iml 1.0.5 Solver for systems of linear equations over the integers

IML is a C library implementing algorithms for computing exact solutions to dense systems of linear equations over the integers. Currently, IML provides the following functionality:

  • 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).