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

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

Synopsis:

Usage: b = isSubmodule(M)

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

Input:

M, an instance of class Module.

Output:

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

No computation is done, so the module may be isomorphic to a submodule of a free module but we don't detect it.

i1 : R = ZZ/101[a,b,c];

i2 : M = R^3;

i3 : N = ideal(a,b) * M



o3 = image | a 0 0 b 0 0 |

           | 0 a 0 0 b 0 |

           | 0 0 a 0 0 b |



                             3

o3 : R-module, submodule of R

i4 : isSubmodule N



o4 = true

i5 : N1 = ideal(a,b) * (R^1 / ideal(a^2,b^2,c^2))



o5 = subquotient (| a b |, | a2 b2 c2 |)



                               1

o5 : R-module, subquotient of R

i6 : isSubmodule N1



o6 = false

Code:

     -- ../../../Macaulay2/m2/modules.m2:37
     isSubmodule Module := M -> not M.?relations