Main Overview

Class Perm

Class Perm
Permutations (from dictionary or cycle representation) Examples (three times the same permutation:
Perm({1:4, 2:3, 3:2, 4:1})
Perm("(1,4)(2,3)")
Perm([[1,4],[2,3]])

Overview:

Constructor

Perm (p)

Operators

OperatorMeaning
x == y
x[i]
x * y
x != y
str(x)

Object Methods

MethodMeaning
check ()check for consistency
cycles ()Cycle representation
fromVector (v)Generation from vector v with argument/value pairs.
inverse ()inverse permutation
inversions ()Inversion number (count of "swapped pairs")
members ()List of the permuted elements
odd ()odd permutation?
reduce ()removes fixed points
sign ()signum

Constructor

Perm

Constructor

Usage: Perm(p)


Operators

x == y

Usage: x == y


x[i]

Usage: x[i]


x * y

product of two Permutations (left first, then right!)

Usage: x * y

Description:


x != y

Usage: x != y


str(x)

Object representation as string (as cycles)

Usage: str(x)

Description:


Object Methods

check

p.check()

Usage: self.check()

Description:
check for consistency


cycles

p.cycles()

Usage: self.cycles()

Description:
Cycle representation


fromVector

p.fromVector(v)

Usage: self.fromVector(v)

Description:
Generation from vector v with argument/value pairs.
Example: p.fromVector([[1,4],[2,3]])


inverse

p.inverse()

Usage: self.inverse()

Description:
inverse permutation


inversions

p.inversions()

Usage: self.inversions()

Description:
Inversion number (count of "swapped pairs")


members

p.members()

Usage: self.members()

Description:
List of the permuted elements


odd

p.odd()

Usage: self.odd()

Description:
odd permutation? (bool)


reduce

p.reduce()

Usage: self.reduce()

Description:
removes fixed points


sign

p.sign()

Usage: self.sign()

Description:
signum
1 for even, -1 for odd permutations