IML is a free library of C source code which implements algorithms for computing
exact solutions to dense systems of linear equations over the integers.

Currently, IML provides the following functionalities:

  - Nonsingular rational system solving: compute the unique rational solution X
    to the system AX=B, where A and B are integer matrices, A nonsingular.
  - Compute the right nullspace or kernel of an integer matrix.
  - Certified linear system solving: compute a minimal denominator solution x to
    a system Ax=b, where b is an integer vector and A is an integer matrix with
    arbitrary shape and rank profile.

In addition, IML provides some low level routines for a variety of mod p matrix
operations: computing the row-echelon form, determinant, rank profile, and
inverse of a mod p matrix. These mod p routines are not general purpose; they
require that p satisfy some preconditions based on the dimension of the input
matrix (usually p should be prime and should be no more than about 20 bits
long).

WWW: https://cs.uwaterloo.ca/~astorjoh/iml.html