de.jtem.riemann.schottky

Class AbelMap

java.lang.Object

de.jtem.riemann.schottky.AbelMap

public class AbelMap
extends Object

This support class performs the numerical integration of the normalized differentials which is needed for abel's map. Analytic integration of the poincaree theta series can not avoid periods generated by the logarithm. To determine these periods we have to integrate the differentials numericly. But this can be done with a low precession (0.01), because one only wants to compare the result with the analytic integral.

Author:

Markus Schmies

Constructor Summary

Constructors

Constructor and Description
AbelMap(Schottky schottky)

Method Summary

Modifier and Type	Method and Description
de.jtem.mfc.field.Complex	eval(de.jtem.mfc.field.Complex A, de.jtem.mfc.field.Complex B, de.jtem.blas.ComplexVector path, double acc) Computes normalized integral of thrid kind along prescribed path.
de.jtem.mfc.field.Complex	eval(int index, de.jtem.blas.ComplexVector path, double acc) Computes normalized integral of first kind with prescribed index along given path.
de.jtem.mfc.field.Complex	numEval(de.jtem.mfc.field.Complex A, de.jtem.mfc.field.Complex B, de.jtem.blas.ComplexVector path, double tol) integrates normalized differential of thrid kind with prescribes poles A and B numerically along given path.
de.jtem.mfc.field.Complex	numEval(int index, de.jtem.blas.ComplexVector path, double tol) integrates normalized differential of first kind with prescribed index numerically along given path with prescribed tol.

Methods inherited from class java.lang.Object

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

Constructor Detail

AbelMap

public AbelMap(Schottky schottky)

Method Detail

eval

public de.jtem.mfc.field.Complex eval(de.jtem.mfc.field.Complex A,
                                      de.jtem.mfc.field.Complex B,
                                      de.jtem.blas.ComplexVector path,
                                      double acc)

Computes normalized integral of thrid kind along prescribed path.

Parameters:

A - singularity with residue -1

B - singularity with residue +1

path - of integration

acc - accurac of integral

eval

public de.jtem.mfc.field.Complex eval(int index,
                                      de.jtem.blas.ComplexVector path,
                                      double acc)

Computes normalized integral of first kind with prescribed index along given path.

Parameters:

index - of normalized differential of first kind

path - of integration

acc - accuracy of integral

numEval

public de.jtem.mfc.field.Complex numEval(de.jtem.mfc.field.Complex A,
                                         de.jtem.mfc.field.Complex B,
                                         de.jtem.blas.ComplexVector path,
                                         double tol)

integrates normalized differential of thrid kind with prescribes poles A and B numerically along given path.

Parameters:

A - singularity with residue -1

B - singularity with residue +1

path - of integration

tol - absolute and relative tolerance of numerical integration, the differential is evaluated with an accuracy of one tenth of tol.

numEval

public de.jtem.mfc.field.Complex numEval(int index,
                                         de.jtem.blas.ComplexVector path,
                                         double tol)

integrates normalized differential of first kind with prescribed index numerically along given path with prescribed tol.

Parameters:

index - of normalized differentil of first kind

path - of integration

tol - absolute and relative tolerance of numerical integration, the differential is evaluated with an accuracy of one tenth of tol.