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--- status: Reviewed
--- author(s): kummini
--- notes:
document {
Key => transpose,
Headline => "transpose a table or a matrix",
-- Usage => "",
-- Inputs => {
-- },
-- Outputs => {
-- },
-- Consequences => {
-- },
"The function ", TT "transpose", " transposes a matrix, a map of chain
complexes or a table.",
-- EXAMPLE {
-- },
-- Caveat => {},
-- SeeAlso => {}
}
document {
Key => (transpose,List),
Headline => " transposes a table",
Usage => "transpose T",
Inputs => {
"T" => List => {"which must be a ", TO "table"}
},
Outputs => {
{"the transpose of the table ", TT "T", ""}
},
"Here is an example.",
EXAMPLE {,
"transpose{{a, b, c},{d, e, f}}"
}
}
document {
Key => {(transpose,Matrix),(transpose,MutableMatrix)},
Headline => "transpose a matrix",
Usage => "transpose f",
Inputs => {
"f" => Matrix
},
Outputs => {
Matrix => { "the transpose of ", TT "f" }
},
"Here is an example.",
EXAMPLE {
"S = ZZ/10007[x,y,z];",
"f = matrix{{x^3,x*y^2},{y*x^2,y^3}}",
"g = transpose f",
},
"The output of ", TT "transpose", " is a map between the duals of the
original source and target free modules. See:",
EXAMPLE {
"degrees f",
"degrees g",
},
Caveat => {
TT "transpose", " works only for maps between free modules.
Use ", TT "dual", " for more general maps."
},
SeeAlso => {dual}
}
document {
Key => (transpose,ChainComplexMap),
Headline => "transpose a map of chain complexes",
Usage => "transpose f",
Inputs => {
"f" => ChainComplexMap
},
Outputs => {
ChainComplexMap => { "the transpose of ", TT "f" }
},
"The output of ", TT "transpose", " is a map from the duals of the
original source and target free modules. See the degree of the target
module in the following example",
EXAMPLE {
"S = ZZ/10007[x,y,z];",
"F = res ideal vars S;",
"F.dd",
"transpose F.dd"
},
"Note that ", TT "M2", " treats the differentials of a chain complex map
as map of degree -1."
}
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