain imprecise coefficients. e.g. t_REAL's. Using poldivrem() on p1/p2 PARI returns > a rational function (t_RFRAC). Is there a way to obtain p1/p2 as a polynomial, i.e. force PARI to divide p1 by p2? Could you give a specific example ? Preferably under gp. GEN q = poldivrem(p1, p2, &r); // Euclidean diviÑion with respect to the *main* variable of [p1,p2] should return a polynomial quotient q (t_POL), with a remainder r which is close to 0. Both q and r have coefficient in the field of fractions of the base ring, whÑch is a field of rational functions in your case. For instance: (10:58) gp > p1 = x^2 - Pi^2*y^2; p2 = x*y - Pi*y^2; divrem(p1, p2) %1 = [1/y*x + 3.1415926535897932384626433832795028842, 0.E-37*y^2]~ \\ [q, r], both t_POL in x whith coefficients in R(y) The only potential problem I see is that division may not occur with repect to the variable you intended. Cheers, K.B. -- Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17 Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50 351, cours de la Liberation http://www.math.u-bordeaux1.fr/~belabas/ F-33405 Talence (France) http://pari.math.u-bordeaux1.fr/ [PARI/GP] `