Function: nffactormod
Section: number_fields
C-Name: nffactormod
Obsolete: 2016-09-18
Prototype: GGG
Help: nffactormod(nf,Q,pr): this routine is obsolete, use nfmodpr and
factormod. Factor polynomial Q modulo prime ideal pr
in number field nf.
Doc: this routine is obsolete, use \kbd{nfmodpr} and \kbd{factormod}.
Factors the univariate polynomial $Q$ modulo the prime ideal \var{pr} in
the number field $\var{nf}$. The coefficients of $Q$ belong to the number
field (scalar, polmod, polynomial, even column vector) and the main variable
of $\var{nf}$ must be of lower priority than that of $Q$ (see
\secref{se:priority}). The prime ideal \var{pr} is either in
\tet{idealprimedec} or (preferred) \tet{modprinit} format. The coefficients
of the polynomial factors are lifted to elements of \var{nf}:
\bprog
? K = nfinit(y^2+1);
? P = idealprimedec(K, 3)[1];
? nffactormod(K, x^2 + y*x + 18*y+1, P)
%3 =
[x + (2*y + 1) 1]
[x + (2*y + 2) 1]
? P = nfmodprinit(K, P); \\ convert to nfmodprinit format
? nffactormod(K, x^2 + y*x + 18*y+1)
%5 =
[x + (2*y + 1) 1]
[x + (2*y + 2) 1]
@eprog\noindent Same result, of course, here about 10\% faster due to the
precomputation.