isQuotientModule Module -- whether a module is evidently a quotient of a free module

isQuotientModule Module -- whether a module is evidently a quotient of a free module

Synopsis:

Usage: b = isQuotientModule(M)

Function: isQuotientModule -- whether a module is evidently a quotient of a free module

Input:

M, an instance of class Module.

Output:

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

No computation is done. This routine simply detects whether the given description of M is such a quotient.

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

i2 : M = R^1/(a^2,b^2,c^2)



o2 = cokernel | a2 b2 c2 |



                            1

o2 : R-module, quotient of R

i3 : isQuotientModule M



o3 = true

i4 : f = M_{0}



o4 = | 1 |



o4 : Matrix

i5 : N = image f



o5 = subquotient (| 1 |, | a2 b2 c2 |)



                               1

o5 : R-module, subquotient of R

Recall (Module _ {...}) that f is a map to the first generator of M so that the module N is the same as M but its description is now as a submodule of M so isQuotientModule returns false. However, these two modules are equal:

i6 : isQuotientModule N



o6 = false

i7 : M == N



o7 = true

Code:

     -- ../../../Macaulay2/m2/modules.m2:41
     isQuotientModule Module := M -> not M.?generators