public class BasicLattice extends GeneralAlgebra implements SmallAlgebra, Lattice
SmallAlgebra.AlgebraType
con, description, monitor, name, operationsMap, similarityType, size, sub, universe
CARDINALITY_COUNTABLE, CARDINALITY_COUNTABLY_INFINITE, CARDINALITY_FINITE, CARDINALITY_INFINITE, CARDINALITY_UNKNOWN
Constructor and Description |
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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.
|
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() |
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
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
parent, parents, resetConAndSub
constantOperations, getDescription, getMonitor, getName, getOperation, getOperationsMap, inputSize, isIdempotent, isSimilarTo, isTotal, isUnary, iterator, makeOperationTables, monitoring, operations, setDescription, setMonitor, setName, similarityType, updateSimilarityType
public BasicLattice(java.lang.String name, org.latdraw.orderedset.OrderedSet poset)
poset
- A (latdraw) posetpublic BasicLattice(java.lang.String name, Lattice lat)
lat
- A Lattice with joinIrreducibles inplemented.public BasicLattice(java.lang.String name, CongruenceLattice lat, boolean label)
lat
- The congruence latticelabel
- indicates if this should be TCT labelledpublic org.latdraw.orderedset.OrderedSet makeOrderedSet(Lattice lat)
lat
- A Lattice with joinIrreducibles implemented.public org.latdraw.diagram.Diagram getDiagram()
public int cardinality()
cardinality
in interface Algebra
cardinality
in class GeneralAlgebra
public org.latdraw.orderedset.POElem zero()
public org.latdraw.orderedset.POElem one()
public java.util.Set universe()
Algebra
universe
in interface Algebra
universe
in class GeneralAlgebra
public java.lang.Object join(java.lang.Object obj1, java.lang.Object obj2)
public java.lang.Object meet(java.lang.Object obj1, java.lang.Object obj2)
public java.util.List<org.latdraw.orderedset.POElem> atoms()
public java.util.List<org.latdraw.orderedset.POElem> coatoms()
public java.util.List<org.latdraw.orderedset.POElem> joinIrreducibles()
Lattice
joinIrreducibles
in interface Lattice
public java.util.List<org.latdraw.orderedset.POElem> meetIrreducibles()
Lattice
meetIrreducibles
in interface Lattice
public java.util.List<org.latdraw.orderedset.POElem> joinIrredsBelow(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.orderedset.POElem> meetIrredsAbove(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.orderedset.POElem> lowerCovers(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.orderedset.POElem> upperCovers(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.orderedset.POElem> irredundantMeetDecomposition(org.latdraw.orderedset.POElem v)
public org.latdraw.orderedset.POElem findMeetIrred(org.latdraw.orderedset.POElem a, org.latdraw.orderedset.POElem b)
a
and not above b
.
Note if a
is covered by b
then
[a,b]
transposes up to [m,m*]
.public java.util.List<org.latdraw.orderedset.POElem> makeIrredundantMeet(java.util.List<org.latdraw.orderedset.POElem> list)
public java.util.List<org.latdraw.orderedset.POElem> irredundantJoinDecomposition(org.latdraw.orderedset.POElem v)
public org.latdraw.orderedset.POElem findJoinIrred(org.latdraw.orderedset.POElem a, org.latdraw.orderedset.POElem b)
a
and not below b
.
Note if a
covers b
then
[b,a]
transposes down to [j_*,j]
.public java.util.List<org.latdraw.orderedset.POElem> makeIrredundantJoin(java.util.List<org.latdraw.orderedset.POElem> list)
public boolean leq(java.lang.Object obj1, java.lang.Object obj2)
Order
public java.util.List<org.latdraw.orderedset.POElem> ideal(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.orderedset.POElem> filter(org.latdraw.orderedset.POElem v)
public java.util.List<org.latdraw.diagram.Vertex> getVertices(java.util.List<org.latdraw.orderedset.POElem> lst)
public BasicLattice dual()
public int elementIndex(java.lang.Object obj)
SmallAlgebra
elementIndex
in interface SmallAlgebra
public java.lang.Object getElement(int k)
SmallAlgebra
getElement
in interface SmallAlgebra
public java.util.List getUniverseList()
SmallAlgebra
getUniverseList
in interface SmallAlgebra
public java.util.Map getUniverseOrder()
SmallAlgebra
getUniverseOrder
in interface SmallAlgebra
public org.latdraw.orderedset.OrderedSet getPoset()
public SubalgebraLattice sub()
SmallAlgebra
sub
in interface SmallAlgebra
sub
in class GeneralAlgebra
public CongruenceLattice con()
SmallAlgebra
con
in interface SmallAlgebra
con
in class GeneralAlgebra
public void convertToDefaultValueOps()
SmallAlgebra
convertToDefaultValueOps
in interface SmallAlgebra
public SmallAlgebra.AlgebraType algebraType()
SmallAlgebra
algebraType
in interface SmallAlgebra
public static void main(java.lang.String[] args) throws java.io.IOException, BadAlgebraFileException, org.latdraw.orderedset.NonOrderedSetException
java.io.IOException
BadAlgebraFileException
org.latdraw.orderedset.NonOrderedSetException
Copyright 2003 Ralph Freese. All Rights Reserved.