algissplit

Function: algissplit
Section: algebras
C-Name: algissplit
Prototype: iGDG
Help: algissplit(al,{pl}): tests whether the central simple algebra al is
 split, i.e. 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 split at the place pl instead.
Doc: Given a central simple algebra \var{al} output by \tet{alginit}, tests
 whether~\var{al} is split, i.e. 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 split at the
 place \var{pl} instead.

 \bprog
 ? nf = nfinit(y^2-5);
 ? A = alginit(nf, [-1,y]);
 ? algissplit(A, 1)
 %3 = 0
 ? algissplit(A, 2)
 %4 = 1
 ? algissplit(A, idealprimedec(nf,2)[1])
 %5 = 0
 ? algissplit(A, idealprimedec(nf,5)[1])
 %6 = 1
 ? algissplit(A)
 %7 = 0
 @eprog