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--- status: Draft
--- author(s): Gregory G. Smith
--- notes:
document {
Key => {isQuotientModule, (isQuotientModule,Thing), (isQuotientModule,Module)},
Headline => "whether something is evidently a quotient of a free module",
Usage => "isQuotientModule M",
Inputs => {
"M" => Thing
},
Outputs => {
Boolean => {TO "true", " if the given representation of ", TT "M", " a quotient of a free module."}
},
"This function checks if the module ", TT "M", " is a quotient of its ", TO "ambient",
" free module by examining its matrix of ", TO2((generators, Module),"generators"), ".",
EXAMPLE {
"R = ZZ/101[a,b,c];",
"M = R^1/(a^2,b^2,c^2)",
"isQuotientModule M"
},
"The image of a map from a free module to the first generator of ", TT "M", " yields an equivalent
module that is ", EM "not", " presented as a quotient.",
EXAMPLE {
"f = M_{0}",
"N = image f",
"M == N",
"isQuotientModule N",
},
SeeAlso => {(symbol_, Module, List), ambient, isFreeModule}
}
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