Function: nfislocalpower
Section: number_fields
C-Name: nfislocalpower
Prototype: lGGGG
Help: nfislocalpower(nf,pr,a,n): true(1) if a is an n-th power in
 the local field K_v, false(0) if not.
Doc: Let \var{nf} be a \var{nf} structure attached to a number field $K$,
 let $a \in K$ and let \var{pr} be a \var{prid} structure attached to a
 maximal ideal $v$. Return $1$ if $a$ is an $n$-th power in the completed
 local field $K_{v}$, and $0$ otherwise.
 \bprog
 ? K = nfinit(y^2+1);
 ? P = idealprimedec(K,2)[1]; \\ the ramified prime above 2
 ? nfislocalpower(K,P,-1, 2) \\ -1 is a square
 %3 = 1
 ? nfislocalpower(K,P,-1, 4) \\ ... but not a 4-th power
 %4 = 0
 ? nfislocalpower(K,P,2, 2)  \\ 2 is not a square
 %5 = 0

 ? Q = idealprimedec(K,5)[1]; \\ a prime above 5
 ? nfislocalpower(K,Q, [0, 32]~, 30)  \\ 32*I is locally a 30-th power
 %7 = 1
 @eprog
