The Basis function computes a basis of the set of Vectors described by A, and returns that basis and the nullspace.

The orient parameter is specified if A is a mod m Matrix.  It indicates to the Basis command whether the vectors of the input Matrix are in rows (orient=row) or columns (orient=column).

The basis and nullsp parameters indicate the format in which the respective Vectors are returned by Basis. They can be any of the following values:

If neither basis or nullsp are false, both the basis and nullspace Vectors are returned as a two element sequence. If both are false, an error results.

For example, if Basis is called with basis=false and nullsp=column, the output would be a list of column Vectors for the nullspace.

The Basis command works with a copy of the input data, using the MatBasis command to perform the computation, so if data storage or efficiency are a concern, the MatBasis command should be used.

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