Karim Belabas on Thu, 24 Jan 2013 16:11:06 +0100 |
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Re: Field inclusion problem |
* Ewan Delanoy [2013-01-24 15:56]: > >The problem is variable priorities. The variable of the polynomial > >defining the "base field" must have *lower* priority then the variable > >of the polynomial to be factored. See ??nffactor > > > The output of ??nffactor contains the following : â(see Section [Label: se:priority])â. What does that refer to ? > Is it a section in the userâs manual or in the online help ? I tried ??Label but to no avail. The online help is directly extracted from the (TeX) documentation (after a rough formatting attempt). Unfortunately it can't follow cross-references. I recommand to read the actual pdf documentation, in the GP User's Manual, Chapter 2, section "Variable priorities, multivariate objects". It's also possible to search a little through the online help: (16:05) gp > ???"se:priority"@ \\ @ means : include all chapters Chapter 3: ========== denominator factornf galoisfixedfield nffactor nffactormod nfroots numerator rnfdisc rnfequation rnfinit writebin See also: Relative extensions Chapter 4: ========== Multivariate objects Type \typ{POLMOD} (polmod) Type \typ{POL} (polynomial) Chapter 2: ========== Polmods (\typ{POLMOD}) Variable priorities, multivariate objects This one is the most interesting: (16:05) gp > ?? "Variable priorities, multivariate objects"@ Variable priorities, multivariate objects: A multivariate polynomial in PARI is just a polynomial (in one variable), whose coefficients are themselves polynomials, arbitrary but for the fact that they do not involve the main variable. (PARI currently has no sparse representation for polynomials, listing only non-zero monomials.) All computations are then done formally on the coefficients as if the polynomial was univariate. This is not symmetrical. So if I enter x + y in a clean session, what happens? This is understood as x^1 + (y^1 + 0*y^0)*x^0 belongs to (Z[y])[x] but how do we know that x is "more important" than y ? Why not y^1 + x*y^0, which is the same mathematical entity after all? [ ...etc...] (But if you never went through GP's documentation, it's easier to read a PDF.) 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] `