Function: idealpow
Section: number_fields
C-Name: idealpow0
Prototype: GGGD0,L,
Help: idealpow(nf,x,k,{flag=0}): k-th power of the ideal x in HNF in the
 number field nf. If (optional) flag is non-null, reduce the result.
Doc: computes the $k$-th power of
 the ideal $x$ in the number field $\var{nf}$; $k\in\Z$.
 If $x$ is an extended
 ideal\sidx{ideal (extended)}, its principal part is suitably
 updated: i.e. raising $[I,t]$ to the $k$-th power, yields $[I^k, t^k]$.

 If $\fl$ is non-zero, reduce the result using \kbd{idealred}, \emph{throughout
 the (binary) powering process}; in particular, this is \emph{not} the same as
 as $\kbd{idealpow}(\var{nf},x,k)$ followed by reduction.

Variant:
 \noindent See also
 \fun{GEN}{idealpow}{GEN nf, GEN x, GEN k} and
 \fun{GEN}{idealpows}{GEN nf, GEN x, long k} ($\fl = 0$).
 Corresponding to $\fl=1$ is \fun{GEN}{idealpowred}{GEN nf, GEN vp, GEN k}.