org.uacalc.lat

Class BasicLattice

java.lang.Object

org.uacalc.alg.GeneralAlgebra

org.uacalc.lat.BasicLattice

All Implemented Interfaces:

Algebra, SmallAlgebra, Lattice, Order

public class BasicLattice
extends GeneralAlgebra
implements SmallAlgebra, Lattice

Nested Class Summary

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

SmallAlgebra.AlgebraType

Field Summary

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

Constructor Summary

Constructors

Constructor and Description
BasicLattice(java.lang.String name, CongruenceLattice lat, boolean label) Make a BasicLattice from a CongruenceLattice.
BasicLattice(java.lang.String name, Lattice lat) Make a BasicLattice from a Lattice.
BasicLattice(java.lang.String name, org.latdraw.orderedset.OrderedSet poset) Make a BasicLattice from a poset.

Method Summary

Modifier and Type	Method and Description
SmallAlgebra.AlgebraType	algebraType() The type of algebra this is, like a quotient algebra.
java.util.List<org.latdraw.orderedset.POElem>	atoms()
int	cardinality()
java.util.List<org.latdraw.orderedset.POElem>	coatoms()
CongruenceLattice	con() The congurence lattice.
void	convertToDefaultValueOps() This is used in the UI.
BasicLattice	dual() Form the dual of the lattice.
int	elementIndex(java.lang.Object obj) This method will return k if elem is the kth element; otherwise -1.
java.util.List<org.latdraw.orderedset.POElem>	filter(org.latdraw.orderedset.POElem v)
org.latdraw.orderedset.POElem	findJoinIrred(org.latdraw.orderedset.POElem a, org.latdraw.orderedset.POElem b) This finds a join irreducible element which is minimal with respect to being below a and not below b.
org.latdraw.orderedset.POElem	findMeetIrred(org.latdraw.orderedset.POElem a, org.latdraw.orderedset.POElem b) This finds a meet irreducible element which is maximal with respect to being above a and not above b.
org.latdraw.diagram.Diagram	getDiagram()
java.lang.Object	getElement(int k) returns the kth element.
org.latdraw.orderedset.OrderedSet	getPoset()
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).
java.util.List<org.latdraw.diagram.Vertex>	getVertices(java.util.List<org.latdraw.orderedset.POElem> lst)
java.util.List<org.latdraw.orderedset.POElem>	ideal(org.latdraw.orderedset.POElem v)
java.util.List<org.latdraw.orderedset.POElem>	irredundantJoinDecomposition(org.latdraw.orderedset.POElem v)
java.util.List<org.latdraw.orderedset.POElem>	irredundantMeetDecomposition(org.latdraw.orderedset.POElem v)
java.lang.Object	join(java.util.List args)
java.lang.Object	join(java.lang.Object obj1, java.lang.Object obj2)
java.util.List<org.latdraw.orderedset.POElem>	joinIrredsBelow(org.latdraw.orderedset.POElem v)
java.util.List<org.latdraw.orderedset.POElem>	joinIrreducibles() An optional operation returning the list of join irreducible elements.
boolean	leq(java.lang.Object obj1, java.lang.Object obj2) The order relation.
java.util.List<org.latdraw.orderedset.POElem>	lowerCovers(org.latdraw.orderedset.POElem v)
static void	main(java.lang.String[] args) An optional operation returning the list of meet irreducible elements.
java.util.List<org.latdraw.orderedset.POElem>	makeIrredundantJoin(java.util.List<org.latdraw.orderedset.POElem> list)
java.util.List<org.latdraw.orderedset.POElem>	makeIrredundantMeet(java.util.List<org.latdraw.orderedset.POElem> list)
org.latdraw.orderedset.OrderedSet	makeOrderedSet(Lattice lat) Make a org.latdraw.orderedset.OrderedSet from a Lattice.
java.lang.Object	meet(java.util.List args)
java.lang.Object	meet(java.lang.Object obj1, java.lang.Object obj2)
java.util.List<org.latdraw.orderedset.POElem>	meetIrredsAbove(org.latdraw.orderedset.POElem v)
java.util.List<org.latdraw.orderedset.POElem>	meetIrreducibles() An optional operation returning the list of meet irreducible elements.
org.latdraw.orderedset.POElem	one()
SubalgebraLattice	sub() The subalgebra lattice.
java.util.Set	universe() We use java.util.Set to hold the universe of the algebra.
java.util.List<org.latdraw.orderedset.POElem>	upperCovers(org.latdraw.orderedset.POElem v)
org.latdraw.orderedset.POElem	zero()

Methods inherited from class org.uacalc.alg.GeneralAlgebra

constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, makeOperationTables, 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

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

Constructor Detail

BasicLattice

public BasicLattice(java.lang.String name,
                    org.latdraw.orderedset.OrderedSet poset)

Make a BasicLattice from a poset.

Parameters:

poset - A (latdraw) poset

BasicLattice

public BasicLattice(java.lang.String name,
                    Lattice lat)

Make a BasicLattice from a Lattice.

Parameters:

lat - A Lattice with joinIrreducibles inplemented.

BasicLattice

public BasicLattice(java.lang.String name,
                    CongruenceLattice lat,
                    boolean label)

Make a BasicLattice from a CongruenceLattice.

Parameters:

lat - The congruence lattice

label - indicates if this should be TCT labelled

Method Detail

makeOrderedSet

public org.latdraw.orderedset.OrderedSet makeOrderedSet(Lattice lat)

Make a org.latdraw.orderedset.OrderedSet from a Lattice.

Parameters:

lat - A Lattice with joinIrreducibles implemented.

getDiagram

public org.latdraw.diagram.Diagram getDiagram()

cardinality

public int cardinality()

Specified by:

cardinality in interface Algebra

Overrides:

cardinality in class GeneralAlgebra

Returns:

the cardinality if possible, else a negative int

zero

public org.latdraw.orderedset.POElem zero()

one

public org.latdraw.orderedset.POElem one()

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

join

public java.lang.Object join(java.util.List args)

Specified by:

join in interface Lattice

join

public java.lang.Object join(java.lang.Object obj1,
                             java.lang.Object obj2)

Specified by:

join in interface Lattice

meet

public java.lang.Object meet(java.util.List args)

Specified by:

meet in interface Lattice

meet

public java.lang.Object meet(java.lang.Object obj1,
                             java.lang.Object obj2)

Specified by:

meet in interface Lattice

atoms

public java.util.List<org.latdraw.orderedset.POElem> atoms()

Specified by:

atoms in interface Lattice

coatoms

public java.util.List<org.latdraw.orderedset.POElem> coatoms()

Specified by:

coatoms in interface Lattice

joinIrreducibles

public java.util.List<org.latdraw.orderedset.POElem> joinIrreducibles()

Description copied from interface: Lattice

An optional operation returning the list of join irreducible elements.

Specified by:

joinIrreducibles in interface Lattice

meetIrreducibles

public java.util.List<org.latdraw.orderedset.POElem> meetIrreducibles()

Description copied from interface: Lattice

An optional operation returning the list of meet irreducible elements.

Specified by:

meetIrreducibles in interface Lattice

joinIrredsBelow

public java.util.List<org.latdraw.orderedset.POElem> joinIrredsBelow(org.latdraw.orderedset.POElem v)

meetIrredsAbove

public java.util.List<org.latdraw.orderedset.POElem> meetIrredsAbove(org.latdraw.orderedset.POElem v)

lowerCovers

public java.util.List<org.latdraw.orderedset.POElem> lowerCovers(org.latdraw.orderedset.POElem v)

upperCovers

public java.util.List<org.latdraw.orderedset.POElem> upperCovers(org.latdraw.orderedset.POElem v)

irredundantMeetDecomposition

public java.util.List<org.latdraw.orderedset.POElem> irredundantMeetDecomposition(org.latdraw.orderedset.POElem v)

findMeetIrred

public org.latdraw.orderedset.POElem findMeetIrred(org.latdraw.orderedset.POElem a,
                                                   org.latdraw.orderedset.POElem b)

This finds a meet irreducible element which is maximal with respect to being above a and not above b. Note if a is covered by b then [a,b] transposes up to [m,m*].

makeIrredundantMeet

public java.util.List<org.latdraw.orderedset.POElem> makeIrredundantMeet(java.util.List<org.latdraw.orderedset.POElem> list)

irredundantJoinDecomposition

public java.util.List<org.latdraw.orderedset.POElem> irredundantJoinDecomposition(org.latdraw.orderedset.POElem v)

findJoinIrred

public org.latdraw.orderedset.POElem findJoinIrred(org.latdraw.orderedset.POElem a,
                                                   org.latdraw.orderedset.POElem b)

This finds a join irreducible element which is minimal with respect to being below a and not below b. Note if a covers b then [b,a] transposes down to [j_*,j].

makeIrredundantJoin

public java.util.List<org.latdraw.orderedset.POElem> makeIrredundantJoin(java.util.List<org.latdraw.orderedset.POElem> list)

leq

public boolean leq(java.lang.Object obj1,
                   java.lang.Object obj2)

Description copied from interface: Order

The order relation.

Specified by:

leq in interface Order

ideal

public java.util.List<org.latdraw.orderedset.POElem> ideal(org.latdraw.orderedset.POElem v)

filter

public java.util.List<org.latdraw.orderedset.POElem> filter(org.latdraw.orderedset.POElem v)

getVertices

public java.util.List<org.latdraw.diagram.Vertex> getVertices(java.util.List<org.latdraw.orderedset.POElem> lst)

dual

public BasicLattice dual()

Form the dual of the lattice.

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 k)

Description copied from interface: SmallAlgebra

returns the kth element.

Specified by:

getElement in interface SmallAlgebra

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

getPoset

public org.latdraw.orderedset.OrderedSet getPoset()

sub

public SubalgebraLattice sub()

Description copied from interface: SmallAlgebra

The subalgebra lattice.

Specified by:

sub in interface SmallAlgebra

Overrides:

sub in class GeneralAlgebra

con

public CongruenceLattice con()

Description copied from interface: SmallAlgebra

The congurence lattice.

Specified by:

con in interface SmallAlgebra

Overrides:

con 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,
                        org.latdraw.orderedset.NonOrderedSetException

An optional operation returning the list of meet irreducible elements.

Throws:

java.io.IOException

BadAlgebraFileException

org.latdraw.orderedset.NonOrderedSetException