Function: algtomatrix
Section: algebras
C-Name: algtomatrix
Prototype: GGD0,L,
Help: algtomatrix(al,x,{abs=1}): left multiplication table of x (table algebra
or abs=1) or image of x under a splitting of al (CSA and abs=0).
Doc: Given an element \var{x} in \var{al}, returns the image of \var{x} under a
homomorphism to a matrix algebra. If \var{al} is a table algebra output by
\kbd{algtableinit} or if~$abs=1$, returns the left multiplication table on the
integral basis; if \var{al} is a central simple algebra and~$abs=0$,
returns~$\phi(x)$ where~$\phi : A\otimes_K L \to M_d(L)$ (where $d$ is the
degree of the algebra and $L$ is an extension of $L$ with~$[L:K]=d$) is an
isomorphism stored in~\var{al}. Also accepts a square matrix with coefficients
in~\var{al}.
\bprog
? A = alginit(nfinit(y), [-1,-1]);
? algtomatrix(A,[0,0,0,2]~)
%2 =
[Mod(x + 1, x^2 + 1) Mod(Mod(1, y)*x + Mod(-1, y), x^2 + 1)]
[Mod(x + 1, x^2 + 1) Mod(-x + 1, x^2 + 1)]
? algtomatrix(A,[0,1,0,0]~,1)
%2 =
[0 -1 1 0]
[1 0 1 1]
[0 0 1 1]
[0 0 -2 -1]
? algtomatrix(A,[0,x]~,1)
%3 =
[-1 0 0 -1]
[-1 0 1 0]
[-1 -1 0 -1]
[ 2 0 0 1]
@eprog
Also accepts matrices with coefficients in \var{al}.