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--- status: Draft
--- author(s): M2Fest 2005 -- Irena
--- notes:
document {
Key => {permanents, (permanents,ZZ,Matrix)},
Headline => "ideal generated by square permanents of a matrix",
Usage => "permanents(n,M)",
Inputs => {"n" => ZZ => "the size of the permanents",
"M" => Matrix
},
Outputs => {Ideal=>{" generated by the permanents of the ",
TT "n", " by ", TT "n", " subpermanents of ", TT "M"}
},
"The permanent of a square matrix ", TT "N",
" has the Laplace transform similar to the Laplace transform
of the determinant of ", TT "N", ": but all signs are positive.
Permanents are used in combinatorics and in probability.
They are computationally difficult.",
EXAMPLE {
"R = ZZ[a..f];",
"M = genericMatrix(R,a,2,3)",
"permanents(2,M)"
},
Caveat => {""
},
SeeAlso => {det, minors, "matrices"}
}
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