Function: rnfidealup
Section: number_fields
C-Name: rnfidealup
Prototype: GG
Help: rnfidealup(rnf,x): lifts the ideal x (of the base field) to the
 relative field.
Doc: let $\var{rnf}$ be a relative number
 field extension $L/K$ as output by \kbd{rnfinit} and let $x$ be an ideal of
 $K$. This function returns the ideal $x\Z_L$ as an absolute ideal of $L/\Q$,
 in the form of a $\Z$-basis, given by a vector of polynomials (modulo
 \kbd{rnf.pol}).

 The reason why we do not return the customary HNF in terms of a fixed
 $\Z$-basis for $\Z_L$ is precisely that no such basis has been explicitly
 specified. On the other hand, if you already computed an (absolute) \var{nf}
 structure \kbd{Labs} associated to $L$, then
 \bprog
   xabs = rnfidealup(L, x);
   xLabs = mathnf(matalgtobasis(Labs, xabs));
 @eprog\noindent computes a traditional HNF \kbd{xLabs} for $x$ in terms of
 the fixed $\Z$-basis \kbd{Labs.zk}.
