algisdivision

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

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