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

   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 ... ]


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]