isFreeModule Module -- whether something is a free module

isFreeModule Module -- whether something is a free module

Synopsis:

Usage: b = isFreeModule(M)

Function: isFreeModule -- whether something is a free module

Input:

M, an instance of class Module.

Output:

b, an instance of class Boolean: whether M is evidently a free module.

No computation is done, so the module may be free but we don't detect it. To try to determine whether M is isomorphic to a free module, one may prune M first.

i1 : R = ZZ/101[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

See also:

prune Module -- minimize generators and relations

Code:

     -- ../../../Macaulay2/m2/modules.m2:33
     isFreeModule Module := M -> not M.?relations and not M.?generators