Karim BELABAS on Thu, 9 Oct 2003 12:57:28 +0200 (MEST) |
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Re: Oddities modulo multivariate polynomials |
On Thu, 9 Oct 2003, Dirk Laurie wrote: > Jeroen Demeyer skryf: >> ? Y /* Make sure Y is defined first */ >> %1 = Y >> ? (Y^2) % (X^3 - Y^2) >> %2 = X^3 >> ? (X^3) % (X^2 + 1) >> %3 = -X >> ? ((Y^2) % (X^3 - Y^2)) % (X^2 + 1) >> %4 = 0 >> >> How come the outputs of the two last statements are different? Is this >> a bug or am I doing something wrong? Any help would be appreciated. > > A very pleasant problem in detection! Let's get some more data. > Start from scratch each time in a new Pari-GP session. [...] > The hypothesis so far stands up. To explain your original > result: I guess that once the decision has been made, it > remains in effect for the whole expression. So that in > an expression like the one giving your %4, the independent > variable is Y, since it was defined first. You can't > have Y as independent in one subexpression and X in the other. > Whereas in %3 there is no ambiguity. There is a section 2.6.2 to explain this in the users manual, unfortunately in the _unstable_ version. [ Sorry, I do not backport documentation changes... ] I would recommand trying out the unstable branch (2.2.*) nowadays. It is very close to beta status, and definitely contains far fewer documented bugs than the stable one. Cheers, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathématiques, Bât. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://www.parigp-home.de/ [PARI/GP]