Iml

Integer Matrix Library

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.