Karim Belabas on Thu, 24 Jan 2013 16:22:32 +0100 |
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Re: Field inclusion problem |
* Karim Belabas [2013-01-24 16:11]: > * 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 > [...] > > (But if you never went through GP's documentation, it's easier to read a PDF.) I just tweaked the online help in 2.6.* to allow following cross-references to some extent, simplifying somewhat the above. Whenever you see a [Label: foo ], you can now directly query 'foo' : (16:19) gp > ??nffactor nffactor(nf,T): Factorization of the univariate polynomial T over the number field nf given by nfinit; T has coefficients in nf (i.e. either scalar, polmod, polynomial or column vector). The factors are sorted by increasing degree. The main variable of nf must be of lower priority than that of T, see Section [Label: se:priority]. [... snip ... ] (16:19) gp > ??"se:priority"@ 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. [... snip ... ] 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] `