Function: algradical
Section: algebras
C-Name: algradical
Prototype: G
Help: algradical(al): Jacobson radical of the algebra al.
Doc: \var{al} being a table algebra output by \tet{algtableinit}, returns a
 basis of the Jacobson radical of the algebra \var{al} over its prime field
 ($\Q$ or $\F_{p}$).

 Here is an example with $A = \Q[x]/(x^{2})$, with the basis~$(1,x)$:
 \bprog
 ? mt = [matid(2),[0,0;1,0]];
 ? A = algtableinit(mt);
 ? algradical(A) \\ = (x)
 %3 =
 [0]

 [1]
 @eprog

 Another one with $2\times 2$ upper triangular matrices over $\Q$, with basis
 $I_{2}$, $a = \kbd{[0,1;0,0]}$ and $b = \kbd{[0,0;0,1]}$, such that $a^{2} =
 0$, $ab = a$, $ba = 0$, $b^{2} = b$:
 \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);
 ? algradical(A) \\ = (a)
 %6 =
 [0]

 [1]

 [0]
 @eprog
