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--- status: DRAFT
--- author(s): blasiak, kummini
--- notes:
document {
Key => {(minors,ZZ,Matrix),
minors,
[minors,First],
[minors,Limit]},
Headline => "ideal generated by minors",
Usage => "minors(n,M)",
Inputs => {
"n" => ZZ => "order of the minor",
"M" => Matrix => "a map between free modules",
First => List => "if given, should be a list of two integer lists, which will be the
first minor computed",
Limit => ZZ => "the maximum number of minors to find"
},
Outputs => {
{"the ideal generated by the ", TT "n", " by ", TT "n", " minors
of the matrix ", TT "M"}
},
"Minors are generated in the same order as that used by ",
TO (subsets,ZZ,ZZ), ".",
EXAMPLE lines ///
R = ZZ[a..f];
M = matrix{{a,b,c},{d,e,f}}
minors(2,M)
minors(2,M,Limit=>1)
///,
PARA {
"When ", TT "n", " is negative, the unit ideal is returned, to preserve the expected ordering
among the resulting ideals."
},
EXAMPLE lines ///
minors(1,M)
minors(0,M)
minors(-1,M)
///,
SeeAlso => {"exteriorPower", "det"},
Subnodes => { TO [minors, Strategy] },
}
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