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document {
Key => {
permutations,
(permutations, ZZ),
(permutations, VisibleList)
},
Headline => "produce all permutations of a list",
Usage => "permutations x",
Inputs => { "x" => { ofClass {VisibleList, ZZ} } },
Outputs => { { "a list of all the permutations of the visible list ", TT "x",
", or, if ", TT "x", " is an integer, of the list of integers from 0 through ", TT "n-1" } },
EXAMPLE {
"permutations {a,b,c,d}",
"permutations 3"
}
}
document {
Key => {
uniquePermutations,
(uniquePermutations, ZZ),
(uniquePermutations, VisibleList)
},
Headline => "produce all unique permutations of a list",
Usage => "uniquePermutations x",
Inputs => { "x" => { ofClass {VisibleList, ZZ} } },
Outputs => { { "a list of all distinct permutations of the visible list ", TT "x",
", or, if ", TT "x", " is an integer, of the list of integers from 0 through ", TT "n-1" } },
EXAMPLE {
"uniquePermutations {a,b,a,b}",
}
}
document {
Key => {
inversePermutation,
(inversePermutation, VisibleList)
},
Headline => "inverse permutation",
Usage => "y = inversePermutation x",
Inputs => {
"x" => List => {"a list of length ", TT "n", " whose elements are the numbers 0, 1, 2, ..., ", TT "n-1", ", in some order,
representing the permutation defined by sending ", TT "i", " to ", TT "x#i"
}
},
Outputs => {
"y" => List => {"the list representing the inverse permutation of ", TT "x" }
},
EXAMPLE lines ///
x = {1,2,3,4,5,0}
y = inversePermutation x
all(#x, i -> x#(y#i) == i)
all(#x, i -> y#(x#i) == i)
///,
PARA { "We compose permutations with ", TT "_", "; see ", TO (symbol_, VisibleList, List), "." },
EXAMPLE lines ///
x_x_x
x_x_x_x_x_x
x_y
y_x
///
}
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