cc.redberry.core.groups.permutations

Class PermutationOneLineInt

java.lang.Object

cc.redberry.core.groups.permutations.PermutationOneLineInt

All Implemented Interfaces:

Permutation, java.lang.Comparable<Permutation>

public final class PermutationOneLineInt
extends java.lang.Object
implements Permutation

The implementation of Permutation based on the one-line notation. The instances of this class are immutable.

The implementation is based on int[] array in one-line notation and provides O(1) complexity for imageOf(int) and O(degree) complexity for composition.

Since:

1.0

See Also:

Permutation, Permutations.createPermutation(boolean, int[]), Permutations.createPermutation(boolean, int[][])

Constructor Summary

Constructors

Constructor and Description
PermutationOneLineInt(boolean antisymmetry, int... permutation) Creates permutation with antisymmetry property from given array in one-line notation and boolean value of antisymmetry (true means antisymmetry)
PermutationOneLineInt(boolean antisymmetry, int[][] cycles) Creates permutation with antisymmetry property from given array of disjoint cycles and boolean value of antisymmetry (true means antisymmetry)
PermutationOneLineInt(int... permutation) Creates permutation from given array in one-line notation
PermutationOneLineInt(int[][] cycles) Creates permutation from a given array of disjoint cycles.

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.
int	compareTo(Permutation t)
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.
boolean	equals(java.lang.Object o)
Permutation	getIdentity() Returns the identity permutation with the degree of this permutation
int	hashCode()
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.
PermutationOneLineInt	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.
PermutationOneLineInt	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> set) 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	toString()
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 class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

PermutationOneLineInt

public PermutationOneLineInt(boolean antisymmetry,
                             int[][] cycles)

Creates permutation with antisymmetry property from given array of disjoint cycles and boolean value of antisymmetry (true means antisymmetry)

Parameters:

antisymmetry - antisymmetry (true - antisymmetry, false - symmetry)

cycles - disjoint cycles

Throws:

java.lang.IllegalArgumentException - if permutation is inconsistent with disjoint cycles notation

java.lang.IllegalArgumentException - if antisymmetry is true and permutation order is odd

PermutationOneLineInt

public PermutationOneLineInt(int[][] cycles)

Creates permutation from a given array of disjoint cycles.

Parameters:

cycles - disjoint cycles

Throws:

java.lang.IllegalArgumentException - if permutation is inconsistent with disjoint cycles notation

PermutationOneLineInt

public PermutationOneLineInt(int... permutation)

Creates permutation from given array in one-line notation

Parameters:

permutation - permutation in one-line notation

Throws:

java.lang.IllegalArgumentException - if permutation array is inconsistent with one-line notation

PermutationOneLineInt

public PermutationOneLineInt(boolean antisymmetry,
                             int... permutation)

Creates permutation with antisymmetry property from given array in one-line notation and boolean value of antisymmetry (true means antisymmetry)

Parameters:

antisymmetry - antisymmetry (true - antisymmetry, false - symmetry)

permutation - permutation in one-line notation

Throws:

java.lang.IllegalArgumentException - if permutation is inconsistent with one-line notation

java.lang.IllegalArgumentException - if antisymmetry is true and permutation order is odd

Method Detail

length

public int length()

Description copied from interface: Permutation

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

Specified by:

length in interface Permutation

Returns:

length of the underlying array (at low-level)

antisymmetry

public boolean antisymmetry()

Description copied from interface: Permutation

Returns true if this permutation is antisymmetry and false otherwise.

Specified by:

antisymmetry in interface Permutation

Returns:

true if this permutation is antisymmetry and false otherwise

toSymmetry

public Permutation toSymmetry()

Description copied from interface: Permutation

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

Specified by:

toSymmetry in interface Permutation

Returns:

same permutation with false antisymmetry

negate

public PermutationOneLineInt negate()

Description copied from interface: Permutation

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

Specified by:

negate in interface Permutation

Returns:

same permutation with changed sign

oneLine

public int[] oneLine()

Description copied from interface: Permutation

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

Specified by:

oneLine in interface Permutation

Returns:

array that represents this permutation in one-line notation

oneLineImmutable

public IntArray oneLineImmutable()

Description copied from interface: Permutation

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

Specified by:

oneLineImmutable in interface Permutation

Returns:

immutable array that represents this permutation in one-line notation

cycles

public int[][] cycles()

Description copied from interface: Permutation

Returns an array of disjoint cycles that represent this permutation.

Specified by:

cycles in interface Permutation

Returns:

array of disjoint cycles that represent this permutation

newIndexOf

public int newIndexOf(int i)

Description copied from interface: Permutation

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

Specified by:

newIndexOf in interface Permutation

Parameters:

i - point

Returns:

image of specified point under the action of this permutation

imageOf

public int imageOf(int i)

Description copied from interface: Permutation

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

Specified by:

imageOf in interface Permutation

Parameters:

i - point

Returns:

image of specified point under the action of this permutation

imageOf

public int[] imageOf(int[] set)

Description copied from interface: Permutation

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

Specified by:

imageOf in interface Permutation

Parameters:

set - set

Returns:

image of specified set under this permutation

permute

public int[] permute(int[] array)

Description copied from interface: Permutation

Permutes array and returns the result.

Specified by:

permute in interface Permutation

Parameters:

array - array

Returns:

permuted array

permute

public char[] permute(char[] array)

Description copied from interface: Permutation

Permutes array and returns the result.

Specified by:

permute in interface Permutation

Parameters:

array - array

Returns:

permuted array

permute

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

Description copied from interface: Permutation

Permutes array and returns the result.

Specified by:

permute in interface Permutation

Parameters:

array - array

Returns:

permuted array

permute

public <T> java.util.List<T> permute(java.util.List<T> set)

Description copied from interface: Permutation

Permutes list and returns the result.

Specified by:

permute in interface Permutation

Parameters:

set - array

Returns:

permuted array

newIndexOfUnderInverse

public int newIndexOfUnderInverse(int i)

Description copied from interface: Permutation

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

Specified by:

newIndexOfUnderInverse in interface Permutation

Parameters:

i - point

Returns:

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

conjugate

public Permutation conjugate(Permutation p)

Description copied from interface: Permutation

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

Specified by:

conjugate in interface Permutation

Parameters:

p - permutation

Returns:

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

commutator

public Permutation commutator(Permutation p)

Description copied from interface: Permutation

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

Specified by:

commutator in interface Permutation

Parameters:

p - permutation

Returns:

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

composition

public Permutation composition(Permutation other)

Description copied from interface: Permutation

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

Specified by:

composition in interface Permutation

Parameters:

other - other permutation

Returns:

the result of this * other

composition

public Permutation composition(Permutation a,
                               Permutation b)

Description copied from interface: Permutation

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

Specified by:

composition in interface Permutation

Parameters:

a - other permutation

b - other permutation

Returns:

the result of this * a * b

composition

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

Description copied from interface: Permutation

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

Specified by:

composition in interface Permutation

Parameters:

a - other permutation

b - other permutation

c - other permutation

Returns:

the result of this * a * b * c

compositionWithInverse

public Permutation compositionWithInverse(Permutation other)

Description copied from interface: Permutation

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

Specified by:

compositionWithInverse in interface Permutation

Parameters:

other - other permutation

Returns:

the result of this * other.inverse()

inverse

public Permutation inverse()

Description copied from interface: Permutation

Returns the inverse permutation of this.

Specified by:

inverse in interface Permutation

Returns:

the inverse permutation of this

isIdentity

public boolean isIdentity()

Description copied from interface: Permutation

Returns true if this represents identity permutation

Specified by:

isIdentity in interface Permutation

Returns:

true if this is identity permutation

getIdentity

public Permutation getIdentity()

Description copied from interface: Permutation

Returns the identity permutation with the degree of this permutation

Specified by:

getIdentity in interface Permutation

Returns:

identity permutation with the degree of this permutation

order

public java.math.BigInteger order()

Description copied from interface: Permutation

Calculates and returns the order of this permutation.

Specified by:

order in interface Permutation

Returns:

order of this permutation

See Also:

Permutations.orderOfPermutation(int[])

orderIsOdd

public boolean orderIsOdd()

Description copied from interface: Permutation

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

Specified by:

orderIsOdd in interface Permutation

Returns:

true if order of this permutation is odd and false otherwise

degree

public int degree()

Description copied from interface: Permutation

Returns a largest moved point plus one.

Specified by:

degree in interface Permutation

Returns:

largest moved point plus one

pow

public Permutation pow(int exponent)

Description copied from interface: Permutation

Returns this raised to the specified exponent.

Specified by:

pow in interface Permutation

Parameters:

exponent - exponent

Returns:

this raised to the specified exponent

equals

public boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

parity

public int parity()

Description copied from interface: Permutation

Returns parity of this permutations.

Specified by:

parity in interface Permutation

Returns:

parity of this permutations

moveRight

public PermutationOneLineInt moveRight(int size)

Description copied from interface: Permutation

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

Specified by:

moveRight in interface Permutation

Parameters:

size - size of the set

lengthsOfCycles

public int[] lengthsOfCycles()

Description copied from interface: Permutation

Returns lengths of cycles in disjoint cycle notation.

Specified by:

lengthsOfCycles in interface Permutation

Returns:

lengths of cycles in disjoint cycle notation

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

toStringOneLine

public java.lang.String toStringOneLine()

Description copied from interface: Permutation

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

Specified by:

toStringOneLine in interface Permutation

Returns:

a string representation of this permutation in one-line notation

toStringCycles

public java.lang.String toStringCycles()

Description copied from interface: Permutation

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

Specified by:

toStringCycles in interface Permutation

Returns:

a string representation of this permutation in disjoint cycles notation

compareTo

public int compareTo(Permutation t)

Specified by:

compareTo in interface java.lang.Comparable<Permutation>