Function: algisramified
Section: algebras
C-Name: algisramified
Prototype: iGDG
Help: algisramified(al,{pl}): tests whether the central simple algebra al is
 ramified, i.e. not isomorphic to a matrix ring over its center. If pl is set,
 it should be a prime ideal of the center or an integer between 1 and r1+r2, and
 in that case tests whether al is locally ramified at the place pl instead.
Doc: Given a central simple algebra \var{al} output by \tet{alginit}, tests
 whether \var{al} is ramified, i.e. not isomorphic to a matrix algebra over its
 center. 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} is
 locally ramified at the place \var{pl} instead.
 \bprog
 ? nf = nfinit(y^2-5);
 ? A = alginit(nf, [-1,y]);
 ? algisramified(A, 1)
 %3 = 1
 ? algisramified(A, 2)
 %4 = 0
 ? algisramified(A, idealprimedec(nf,2)[1])
 %5 = 1
 ? algisramified(A, idealprimedec(nf,5)[1])
 %6 = 0
 ? algisramified(A)
 %7 = 1
 @eprog
