algindex

Function: algindex
Section: algebras
C-Name: algindex
Prototype: lGDG
Help: algindex(al,{pl}): the index of the central simple algebra al. 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 return the local index at the place pl instead.
Doc: Returns the index of the central simple algebra~$A$ over~$K$ (as output by
 alginit), that is the degree~$e$ of the unique central division algebra~$D$
 over $K$ such that~$A$ is isomorphic to some matrix algebra~$M_k(D)$. 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 return the local index at the place \var{pl}
 instead.

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