jhypercomplex

Class MonteCarlo

java.lang.Object

jhypercomplex.MonteCarlo

public class MonteCarlo
extends java.lang.Object

Copyright © 2005-2015 by Markus Maute. All rights reserved.

Author:

Markus Maute (http:///www.jalgebra.com)

Constructor Summary

Constructors

Constructor and Description
MonteCarlo()

Method Summary

Methods

Modifier and Type	Method and Description
static void	findGeneralOctonionRotation() A most general quaternion rotation is given by q --> r*q*r-1.
static java.util.HashSet<BinaryProductStructure>	getIdemotents(java.lang.Class class_, int nonzero_elements) Idempotents (modulo '-1') are determined.
static java.util.HashSet<java.lang.String>	getNonassociativeSpacetimeQuadruples()
static java.util.HashSet<java.lang.String>	getNonassociativeSpacetimeTriples()
java.util.HashSet<java.lang.String>	getNucleus() Every component is randomly set to -1,0 or 1.
static int	getRandomInteger(int from, int to)
static int	getRandomInteger(int from, int to, java.util.HashSet<java.lang.String> excluded_elements)
static java.util.HashSet<java.lang.String>	getTetrads(int n) For a given number of elements all possible tetrads (4-sets) are generated.
static java.util.HashSet<java.lang.String>	getTriads(int n) For a given number of elements all possible triads are generated.
static java.util.HashSet<java.lang.String>	getZeroDivisors(int nonzero_components)
static void	printQuintIdentities()
static void	setNumberOfIterations(int n) Any Monte Carlo simulation is carried out in a loop.
static void	testGeneratePossibleHadamardTables() Given a n x n -matrix with n mod 4 = 0, how many different Hadamard matrices can one construct ?

Methods inherited from class java.lang.Object

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

Constructor Detail

MonteCarlo

public MonteCarlo()

Method Detail

setNumberOfIterations

public static void setNumberOfIterations(int n)

Any Monte Carlo simulation is carried out in a loop.

Parameters:

n - Number of times to cycle through the loop.

testGeneratePossibleHadamardTables

public static void testGeneratePossibleHadamardTables()
                                               throws java.lang.Exception

Given a n x n -matrix with n mod 4 = 0, how many different Hadamard matrices can one construct ?

Throws:

java.lang.Exception

findGeneralOctonionRotation

public static void findGeneralOctonionRotation()
                                        throws java.lang.Exception

A most general quaternion rotation is given by q --> r*q*r-1. Does this work for octonions as well or do we need more multiplications ?

Throws:

java.lang.Exception

getNucleus

public java.util.HashSet<java.lang.String> getNucleus()

Every component is randomly set to -1,0 or 1. The resulting vector is added to the resulting set if it is contained in the nucleus.

Returns:

Basis elements of the nucleus.

getIdemotents

public static java.util.HashSet<BinaryProductStructure> getIdemotents(java.lang.Class class_,
                                                      int nonzero_elements)
                                                               throws java.lang.Exception

Idempotents (modulo '-1') are determined. I.e. we generate n random components of a hypernumber and multiply it with itself. If the condition h*h = +/-h is satisfied, we return the number.

Parameters:

nonzero_elements - Number of components set to +1 or -1 (randomly).

Returns:

Set of idempotents.

Throws:

java.lang.Exception

getTriads

public static java.util.HashSet<java.lang.String> getTriads(int n)

For a given number of elements all possible triads are generated. The overall number is given by the binomial coefficient: Bin(n,3).

Parameters:

n - Number of possible elements in a triad.

Returns:

Set with the triads.

getTetrads

public static java.util.HashSet<java.lang.String> getTetrads(int n)

For a given number of elements all possible tetrads (4-sets) are generated. The overall number is given by the binomial coefficient: Bin(n,4).

Parameters:

n - Number of possible elements in a tetrad.

Returns:

Set with the tetrads.

getNonassociativeSpacetimeTriples

public static java.util.HashSet<java.lang.String> getNonassociativeSpacetimeTriples()

Returns:

Triples of the form x(yz), x(tz), t(zy)

getNonassociativeSpacetimeQuadruples

public static java.util.HashSet<java.lang.String> getNonassociativeSpacetimeQuadruples()

Returns:

Quadruples of the form (x(yz))t, y(x(tz)), t(z(yx))

printQuintIdentities

public static void printQuintIdentities()
                                 throws java.lang.Exception

Throws:

java.lang.Exception

getRandomInteger

public static int getRandomInteger(int from,
                   int to,
                   java.util.HashSet<java.lang.String> excluded_elements)

getRandomInteger

public static int getRandomInteger(int from,
                   int to)

getZeroDivisors

public static java.util.HashSet<java.lang.String> getZeroDivisors(int nonzero_components)
                                                           throws java.lang.Exception

Parameters:

nonzero_elements - Number of components to be randomly set to "-1" or "+1" for both numbers to be multiplied.

Returns:

Throws:

java.lang.Exception