Function: matdetint
Section: linear_algebra
C-Name: detint
Prototype: G
Help: matdetint(x): some multiple of the determinant of the lattice
 generated by the columns of x (0 if not of maximal rank). Useful with
 mathnfmod.
Doc:
 $x$ being an $m\times n$ matrix with integer
 coefficients, this function computes a non-zero \emph{multiple} of the
 determinant of
 the lattice generated by the columns of $x$ if it has maximal rank $m$, and
 returns zero otherwise, using the Gauss-Bareiss algorithm. When $x$ is square,
 the exact determinant is obtained.

 This function is useful in conjunction with \kbd{mathnfmod}, which needs to
 know such a multiple. If the rank is maximal and the matrix non-square,
 you can obtain the exact determinant using
 \bprog
   matdet( mathnfmod(x, matdetint(x)) )
 @eprog\noindent
 Note that as soon as one of the dimensions gets large ($m$ or $n$ is larger
 than 20, say), it will often be much faster to use \kbd{mathnf(x, 1)} or
 \kbd{mathnf(x, 4)} directly.
