check(K,P,T) = [nfislocalpower(K,P,v[1],v[2]) | v<-T];

K=bnfinit(y^2+1);
P=idealprimedec(K,2)[1];
check(K,P, [[2,2], [-1,2], [-1,4]])

P=idealprimedec(K,5)[1];
check(K,P, [[P.gen[2],2], [P.gen[2],5], [y,5], [y,10], [Mod(y+1,K.pol)^10,10]])

p=406969676467377719018888256331; P=idealprimedec(K,p)[1];
check(K,P, [[y,2], [y,p]])

P=idealprimedec(K,5)[1];
check(K,P, [[1/25,2], [P.gen[2]/5,2], [1/6,2^64], [y/7,2]])

P=idealprimedec(K,3)[1];
nfislocalpower(K, P, y/7,32)

K=nfinit(x^2-155);P=idealprimedec(K,5)[1];
nfislocalpower(K, P, 20*x-249, 5)

K=nfinit(y^3-2);
P=idealprimedec(K,3)[1];
check(K,P, [[2^18,54], [y,3], [y,0], [1,0]])

P=idealprimedec(K,7)[1];
nfislocalpower(K,P,((y+1)/2)^32,32)

\\ ERRORS
nfislocalpower(K,"",1,0)
nfislocalpower(K,"","",0)
