Uses of Interface
repthy.GroupElt

Uses of GroupElt in repthy

Classes in repthy that implement GroupElt

class	MatrixModp Square matrices with byte entries modulo a rational prime p.
class	PermGpElt Stores a permutation of the integers 0, 1, ..., deg-1.
class	PMatrixModp Square matrices modulo a byte p as in the superclass MatrixModp, but modulo scalar multiples of the identity.
class	ProductGroupElt An element of a ProductGroup.
class	PSLEltModp A PMatrixModp that's known at construction time to have determinant equal to an n-th root of unity.
class	QuotientGroupElt An element "g modulo H", where g is an element of the group G and H is a subgroup of G.

Fields in repthy declared as GroupElt

protected GroupElt[]

HeckeAlgebra.dblCosetReps Caches the result of HeckeAlgebra.makeDblCosetReps().

Methods in repthy that return GroupElt

protected GroupElt[]	HeckeAlg_PGL_U.makeDblCosetReps()
GroupElt	QuotientGroupElt.mult(GroupElt y)
GroupElt	QuotientGroupElt.inverse()
GroupElt	QuotientGroupElt.getIdentity()
GroupElt	QuotientGroupElt.conjugate(GroupElt y)
GroupElt	QuotientGroupElt.conjugateYinvXY(GroupElt y)
GroupElt	QuotientGroupElt.power(int i)
protected GroupElt[]	HeckeAlg_GL_U.makeDblCosetReps()
GroupElt	C_n.getGenerator()
GroupElt	ProductGroupElt.mult(GroupElt y)
GroupElt	ProductGroupElt.inverse()
GroupElt	ProductGroupElt.getIdentity()
GroupElt	ProductGroupElt.conjugate(GroupElt y)
GroupElt	ProductGroupElt.conjugateYinvXY(GroupElt y)
GroupElt	ProductGroupElt.power(int i)
GroupElt	ProductGroupElt.getFactor1()
GroupElt	ProductGroupElt.getFactor2()
GroupElt	PMatrixModp.mult(GroupElt y)
GroupElt	PMatrixModp.inverse()
GroupElt	PMatrixModp.getIdentity()
GroupElt	PMatrixModp.conjugate(GroupElt y)
GroupElt	PMatrixModp.conjugateYinvXY(GroupElt y)
GroupElt	MatrixModp.mult(GroupElt y)
GroupElt	MatrixModp.inverse()
GroupElt	MatrixModp.getIdentity()
GroupElt	MatrixModp.conjugate(GroupElt y)
GroupElt	MatrixModp.conjugateYinvXY(GroupElt y)
GroupElt	MatrixModp.power(int i)
protected GroupElt[]	HeckeAlg_GL_B.makeDblCosetReps()
protected abstract GroupElt[]	HeckeAlgebra.makeDblCosetReps() Returns an array of double-coset representatives for H\G/H.
GroupElt[]	HeckeAlgebra.getDblCosetReps() Returns a clone of the array of double-coset representatives provided by HeckeAlgebra.makeDblCosetReps().
GroupElt	HomomorphismFunc.apply(GroupElt g)
GroupElt	PermGpElt.mult(GroupElt y) Returns this * y, that is, the permutation whose value on i is this(y(i)).
GroupElt	PermGpElt.inverse()
GroupElt	PermGpElt.conjugate(GroupElt y) Returns y * this * y^(-1).
GroupElt	PermGpElt.conjugateYinvXY(GroupElt y)
GroupElt	PermGpElt.getIdentity()
GroupElt	PermGpElt.power(int i)
GroupElt	Homomorphism.apply(GroupElt g) Returns the value of this homomorphism on the element g of the source.
GroupElt	GroupElt.mult(GroupElt y) Returns the product this * y.
GroupElt	GroupElt.inverse() Returns the inverse element for this.
GroupElt	GroupElt.getIdentity() Returns the identity element of the same class as this.
GroupElt	GroupElt.conjugate(GroupElt y) Returns y * this * y^(-1).
GroupElt	GroupElt.conjugateYinvXY(GroupElt y) Returns y^(-1) * this * y.
GroupElt	GroupElt.power(int i) Returns the i-th power of this element.
GroupElt	Group.getConjClassRep(int i) Returns some element of the i-th conjugacy class.
GroupElt	Group.getIdentity() Returns a GroupElt that is the identity for this group, up to equals(java.lang.Object).
static GroupElt	Group.power(GroupElt g, int i) Returns the i-th power of g.

Methods in repthy with parameters of type GroupElt

GroupElt	QuotientGroupElt.mult(GroupElt y)
GroupElt	QuotientGroupElt.conjugate(GroupElt y)
GroupElt	QuotientGroupElt.conjugateYinvXY(GroupElt y)
boolean	QuotientGroupElt.commutesWith(GroupElt y)
int	C_n.getConjClassIndex(GroupElt x) Returns i such that x is in the i-th conjugacy class.
int	PSL3b.getConjClassIndex(GroupElt g)
GroupElt	ProductGroupElt.mult(GroupElt y)
GroupElt	ProductGroupElt.conjugate(GroupElt y)
GroupElt	ProductGroupElt.conjugateYinvXY(GroupElt y)
boolean	ProductGroupElt.commutesWith(GroupElt y)
GroupElt	PMatrixModp.mult(GroupElt y)
GroupElt	PMatrixModp.conjugate(GroupElt y)
GroupElt	PMatrixModp.conjugateYinvXY(GroupElt y)
boolean	PMatrixModp.commutesWith(GroupElt y)
GroupElt	MatrixModp.mult(GroupElt y)
GroupElt	MatrixModp.conjugate(GroupElt y)
GroupElt	MatrixModp.conjugateYinvXY(GroupElt y)
boolean	MatrixModp.commutesWith(GroupElt y)
int	HeckeAlgebra.getDblCosetIndex(GroupElt g) Returns i such that the argument is in the i-th double coset.
GroupElt	HomomorphismFunc.apply(GroupElt g)
GroupElt	PermGpElt.mult(GroupElt y) Returns this * y, that is, the permutation whose value on i is this(y(i)).
GroupElt	PermGpElt.conjugate(GroupElt y) Returns y * this * y^(-1).
GroupElt	PermGpElt.conjugateYinvXY(GroupElt y)
boolean	PermGpElt.commutesWith(GroupElt y) Returns whether this and the argument commute.
static HashHomom	HashHomom.make(Group sou, GroupElt[] souGen, Group tar, GroupElt[] tarImages) Returns the homomorphism from sou to tar sending the generators souGen to the corresponding elements tarImages, or returns null to indicate that such a homomorphism does not exist.
GroupElt	Homomorphism.apply(GroupElt g) Returns the value of this homomorphism on the element g of the source.
Complex	ClassFunction.apply(GroupElt g) Returns the value of the function at g.
GroupElt	GroupElt.mult(GroupElt y) Returns the product this * y.
GroupElt	GroupElt.conjugate(GroupElt y) Returns y * this * y^(-1).
GroupElt	GroupElt.conjugateYinvXY(GroupElt y) Returns y^(-1) * this * y.
boolean	GroupElt.commutesWith(GroupElt y) Whether this and y commute.
abstract int	Group.getConjClassIndex(GroupElt g) Returns i such that g is in the i-th conjugacy class.
static int	Group.getEltOrder(GroupElt g, Group G) Finds the order of the element g.
static int	Group.getEltOrder(GroupElt g, int N, int[][] fac) Finds the order of the element g.
static GroupElt	Group.power(GroupElt g, int i) Returns the i-th power of g.
Subgroup	Group.getCentralizer(GroupElt g) Returns the centralizer of g in this group.
boolean	Group.isCentral(GroupElt g) Whether the argument is in the center of this group.
int	HashGroup.getConjClassIndex(GroupElt g) Returns i such that g is in the i-th conjugacy class.

Constructors in repthy with parameters of type GroupElt

QuotientGroupElt(GroupElt g, Subgroup GcontainingH)
Constructor.

C_n(GroupElt g)
Constructor.

ProductGroupElt(GroupElt g1, GroupElt g2)

HeckeAlgebraElt(HeckeAlgebra alg, GroupElt g)
Constructs the element 1*(g) in the algebra.

HashGroup(GroupElt[] generators)
Constructs the group with the given generators.