Function: alglathnf
Section: algebras
C-Name: alglathnf
Prototype: GGDG
Help: alglathnf(al,m,{d=0}): the lattice generated by the columns of m, assuming
 that this lattice contains d times the integral basis of al.
Doc: Given an algebra \var{al} and a matrix \var{m} with columns representing
 elements of \var{al}, returns the lattice $L$ generated by the columns of
 \var{m}. If provided, \var{d} must be a rational number such that $L$ contains
 \var{d} times the natural basis of~\var{al}. The argument \var{m} is also
 allowed to be a \typ{VEC} of \typ{MAT}, in which case \var{m} is replaced by
 the concatenation of the matrices, or a \typ{COL}, in which case \var{m} is
 replaced by its left multiplication table as an element of \var{al}. The output is a 2-component \typ{VEC} $[I,t]$ representing $L=tI$.
 \bprog
 ? al = alginit(nfinit(y^2+7), [-1,-1]);
 ? a = [1,1,-1/2,1,1/3,-1,1,1]~;
 ? mt = algtomatrix(al,a,1);
 ? lat = alglathnf(al,mt);
 ? lat[2]
 %5 = 1/6
 @eprog
