Function: rnfidealreltoabs
Section: number_fields
C-Name: rnfidealreltoabs
Prototype: GG
Help: rnfidealreltoabs(rnf,x): transforms the ideal x from relative to
 absolute representation.
Doc: let $\var{rnf}$ be a relative
 number field extension $L/K$ as output by \kbd{rnfinit} and let $x$ be a
 relative ideal, given as a $\Z_K$-module by a pseudo matrix $[A,I]$.
 This function returns the ideal $x$ 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) \kbd{nf}
 structure \kbd{Labs} associated to $L$, then
 \bprog
   xabs = rnfidealreltoabs(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}.
