isFreeModule -- whether something is a free module

Usage:

isFreeModule M
Inputs:
- M, a thing
Outputs:
- a Boolean value, true if the given representation of M is a free module and false otherwise

Description

This function checks if the module M is equal to its ambient free module by examining its matrix of generators and its matrix of relations.

To determine whether M is isomorphic to a free module, use prune M.

i1 : R = ZZ/7[x,y];

i2 : M = kernel vars R

o2 = image {1} | -y |
           {1} | x  |

                             2
o2 : R-module, submodule of R

i3 : isFreeModule M

o3 = false

i4 : isFreeModule prune M

o4 = true

The source of this document is in Macaulay2Doc/functions/isFreeModule-doc.m2:30:0.