QuotientAlgebra (Universal Algebra Calculator API)

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:

$Id$

Author:

Ralph Freese

Nested Class Summary
- Nested classes/interfaces inherited from interface org.uacalc.alg.SmallAlgebra
  SmallAlgebra.AlgebraType

Field Summary

Fields
Modifier and Type Field and Description

protected Partition congruence

protected int[] representatives

protected SmallAlgebra superAlgebra
- Fields inherited from class org.uacalc.alg.GeneralAlgebra
  con, description, monitor, name, operationsMap, similarityType, size, sub, universe
- Fields inherited from interface org.uacalc.alg.Algebra
  CARDINALITY_COUNTABLE, CARDINALITY_COUNTABLY_INFINITE, CARDINALITY_FINITE, CARDINALITY_INFINITE, CARDINALITY_UNKNOWN

Fields
Modifier and Type	Field and Description
`protected Partition`	`congruence`
`protected int[]`	`representatives`
`protected SmallAlgebra`	`superAlgebra`

Constructor Summary

Constructors
Constructor and Description
`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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`SmallAlgebra.AlgebraType`	`algebraType()` The type of algebra this is, like a quotient algebra.
`int`	`canonicalHomomorphism(int e)` If `e` is the index of an element of the parent algebra, this returns the corresponding element of the 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 `k`th element; otherwise -1.
`Partition`	`getCongruence()` Get the congruence on the super algebra giving this algebra.
`java.lang.Object`	`getElement(int index)` returns the `k`th 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, updateSimilarityType

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, updateSimilarityType

- 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
  - canonicalHomomorphism
```
public int canonicalHomomorphism(int e)
```
    If e is the index of an element of the parent algebra, this returns the corresponding element of the quotient algebra.
    
    Parameters:
    
    e - the index of an element in the parent algebra
    
    Returns:
    
    the index of its image
  - 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

Class QuotientAlgebra

Nested Class Summary

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

Field Summary

Fields inherited from class org.uacalc.alg.GeneralAlgebra

Fields inherited from interface org.uacalc.alg.Algebra

Constructor Summary

Method Summary

Methods inherited from class org.uacalc.alg.GeneralAlgebra

Methods inherited from class java.lang.Object

Methods inherited from interface org.uacalc.alg.SmallAlgebra

Methods inherited from interface org.uacalc.alg.Algebra

Field Detail

superAlgebra

representatives

congruence

Constructor Detail

QuotientAlgebra

QuotientAlgebra

Method Detail

makeOperationTables

superAlgebra

getCongruence

con

sub

elementIndex

getElement

representativeIndex

canonicalHomomorphism

getUniverseList

getUniverseOrder

makeUniverse

universe

convertToDefaultValueOps

algebraType

main