# isQuotientModule -- whether something is evidently a quotient of a free module

## Synopsis

• Usage:
isQuotientModule M
• Inputs:
• M,
• Outputs:
• , true if the given representation of M a quotient of a free module.

## Description

This function checks if the module M is a quotient of its ambient free module by examining its matrix of generators.
 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
The image of a map from a free module to the first generator of M yields an equivalent module that is not presented as a quotient.
 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 i6 : M == N o6 = true i7 : isQuotientModule N o7 = false