Function: algbasistoquat
Section: algebras
C-Name: algbasistoquat
Prototype: GG
Help: algbasistoquat(al,x): transforms the column vector x on the integral basis
 of al into a quaternion x expressed on the basis (1,i,j,ij).
Doc: Given an element \var{x} in the quaternion algebra \var{al} output
 by \tet{alginit}, transforms it to a quaternion expressed on the
 basis~$(1,i,j,ij)$. This function is provided for convenience, as algebra
 functions do not support elements represented on this basis. This is the
 inverse function of \tet{algquattobasis}.
 \bprog
 ? nf = nfinit(y^2+1);
 ? alg = alginit(nf, [3,2*y-1]);
 ? algbasistoquat(alg, [1..8]~)
 % = [Mod(-4*y + 3, y^2 + 1), ... , Mod(-4*y - 3, y^2 + 1)]~
 @eprog
