The basis of a module is given by vectors. However, more complete information can be supplied which includes the ideals.
A sequence of vectors which correspond to a pseudo basis of the module M.
A sequence of tuples containing ideals and vectors which generate the module M. The vectors are guaranteed to be linearly independent.
A sequence of tuples containing ideals and vectors which generate the module M. This will return the data used to define the module, so that in contrast to PseudoBasis the vectors will in general not be independent.