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-- -*- coding: utf-8 -*-
--- status: Draft
--- author(s): MES
--- notes:
document {
Key => {isWellDefined,(isWellDefined,Matrix),(isWellDefined,RingMap)},
Headline => "whether a map is well defined",
Usage => "isWellDefined f",
Inputs => {
"f" => ofClass{Matrix, RingMap}
},
Outputs => {
Boolean => {"whether ", TT "f", " is a well-defined map"}
},
"In order to check whether a matrix, whose source module is not free, is well defined,
then a Gröbner basis computation will probably be required.",
EXAMPLE lines ///
R = QQ[a..d];
f = map(R^1,coker vars R,{{1_R}})
isWellDefined f
isWellDefined map(coker vars R, R^1, {{1_R}})
///,
"In order to check whether a ring map is well defined,
it is often necessary to check that the image of an ideal
under a related ring map is zero. This often requires
a Gröbner basis as well.",
EXAMPLE lines ///
A = ZZ/5[a]
factor(a^3-a-2)
B = A/(a^3-a-2);
isWellDefined map(A,B)
isWellDefined map(B,A)
///,
SeeAlso => {
map
}
}
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