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Rank

rank of a module

Syntax

Rank(M:MODULE):INT Rank(M:MAT):INT

Description

This function computes the rank of M. For a module M this is defined as the vector space dimension of the subspace generated by the generators of M over the quotient field of the base ring -- contrast this with the function NumComps which simply counts the number of components the module has.

Example

Use R ::= QQ[x,y,z]; Rank(Module([x,y,z,0])); 1 ------------------------------- Rank(Module([[1,2,3],[2,4,6]])); 1 ------------------------------- Rank(Module([[1,2,3],[2,5,6]])); 2 -------------------------------