Function: rnfislocalcyclo
Section: number_fields
C-Name: rnfislocalcyclo
Prototype: lG
Help: rnfislocalcyclo(rnf): true(1) if the l-extension attached to rnf
 is locally cyclotomic (locally contained in the Z_l extension of K_v at
 all places v | l), false(0) if not.
Doc: Let \var{rnf} be a relative number field extension $L/K$ as output
 by \kbd{rnfinit} whose degree $[L:K]$ is a power of a prime $\ell$.
 Return $1$ if the $\ell$-extension is locally cyclotomic (locally contained in
 the cyclotomic $\Z_\ell$-extension of $K_v$ at all places $v | \ell$), and
 $0$ if not.
 \bprog
 ? K = nfinit(y^2 + y + 1);
 ? L = rnfinit(K, x^3 - y); /* = K(zeta_9), globally cyclotomic */
 ? rnfislocalcyclo(L)
 %3 = 1
 \\ we expect 3-adic continuity by Krasner's lemma
 ? vector(5, i, rnfislocalcyclo(rnfinit(K, x^3 - y + 3^i)))
 %5 = [0, 1, 1, 1, 1]
 @eprog
