de.jtem.riemann.theta

Class ModularTransformation

java.lang.Object

de.jtem.riemann.theta.ModularTransformation

All Implemented Interfaces:

Serializable, Cloneable

public class ModularTransformation
extends Object
implements Serializable, Cloneable

An instance of this class represents an element of the modular group. The modular group consists of square integer matrices

σ =	/ A B \ \ C D / ,

with A,B,C,D∈Zg×g, that leave the symplectic structure invariant, e.g.:

σt

/ 0 1 \ \-1 0 /

σ =

/ 0 1 \ \-1 0 /

Author:

Markus Schmies

See Also:

ModularPropertySupport, SiegelReduction, Serialized Form

Constructor Summary

Constructors

Constructor and Description
ModularTransformation(int g) Creates identity in molular group of degree 2g.
ModularTransformation(de.jtem.blas.IntegerMatrix A, de.jtem.blas.IntegerMatrix B, de.jtem.blas.IntegerMatrix C, de.jtem.blas.IntegerMatrix D) Creates element with prescribed sub-matrices A,B,C and, D.
ModularTransformation(ModularTransformation T) Creates a copy of T.

Method Summary

Modifier and Type	Method and Description
void	assign(ModularTransformation T) Assigns this with T.
void	assignDivide(ModularTransformation M) Assigns this with product of itself and inverse of M.
void	assignDivide(ModularTransformation M, ModularTransformation N) Assigns this with product of M and inverse of N.
void	assignId() Assigns this with identity in modular group.
void	assignInvert(ModularTransformation T) Assigns this with inverse of T.
void	assignTimes(ModularTransformation M) Assigns this with product of itself and M.
void	assignTimes(ModularTransformation M, ModularTransformation N) Assigns this with product of M and N.
ModularTransformation	divide(ModularTransformation M) Returns product of this and inverse ofM.
de.jtem.blas.IntegerMatrix	getA() Queries sub-matrix a.
de.jtem.blas.IntegerMatrix	getB() Queries sub-matrix b.
de.jtem.blas.IntegerMatrix	getC() Queries sub-matrix c.
de.jtem.blas.IntegerMatrix	getD() Queries sub-matrix d.
int	getDegree() Returns degree of modular group.
ModularTransformation	invert() Returns inverse of this.
boolean	isId() Tests if this is the identity in modular group.
ModularTransformation	times(ModularTransformation M) Returns product of this and M.
String	toString() Returns the for sub-matrices as string.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ModularTransformation

public ModularTransformation(int g)

Creates identity in molular group of degree 2g.

ModularTransformation

public ModularTransformation(de.jtem.blas.IntegerMatrix A,
                             de.jtem.blas.IntegerMatrix B,
                             de.jtem.blas.IntegerMatrix C,
                             de.jtem.blas.IntegerMatrix D)

Creates element with prescribed sub-matrices A,B,C and, D.

Parameters:

A - square integer matrix of degree dim

B - square integer matrix of degree dim

C - square integer matrix of degree dim

D - square integer matrix of degree dim

ModularTransformation

public ModularTransformation(ModularTransformation T)

Creates a copy of T.

Method Detail

assign

public void assign(ModularTransformation T)

Assigns this with T.

assignDivide

public void assignDivide(ModularTransformation M)

Assigns this with product of itself and inverse of M.

Parameters:

M - element with the same degree as this

assignDivide

public void assignDivide(ModularTransformation M,
                         ModularTransformation N)

Assigns this with product of M and inverse of N.

Parameters:

M - element with the same degree as N

N - element with the same degree as M

assignId

public void assignId()

Assigns this with identity in modular group.

assignInvert

public void assignInvert(ModularTransformation T)

Assigns this with inverse of T.

assignTimes

public void assignTimes(ModularTransformation M)

Assigns this with product of itself and M.

Parameters:

M - element with the same degree as this

assignTimes

public void assignTimes(ModularTransformation M,
                        ModularTransformation N)

Assigns this with product of M and N.

Parameters:

M - element with the same degree as N

N - element with the same degree as M

divide

public ModularTransformation divide(ModularTransformation M)

Returns product of this and inverse ofM.

Parameters:

M - element with the same degree as this

getA

public de.jtem.blas.IntegerMatrix getA()

Queries sub-matrix a.

Returns:

sub-matrix a

getB

public de.jtem.blas.IntegerMatrix getB()

Queries sub-matrix b.

Returns:

sub-matrix b

getC

public de.jtem.blas.IntegerMatrix getC()

Queries sub-matrix c.

Returns:

sub-matrix c

getD

public de.jtem.blas.IntegerMatrix getD()

Queries sub-matrix d.

Returns:

sub-matrix d

getDegree

public int getDegree()

Returns degree of modular group.

invert

public ModularTransformation invert()

Returns inverse of this.

isId

public boolean isId()

Tests if this is the identity in modular group.

times

public ModularTransformation times(ModularTransformation M)

Returns product of this and M.

Parameters:

M - element with the same degree as this

toString

public String toString()

Returns the for sub-matrices as string.

Overrides:

toString in class Object