isSubmodule -- whether a module is evidently a submodule of a free module

Usage:

isSubmodule M
Inputs:
- M, a thing
Outputs:
- true if M is evidently a submodule of a free module and false otherwise

Description

No computation is done -- M may be a isomorphic to a submodule of a free module although this function will not detect it.

i1 : R = ZZ/5[a,b,c];

i2 : M = R^3;

i3 : isSubmodule M

o3 = true

i4 : N = ideal(a,b) * M

o4 = image | a 0 0 b 0 0 |
           | 0 a 0 0 b 0 |
           | 0 0 a 0 0 b |

                             3
o4 : R-module, submodule of R

i5 : isSubmodule N

o5 = true

i6 : N' = ideal(a,b) * (R^1 / ideal(a^2,b^2,c^2))

o6 = subquotient (| a b |, | a2 b2 c2 |)

                               1
o6 : R-module, subquotient of R

i7 : isSubmodule N'

o7 = false

Ways to use isSubmodule:

isSubmodule(Module)
isSubmodule(Thing)

For the programmer

The object isSubmodule is a method function.

The source of this document is in Macaulay2Doc/functions/isSubmodule-doc.m2:28:0.