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

• Usage:

  permutationMatrix c,

  permutationMatrix(n , c),

  permutationMatrix(n, p),

  permutationMatrix p

• Inputs:
  • c, an array, of positive integers representing a permutation in one-line notation or representing a cyclic permutation
  • p, a list, of arrays representing a permutation as a product of cycles
  • n, an integer, giving the number of integers being permuted
• Optional inputs:
  • EntryMode => ..., default value "one-line"
• Outputs:
  • a matrix, the matrix representation of the permutation

i1 : M = permutationMatrix [2, 1, 3]

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

              3       3
o1 : Matrix ZZ  <-- ZZ

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], EntryMode => "cycle")

o3 = | 0 1 |
     | 1 0 |

              2       2
o3 : Matrix ZZ  <-- ZZ

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