# Author : Fabian Jakobs, Pierre Schnizer
# Date: 2003?, 2017
"""Permutation
This chapter describes functions for creating and manipulating
permutations. A permutation p is represented by an array of n integers
in the range 0 .. n-1, where each value :math:`p_i` occurs once and only once.
The application of a permutation p to a vector :math:`v` yields a new vector
:math:`v'` where :math:`v'_i = v_{p_i}.` For example, the array (0,1,3,2) represents a
permutation which exchanges the last two elements of a four element
vector. The corresponding identity permutation is (0,1,2,3).
"""
from . import gslwrap
[docs]
class Permutation(gslwrap.Permutation):
[docs]
def linear_to_canonical(self):
"""Computes the canonical form of the current permutation and returns it
in a new permutation
"""
q = Permutation(len(self))
self._linear_to_canonical(q)
return q
[docs]
def canonical_to_linear(self):
"""Computes the linear form of the current permutation and returns it
in a new permutation
"""
q = Permutation(len(self))
self._canonical_to_linear(q)
return q
[docs]
def inverse(self):
"""Computes the inverse form of the current permutation and returns it
in a new permutation.
"""
inv = Permutation(len(self))
self._inverse(inv)
return inv
[docs]
def mul(self, b):
"""Mutliplies this permutation with an other permutation and returns the
result in a new permutation.
"""
mul = Permutation(len(self))
self._mul(mul, b)
return mul
def __str__(self):
return self.tolist().__str__()