org.uacalc.alg
Class QuotientAlgebra

java.lang.Object
  org.uacalc.alg.GeneralAlgebra
      org.uacalc.alg.QuotientAlgebra

All Implemented Interfaces:

Algebra, SmallAlgebra

public class QuotientAlgebra
extends GeneralAlgebra
implements SmallAlgebra

This class represents a quotient algebra of a SmallAlgebra. The elements are just the elements of the superAlgebra corresponding to the representatives of the congruence. We may want to make special element objects having an element of the super algebra and the congruence.

Version:

$Id: QuotientAlgebra.java,v 1.9 2008/08/20 21:49:04 ralphfreese Exp $

Author:

Ralph Freese

Nested Class Summary

Nested classes/interfaces inherited from interface org.uacalc.alg.SmallAlgebra

SmallAlgebra.AlgebraType

Field Summary

protected Partition	congruence
protected int[]	representatives
protected SmallAlgebra	superAlgebra

Fields inherited from class org.uacalc.alg.GeneralAlgebra

con, description, monitor, name, operations, operationsMap, similarityType, size, sub, universe

Fields inherited from interface org.uacalc.alg.Algebra

CARDINALITY_COUNTABLE, CARDINALITY_COUNTABLY_INFINITE, CARDINALITY_FINITE, CARDINALITY_INFINITE, CARDINALITY_UNKNOWN

Constructor Summary

QuotientAlgebra(SmallAlgebra alg, Partition congruence)

QuotientAlgebra(java.lang.String name, SmallAlgebra alg, Partition congruence)
Form the quotient algebra of the super algebra by congruence.

Method Summary

SmallAlgebra.AlgebraType	algebraType() The type of algebra this is, like a quotient algebra.
CongruenceLattice	con() The congurence lattice.
void	convertToDefaultValueOps() This is used in the UI.
int	elementIndex(java.lang.Object obj) This method will return k if elem is the kth element; otherwise -1.
Partition	getCongruence() Get the congruence on the super algebra giving this algebra.
java.lang.Object	getElement(int index) returns the kth element.
java.util.List	getUniverseList() The universe as a List such getElement(k) will equal the kth element of the List.
java.util.Map	getUniverseOrder() A map that can be used for elementIndex(a).
static void	main(java.lang.String[] args)
void	makeOperationTables() Make operation tables to speed up the evaluation of operations at the cost using more space.
protected java.util.Set	makeUniverse() Notes: this is need a class for congruence classes.
int	representativeIndex(int rep) Find the index of rep in representatives.
SubalgebraLattice	sub() The subalgebra lattice.
SmallAlgebra	superAlgebra()
java.util.Set	universe() We use java.util.Set to hold the universe of the algebra.

Methods inherited from class org.uacalc.alg.GeneralAlgebra

cardinality, constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, monitoring, operations, parent, parents, resetConAndSub, setDescription, setMonitor, setName, setOperations, setUniverse, similarityType

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.uacalc.alg.SmallAlgebra

parent, parents, resetConAndSub

Methods inherited from interface org.uacalc.alg.Algebra

cardinality, constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, monitoring, operations, setDescription, setMonitor, setName, similarityType

Field Detail

superAlgebra

protected final SmallAlgebra superAlgebra

representatives

protected final int[] representatives

congruence

protected Partition congruence

Constructor Detail

QuotientAlgebra

public QuotientAlgebra(SmallAlgebra alg,
                       Partition congruence)

QuotientAlgebra

public QuotientAlgebra(java.lang.String name,
                       SmallAlgebra alg,
                       Partition congruence)

Form the quotient algebra of the super algebra by congruence.

Method Detail

makeOperationTables

public void makeOperationTables()

Description copied from interface: Algebra

Make operation tables to speed up the evaluation of operations at the cost using more space.

Specified by:

makeOperationTables in interface Algebra

Overrides:

makeOperationTables in class GeneralAlgebra

See Also:

Operation.makeTable

superAlgebra

public SmallAlgebra superAlgebra()

getCongruence

public Partition getCongruence()

Get the congruence on the super algebra giving this algebra.

con

public CongruenceLattice con()

Description copied from interface: SmallAlgebra

The congurence lattice.

Specified by:

con in interface SmallAlgebra

Overrides:

con in class GeneralAlgebra

sub

public SubalgebraLattice sub()

Description copied from interface: SmallAlgebra

The subalgebra lattice.

Specified by:

sub in interface SmallAlgebra

Overrides:

sub in class GeneralAlgebra

elementIndex

public int elementIndex(java.lang.Object obj)

Description copied from interface: SmallAlgebra

This method will return k if elem is the kth element; otherwise -1. (Should we have it throw an error instead?)

Specified by:

elementIndex in interface SmallAlgebra

getElement

public java.lang.Object getElement(int index)

Description copied from interface: SmallAlgebra

returns the kth element.

Specified by:

getElement in interface SmallAlgebra

representativeIndex

public int representativeIndex(int rep)

Find the index of rep in representatives. This is the index of the algebra element.

Parameters:

rep - a member of the array representatives

Returns:

the index of rep in representatives

getUniverseList

public java.util.List getUniverseList()

Description copied from interface: SmallAlgebra

The universe as a List such getElement(k) will equal the kth element of the List. It is allowed to be null.

Specified by:

getUniverseList in interface SmallAlgebra

getUniverseOrder

public java.util.Map getUniverseOrder()

Description copied from interface: SmallAlgebra

A map that can be used for elementIndex(a). It is allowed to be null.

Specified by:

getUniverseOrder in interface SmallAlgebra

makeUniverse

protected java.util.Set makeUniverse()

Notes: this is need a class for congruence classes. Something that will print like a/\theta.

universe

public java.util.Set universe()

Description copied from interface: Algebra

We use java.util.Set to hold the universe of the algebra. In order to accomodate infinite algebras and algebras with unknown cardinality, we allow the following changes:

• size can return a negative value if the cardinality is infinite or unknown or is larger that the largest int. In this case we may want to specify some information about the cardinality in another method but we have not decided on this yet.
• it is allowed that the iterator method of Set throw an UnsupportedOperationException.
• when extending AbstractSet, the contains method should be overwritten.

Specified by:

universe in interface Algebra

Overrides:

universe in class GeneralAlgebra

convertToDefaultValueOps

public void convertToDefaultValueOps()

Description copied from interface: SmallAlgebra

This is used in the UI. Only valid for BASIC algebras.

Specified by:

convertToDefaultValueOps in interface SmallAlgebra

algebraType

public SmallAlgebra.AlgebraType algebraType()

Description copied from interface: SmallAlgebra

The type of algebra this is, like a quotient algebra.

Specified by:

algebraType in interface SmallAlgebra

Returns:

main

public static void main(java.lang.String[] args)
                 throws java.io.IOException,
                        BadAlgebraFileException

Throws:

java.io.IOException

BadAlgebraFileException