The MatBasis function computes a basis of the set of vectors in the first nrow rows of A. Optionally, a basis for the nullspace can also be computed. On successful completion, the number of rows in A containing vectors (labeled r) is returned (the dimension of the basis).

Computation of the basis does not require that m be a prime, but computation of the nullspace does. In some cases, it is possible to compute the nullspace with m composite. If this is not possible, the function returns an error indicating that the algorithm failed because m is composite.

To request a nullspace, set nullflag=true. If the nullspace is requested, the input Matrix must have at least as many rows as columns, and the basis of the nullspace is specified in the trailing  rows of the Matrix, where  is the number of columns, and  is the return value (the dimension of the basis for the input vectors).

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form MatBasis(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][MatBasis](..).