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--- status: Draft
--- author(s): Gregory G. Smith
--- notes:
document {
Key => {genericSkewMatrix, (genericSkewMatrix,Ring,RingElement,ZZ), (genericSkewMatrix,Ring,ZZ)},
Headline => "make a generic skew symmetric matrix of variables",
Usage => "genericSkewMatrix(R,r,n)",
Inputs => {
"R" => Ring,
"r" => RingElement => {"which is a variable in the ring ", TT "R", " (this input is optional)"},
"n" => ZZ
},
Outputs => {
{"a skew symmetric ", TO2("Matrix","matrix"), " with ", TT "n",
" rows whose entries above the diagonal are the variables of ", TT "R",
" starting with ", TT "r"}
},
"A square ", TO2("Matrix","matrix"), " ", TT "M", " is ", EM "skew symmetric",
" if ", TT "transpose(M) + M == 0", ".",
EXAMPLE {
"R = ZZ[a..z];",
"M = genericSkewMatrix(R,a,3)",
"transpose(M) + M == 0",
"genericSkewMatrix(R,d,5)"
},
PARA{},
"Omitting the input ", TT "r", " is the same as having ", TT "r",
" be the first variable in ", TT "R", ".",
EXAMPLE{
"genericSkewMatrix(R,3)",
"genericSkewMatrix(R,5)"
},
SeeAlso => {(vars, Ring), genericMatrix, genericSymmetricMatrix}
}
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