cc.redberry.core.groups.permutations

Class BSGSElement

java.lang.Object

cc.redberry.core.groups.permutations.BSGSElement

Direct Known Subclasses:

BSGSCandidateElement

public class BSGSElement
extends java.lang.Object

This class holds i-th base point (β_i), generators of G⁽ⁱ⁾ = G_{β1β2...βi-1} - stabilizer of all base points from 0-th to (i-1)-th as described in Sec. 4.4.1 in [Holt05].

Additionally it provides access to Δ⁽ⁱ⁾ - the orbit of β_i under G⁽ⁱ⁾, right transversals of H⁽ⁱ⁾_βi - stabilizer of β_i in G⁽ⁱ⁾. This access is based on Schreier vector as described in Sec. 4.1.1 of [Holt05].

Since:

1.1.6

Field Summary

Fields

Modifier and Type	Field and Description
int	basePoint i-th base point (βi)

Method Summary

Modifier and Type	Method and Description
BSGSCandidateElement	asBSGSCandidateElement() Returns a mutable copy of this BSGS element.
BSGSElement	asBSGSElement() Returns an immutable representation of this BSGS element
boolean	belongsToOrbit(int point) Returns true if specified point belongs to the orbit of this βi.
Permutation	getInverseTransversalOf(int point) Calculates the inverse transversal corresponding to the specified point (uβ), i.e.
int	getOrbitPoint(int i) Returns i-th point in orbit.
java.util.List<Permutation>	getStabilizerGeneratorsReference() Returns a reference to the list of stabilizers.
Permutation	getTransversalOf(int point) Calculates the transversal of specified point (uβ), i.e.
int	internalDegree()
int	orbitSize() Returns size of orbit.
java.lang.String	toString()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

basePoint

public final int basePoint

i-th base point (β_i)

Method Detail

getStabilizerGeneratorsReference

public java.util.List<Permutation> getStabilizerGeneratorsReference()

Returns a reference to the list of stabilizers.

Returns:

reference to the list of stabilizers

getTransversalOf

public Permutation getTransversalOf(int point)

Calculates the transversal of specified point (u_β), i.e. the element u_β such that β_i^u_β = β.

Parameters:

point - point

Returns:

element that maps this base point to the specified point.

See Also:

getInverseTransversalOf(int)

getInverseTransversalOf

public Permutation getInverseTransversalOf(int point)

Calculates the inverse transversal corresponding to the specified point (u_β), i.e. the element u_β^(-1) such that β_i^u_β = β.

Parameters:

point - point

Returns:

inverse of the element that maps this base point to the specified point.

asBSGSElement

public BSGSElement asBSGSElement()

Returns an immutable representation of this BSGS element

Returns:

immutable representation of this BSGS element

belongsToOrbit

public boolean belongsToOrbit(int point)

Returns true if specified point belongs to the orbit of this β_i.

Parameters:

point -

Returns:

true if specified point belongs to the orbit of this β_i.

asBSGSCandidateElement

public BSGSCandidateElement asBSGSCandidateElement()

Returns a mutable copy of this BSGS element.

Returns:

a mutable copy of this BSGS element

orbitSize

public int orbitSize()

Returns size of orbit.

Returns:

size of orbit

getOrbitPoint

public int getOrbitPoint(int i)

Returns i-th point in orbit.

Parameters:

i - position in orbit

Returns:

i-th point in orbit

internalDegree

public int internalDegree()

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object