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

Usage:

isQuotientModule M
Inputs:
- M, a thing
Outputs:
- a Boolean value, 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 |

                   1
o4 : Matrix M <-- R

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

The source of this document is in Macaulay2Doc/functions/isQuotientModule-doc.m2:32:0.