cc.redberry.core.groups.permutations

Interface Permutation

All Superinterfaces:

java.lang.Comparable<Permutation>

All Known Implementing Classes:

PermutationOneLineByte, PermutationOneLineInt, PermutationOneLineShort

public interface Permutation
extends java.lang.Comparable<Permutation>

Interface describing a single permutation. See Permutations.createPermutation(boolean, int[]) and Permutations.createPermutation(boolean, int[][]) on how to construct permutations.

Since:

1.0

See Also:

Permutations.createPermutation(boolean, int[]), Permutations.createPermutation(boolean, int[][]), PermutationOneLineInt, PermutationOneLineShort, PermutationOneLineByte

Method Summary

Modifier and Type	Method and Description
boolean	antisymmetry() Returns true if this permutation is antisymmetry and false otherwise.
Permutation	commutator(Permutation p) Returns commutator of this and specified permutation, i.e.
Permutation	composition(Permutation other) Returns the result of this * other.
Permutation	composition(Permutation a, Permutation b) Returns the result of this * a * b.
Permutation	composition(Permutation a, Permutation b, Permutation c) Returns the result of this * a * b * c.
Permutation	compositionWithInverse(Permutation other) Returns the result of this * other.inverse().
Permutation	conjugate(Permutation p) Returns conjugation of specified element by this permutation, i.e.
int[][]	cycles() Returns an array of disjoint cycles that represent this permutation.
int	degree() Returns a largest moved point plus one.
Permutation	getIdentity() Returns the identity permutation with the degree of this permutation
int	imageOf(int i) Returns image of specified point under the action of this permutation.
int[]	imageOf(int[] set) Returns image of specified set of points under the action of this permutation.
Permutation	inverse() Returns the inverse permutation of this.
boolean	isIdentity() Returns true if this represents identity permutation
int	length() Returns length of the underlying array (at low-level).
int[]	lengthsOfCycles() Returns lengths of cycles in disjoint cycle notation.
Permutation	moveRight(int size) Inserts identity action on the set [0, 1, ..., size - 1]; as result the degree of resulting permutation will be size + degree of this.
Permutation	negate() Changes sign (symmetry to antisymmetry and vice versa) of this permutation
int	newIndexOf(int i) Returns image of specified point under the action of this permutation.
int	newIndexOfUnderInverse(int i) Returns image of specified point under the action of inverse of this permutation.
int[]	oneLine() Returns array that represents this permutation in one-line notation.
IntArray	oneLineImmutable() Returns immutable array that represents this permutation in one-line notation.
java.math.BigInteger	order() Calculates and returns the order of this permutation.
boolean	orderIsOdd() Returns true if order of this permutation is odd and false otherwise.
int	parity() Returns parity of this permutations.
char[]	permute(char[] array) Permutes array and returns the result.
int[]	permute(int[] array) Permutes array and returns the result.
<T> java.util.List<T>	permute(java.util.List<T> array) Permutes list and returns the result.
<T> T[]	permute(T[] array) Permutes array and returns the result.
Permutation	pow(int exponent) Returns this raised to the specified exponent.
java.lang.String	toStringCycles() Returns a string representation of this permutation in disjoint cycles notation.
java.lang.String	toStringOneLine() Returns a string representation of this permutation in one-line notation.
Permutation	toSymmetry() If this is antisymmetry, then converts this permutation to symmetry.

Methods inherited from interface java.lang.Comparable

compareTo

Method Detail

oneLine

int[] oneLine()

Returns array that represents this permutation in one-line notation.

Returns:

array that represents this permutation in one-line notation

oneLineImmutable

IntArray oneLineImmutable()

Returns immutable array that represents this permutation in one-line notation.

Returns:

immutable array that represents this permutation in one-line notation

cycles

int[][] cycles()

Returns an array of disjoint cycles that represent this permutation.

Returns:

array of disjoint cycles that represent this permutation

newIndexOf

int newIndexOf(int i)

Returns image of specified point under the action of this permutation.

Parameters:

i - point

Returns:

image of specified point under the action of this permutation

imageOf

int imageOf(int i)

Returns image of specified point under the action of this permutation. This method is absolutely same as newIndexOf(int) without any difference.

Parameters:

i - point

Returns:

image of specified point under the action of this permutation

imageOf

int[] imageOf(int[] set)

Returns image of specified set of points under the action of this permutation.

Parameters:

set - set

Returns:

image of specified set under this permutation

permute

int[] permute(int[] array)

Permutes array and returns the result.

Parameters:

array - array

Returns:

permuted array

permute

char[] permute(char[] array)

Permutes array and returns the result.

Parameters:

array - array

Returns:

permuted array

permute

<T> T[] permute(T[] array)

Permutes array and returns the result.

Parameters:

array - array

Returns:

permuted array

permute

<T> java.util.List<T> permute(java.util.List<T> array)

Permutes list and returns the result.

Parameters:

array - array

Returns:

permuted array

conjugate

Permutation conjugate(Permutation p)

Returns conjugation of specified element by this permutation, i.e. this^-1 * p * this

Parameters:

p - permutation

Returns:

conjugation of specified element by this permutation, i.e. this^-1 * p * this

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd parity of permutation)

commutator

Permutation commutator(Permutation p)

Returns commutator of this and specified permutation, i.e. this^-1 * p^-1 * this * p.

Parameters:

p - permutation

Returns:

commutator of this and specified permutation, i.e. this^-1 * p^-1 * this * p

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd parity of permutation)

newIndexOfUnderInverse

int newIndexOfUnderInverse(int i)

Returns image of specified point under the action of inverse of this permutation.

Parameters:

i - point

Returns:

image of specified point under the action of inverse of this permutation

antisymmetry

boolean antisymmetry()

Returns true if this permutation is antisymmetry and false otherwise.

Returns:

true if this permutation is antisymmetry and false otherwise

toSymmetry

Permutation toSymmetry()

If this is antisymmetry, then converts this permutation to symmetry.

Returns:

same permutation with false antisymmetry

negate

Permutation negate()

Changes sign (symmetry to antisymmetry and vice versa) of this permutation

Returns:

same permutation with changed sign

composition

Permutation composition(Permutation other)

Returns the result of this * other. Applying the resulting permutation is equivalent to applying other after this.

Parameters:

other - other permutation

Returns:

the result of this * other

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd parity of permutation)

composition

Permutation composition(Permutation a,
                        Permutation b)

Returns the result of this * a * b. Applying the resulting permutation is equivalent to applying b after a after this.

Parameters:

a - other permutation

b - other permutation

Returns:

the result of this * a * b

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd permutation parity)

composition

Permutation composition(Permutation a,
                        Permutation b,
                        Permutation c)

Returns the result of this * a * b * c. Applying the resulting permutation is equivalent to applying c after b after a after this.

Parameters:

a - other permutation

b - other permutation

c - other permutation

Returns:

the result of this * a * b * c

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd permutation parity)

compositionWithInverse

Permutation compositionWithInverse(Permutation other)

Returns the result of this * other.inverse(). Applying the resulting permutation is equivalent to applying other.inverse() after this.

Parameters:

other - other permutation

Returns:

the result of this * other.inverse()

Throws:

InconsistentGeneratorsException - if the result of composition is inconsistent symmetry (antisymmetry with odd permutation parity)

inverse

Permutation inverse()

Returns the inverse permutation of this.

Returns:

the inverse permutation of this

isIdentity

boolean isIdentity()

Returns true if this represents identity permutation

Returns:

true if this is identity permutation

getIdentity

Permutation getIdentity()

Returns the identity permutation with the degree of this permutation

Returns:

identity permutation with the degree of this permutation

order

java.math.BigInteger order()

Calculates and returns the order of this permutation.

Returns:

order of this permutation

See Also:

Permutations.orderOfPermutation(int[])

orderIsOdd

boolean orderIsOdd()

Returns true if order of this permutation is odd and false otherwise.

Returns:

true if order of this permutation is odd and false otherwise

degree

int degree()

Returns a largest moved point plus one.

Returns:

largest moved point plus one

length

int length()

Returns length of the underlying array (at low-level).

Returns:

length of the underlying array (at low-level)

pow

Permutation pow(int exponent)

Returns this raised to the specified exponent.

Parameters:

exponent - exponent

Returns:

this raised to the specified exponent

parity

int parity()

Returns parity of this permutations.

Returns:

parity of this permutations

moveRight

Permutation moveRight(int size)

Inserts identity action on the set [0, 1, ..., size - 1]; as result the degree of resulting permutation will be size + degree of this.

Parameters:

size - size of the set

lengthsOfCycles

int[] lengthsOfCycles()

Returns lengths of cycles in disjoint cycle notation.

Returns:

lengths of cycles in disjoint cycle notation

toStringOneLine

java.lang.String toStringOneLine()

Returns a string representation of this permutation in one-line notation.

Returns:

a string representation of this permutation in one-line notation

toStringCycles

java.lang.String toStringCycles()

Returns a string representation of this permutation in disjoint cycles notation.

Returns:

a string representation of this permutation in disjoint cycles notation