isFreeModule -- whether something is a free module

Synopsis

• 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

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

See also

• ambient -- ambient free module of a subquotient, or ambient ring
• prune(Module) -- minimal presentation of a module