Function: algisisom
Section: algebras
C-Name: algisisom
Prototype: iGGDG
Help: algisisom(al,al2,{pl}): tests whether the central simple algebras al and
 al2 are isomorphic. If pl is set, test isomorphism locally at the place pl
 instead.
Doc: Given central simple algebras \var{al} and \var{al2} output by
 \tet{alginit} and defined over the same number field~$K$, tests
 whether~\var{al} and \var{al2} are isomorphic as~$K$-algebras.
 If \var{pl} is set, it should be a prime ideal of~$K$ or an integer between~$1$
 and~$r_{1}+r_{2}$, and in that case tests whether \var{al} and \var{al2} are
 locally isomorphic at the place \var{pl} instead.
 \bprog
 ? nf = nfinit(y^2-2);
 ? al = alginit(nf, [1+y, -7]);
 ? al2 = alginit(nf, [-1, 2*y-1]);
 ? al3 = alginit(nf, [1-y, -7]);
 ? algisisom(al,al2)
 % = 1
 ? algisisom(al,al3) \\ isomorphic over Q but not as K-algebras
 % = 0
 ? pr = idealprimedec(nf,2)[1];
 ? algisisom(al,al3,pr)
 % = 1 \\ isomorphic locally at the prime ideal pr
 ? algisisom(al,al3,1)
 % = 0 \\ not isomorphic locally at the first place at infinity
 @eprog
