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--- status: moved December 2020
document {
Key => cover,
Headline => "get the covering free module",
TT "cover M", " -- yields the free module whose basis elements correspond
to the generators of M.",
SeeAlso => {"ambient", "super"}}
document {
Key => {(cover,Matrix)},
Headline => "get the map between the covering free modules",
Usage => "cover f",
Inputs => {"f"},
Outputs => {{"the corresponding map of free modules between the covers of the source and target of ", TT "f" }},
SeeAlso => {(cover,Module)}
}
document {
Key => (cover, Module),
Headline => "get the covering free module",
Usage => "F = cover M",
Inputs => {"M"},
Outputs => {"F" => {"the free module whose basis elements correspond to the generators of ", TT "M", "."}},
"The free module ", TT "F", " is the source of the generator matrix
of ", TT "M", ".",
EXAMPLE {
"R = QQ[a..f];",
"g = matrix{{a,b},{c,d},{e,f}}",
"M = subquotient(g,matrix{{b},{c},{d}})",
"cover M",
"cover M == source generators M"},
SeeAlso => {(ambient,Module), (super,Module)}}
document {
Key => {(coverMap,Module),coverMap},
Headline => "the surjective map from a free module to a module corresponding to the generators",
Usage => "coverMap M",
Inputs => {"M"},
Outputs => {{"the surjective map from a free module to ", TT "M", " corresponding to the generators"}},
EXAMPLE lines ///
M = image matrix {{2},{0}}
f = coverMap M
isSurjective f
///
}
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