algissimple

Function: algissimple
Section: algebras
C-Name: algissimple
Prototype: iGD0,L,
Help: algissimple(al, {ss = 0}): test whether the algebra al is simple.
Doc: \var{al} being a table algebra output by \tet{algtableinit} or a central
 simple algebra output by \tet{alginit}, tests whether the algebra \var{al} is
 simple. If $\var{ss}=1$, assumes that the algebra~\var{al} is semisimple
 without testing it.
 \bprog
 ? mt = [matid(3),[0,0,0;1,0,1;0,0,0],[0,0,0;0,0,0;1,0,1]];
 ? A = algtableinit(mt); \\ matrices [*,*; 0,*]
 ? algissimple(A)
 %3 = 0
 ? algissimple(A,1) \\ incorrectly assume that A is semisimple
 %4 = 1
 ? m_i=[0,-1,0,0;1,0,0,0;0,0,0,-1;0,0,1,0];
 ? m_j=[0,0,-1,0;0,0,0,1;1,0,0,0;0,-1,0,0];
 ? m_k=[0,0,0,-1;0,0,b,0;0,1,0,0;1,0,0,0];
 ? mt = [matid(4), m_i, m_j, m_k];
 ? A = algtableinit(mt); \\ quaternion algebra (-1,-1)
 ? algissimple(A)
 %10 = 1
 ? mt = [matid(3), [0,0,0; 1,1,0; 0,0,0], [0,0,1; 0,0,0; 1,0,1]];
 ? A = algtableinit(mt,2); \\ direct product F_4 x F_2
 ? algissimple(A)
 %13 = 0
 @eprog