Function: nffactormod
Section: number_fields
C-Name: nffactormod
Prototype: GGG
Help: nffactormod(nf,Q,pr): factor polynomial Q modulo prime ideal pr
 in number field nf.
Doc: 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)
 [x + (2*y + 1) 1]

 [x + (2*y + 2) 1]
 @eprog\noindent Same result, of course, here about 10\% faster due to the
 precomputation.