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InvariantRing :: permutationMatrix

permutationMatrix -- convert a one-line notation or cyclic notation of a permutation to a matrix representation

Synopsis

Description

This function is provided by the package InvariantRing.

The following example converts the one-line notation of a transposition into a matrix representation.

i1 : M = permutationMatrix toString 213

o1 = | 0 1 0 |
     | 1 0 0 |
     | 0 0 1 |

              3        3
o1 : Matrix ZZ  <--- ZZ

The following example converts the cyclic notation of the same transposition into a matrix representation. Without n the function assumes n is the largest integer that appears in your array or list of arrays.

i2 : M = permutationMatrix(3,[1,2])

o2 = | 0 1 0 |
     | 1 0 0 |
     | 0 0 1 |

              3        3
o2 : Matrix ZZ  <--- ZZ
i3 : M = permutationMatrix [1,2]

o3 = | 0 1 |
     | 1 0 |

              2        2
o3 : Matrix ZZ  <--- ZZ

The following example converts the cyclic notation of a permutation of 4 into a matrix representation.

i4 : M = permutationMatrix(4,{[1,2],[3,4]})

o4 = | 0 1 0 0 |
     | 1 0 0 0 |
     | 0 0 0 1 |
     | 0 0 1 0 |

              4        4
o4 : Matrix ZZ  <--- ZZ
i5 : M = permutationMatrix {[1,2],[3,4]}

o5 = | 0 1 0 0 |
     | 1 0 0 0 |
     | 0 0 0 1 |
     | 0 0 1 0 |

              4        4
o5 : Matrix ZZ  <--- ZZ

Ways to use permutationMatrix :

For the programmer

The object permutationMatrix is a method function.