algisassociative

Function: algisassociative
Section: algebras
C-Name: algisassociative
Prototype: iGD0,G,
Help: algisassociative(mt,p=0): true (1) if the multiplication table mt is
 suitable for algtableinit(mt,p), false (0) otherwise.
Doc: Returns 1 if the multiplication table \kbd{mt} is suitable for
 \kbd{algtableinit(mt,p)}, 0 otherwise. More precisely, \kbd{mt} should be
 a \typ{VEC} of $n$ matrices in $M_n(K)$, giving the left multiplications
 by the basis elements $e_1, \dots, e_n$ (structure constants).
 We check whether the first basis element $e_1$ is $1$ and $e_i(e_je_k) =
 (e_ie_j)e_k$ for all $i,j,k$.
 \bprog
  ? mt = [matid(3),[0,0,0;1,0,1;0,0,0],[0,0,0;0,0,0;1,0,1]];
  ? algisassociative(mt)
  %2 = 1
 @eprog

 May be used to check a posteriori an algebra: we also allow \kbd{mt} as
 output by \tet{algtableinit} ($p$ is ignored in this case).