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