A B C D E F G H I K L M N O P R S T U W Y 

A

add(F2) - Method in class homology.f2homology.F2
Returns the sum of this element and another one.
add(Pair<E, E>) - Method in class topology.BinaryRelation
Adds a pair to the pairs of this BinaryRelation.
addAll(Set<Pair<E, E>>) - Method in class topology.BinaryRelation
Adds a set of pairs to the pairs of this BinaryRelation.
addAllPair(Set<Pair<E, E>>) - Method in class topology.FiniteSpace
Adds a set of pairs to the topology-defining relation of a finite topological space, if the pairs' key and value belong to the point set.
addAllPoint(Set<E>) - Method in class topology.FiniteSpace
Adds a set of points to the point set of a finite topological space.
addPair(Pair<E, E>) - Method in class topology.FiniteSpace
Adds a pair to the topology-defining relation of a finite topological space, if the pair's key and value belong to the point set.
addPoint(E) - Method in class topology.FiniteSpace
Adds a point to the point set of a finite topological space.
allPaths(E, E) - Method in class topology.FiniteSpace
Returns all paths from a source to a destination point.
arrayOfSimplices() - Method in class homology.OrderComplex
Returns an array of all simplices.

B

basis() - Method in class homology.f2homology.F2Module
Returns a basis of the module.
Betti<K extends java.lang.Comparable<K>> - Class in homology
This class provides methods for computing the homology of finite topological spaces.
Betti() - Constructor for class homology.Betti
Creates a new Betti object.
Betti(FiniteSpace<K>) - Constructor for class homology.Betti
Creates an instance of the Betti class for a given finite topological space.
BettiNumbers() - Method in class homology.f2homology.F2ChainComplex
Returns the Betti numbers of the chain complex.
BinaryRelation<E extends java.lang.Comparable<E>> - Class in topology
The class BinaryRelation defines a set of pairs as a binary relation on the domain defined by the pairs themselves.
BinaryRelation() - Constructor for class topology.BinaryRelation
Creates an empty binary relation.
BinaryRelation(Set<Pair<E, E>>) - Constructor for class topology.BinaryRelation
Creates a new BinaryRelation given by a set of pairs.
BinaryRelation(BinaryRelation<E>) - Constructor for class topology.BinaryRelation
Creates a new BinaryRelation given by a BinaryRelation

C

circle() - Static method in class topology.TopologyExamples
Returns a circle.
closure(E) - Method in class topology.FiniteSpace
Returns the closure of a point in this finite topological space.
columnList() - Method in class homology.f2homology.F2Matrix
Returns a list of column indices of this F2Matrix.
columns() - Method in class homology.f2homology.F2Matrix
Returns the column set of this F2Matrix.
ComparablePair<K extends java.lang.Comparable<K>,V extends java.lang.Comparable<V>> - Class in topology
The class ComparablePair defines pairs of Comparable objects.
ComparablePair() - Constructor for class topology.ComparablePair
Initialises a ComparablePair.
ComparablePair(K, V) - Constructor for class topology.ComparablePair
Creates a ComparablePair with given key and value.
compare(List<E>, List<E>) - Method in class topology.ListComparator
Returns the compare-value of two lists with respect to lexicographical ordering: a positive number if the second list is before the first list, a negative number if the first list is before the second list, and zero if both lists are the same.
compare(TreeSet<E>, TreeSet<E>) - Method in class topology.TreeSetComparator
Returns the compare-value of two TreeSets with respect to lexicographical ordering: a positive value if the second tree set is before the first tree set, a negative value if the first tree set is before the second tree set, and zero if both are the same.
compareTo(Pair<K, V>) - Method in class topology.ComparablePair
Compares a ComparablePair with a pair.
componentNumber() - Method in class topology.PrimMST
Returns the number of connected components.

D

diagonal() - Method in class topology.BinaryRelation
Returns all pairs (e,e) where e is in BinaryRelation with some element or some element is in BinaryRelation with e.
dimension() - Method in class homology.OrderComplex
Returns the dimension of this order complex.
dimension() - Method in class topology.FiniteSpace
Returns the Krull dimension of this finite topological space.
downBeatPoints(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns the set of down beat points of the Kolmogorov quotient of a finite topological space.
dual() - Method in class topology.FiniteSpace
Returns the Alexandrov dual of this finite topological space.

E

emptySpace() - Static method in class topology.TopologyExamples
Returns the empty space.
equalArray(F2Matrix<K, L>) - Method in class homology.f2homology.F2Matrix
Compares the specified F2Matrix with this F2Matrix for equality in their arrays.
equals(F2) - Method in class homology.f2homology.F2
Returns true if this element equals another element.
equals(Object) - Method in class homology.f2homology.F2
Returns true if this element equals another object.
equals(F2Matrix<K, L>) - Method in class homology.f2homology.F2Matrix
Compares the specified F2Matrix with this F2Matrix for equality in their row sets, column sets and individual entries.
equals(F2Vector<K>) - Method in class homology.f2homology.F2Vector
Compares the specified F2Vector with this F2Vector for equality.
equals(BinaryRelation<F>) - Method in class topology.BinaryRelation
Checks equality of this BinaryRelation with another BinaryRelation.
equals(FiniteSpace<F>) - Method in class topology.FiniteSpace
Checks equality of this finite topological space with a given finite topological space.

F

F2 - Class in homology.f2homology
This class represents an element of the field with two elements.
F2(int) - Constructor for class homology.f2homology.F2
Constructs an element of F2 from an integer number by taking it modulo 2.
F2BettiNumbers() - Method in class homology.Betti
Returns the Betti numbers over the finite field with two elements.
F2ChainComplex<K extends java.lang.Comparable<K>> - Class in homology.f2homology
This class represents a chain complex over the finite field with two elements.
F2ChainComplex() - Constructor for class homology.f2homology.F2ChainComplex
Constructs an empty chain complex.
F2ChainComplex(List<F2Matrix<K, K>>) - Constructor for class homology.f2homology.F2ChainComplex
Constructs a chain complex from an list of F2Matrices.
F2ChainComplex() - Method in class homology.OrderComplex
Returns the chain complex over the field F2 associated to this order complex.
F2HomologicalDimension() - Method in class homology.Betti
Returns the homological dimension over the finite field with two elements.
F2Matrix<K extends java.lang.Comparable<K>,L extends java.lang.Comparable<L>> - Class in homology.f2homology
This class represents a matrix over the finite field F2, viewed as a linear map from F2Vectors parametrised by index type L to F2Vectors parametrised by index type K.
F2Matrix() - Constructor for class homology.f2homology.F2Matrix
Creates a new empty F2Matrix.
F2Matrix(Set<K>, Set<L>) - Constructor for class homology.f2homology.F2Matrix
Constructs an empty F2Matrix with specified row set and column set.
F2Matrix(Set<K>, Set<L>, F2) - Constructor for class homology.f2homology.F2Matrix
Constructs a constant F2Matrix.
F2Matrix(Map<ComparablePair<K, L>, F2>) - Constructor for class homology.f2homology.F2Matrix
Constructs an F2Matrix from a Map (a partial matrix).
F2Module<K extends java.lang.Comparable<K>> - Class in homology.f2homology
This class represents a module over the finite field with two elements, i.e.
F2Module() - Constructor for class homology.f2homology.F2Module
Constructs a new empty F2Module.
F2Module(List<F2Vector<K>>) - Constructor for class homology.f2homology.F2Module
Constructs a module (in fact a vector space) with given generating System of F2Vectors;
F2OrderComplexQuotient<E extends java.lang.Comparable<E>> - Class in homology.f2homology
This class computes the quotient of the order complex of a finite space with the order complex of a second space whose point set coincides with the point set of the first space, and whose Hasse diagram is contained in the Hasse diagram of the first space.
F2OrderComplexQuotient() - Constructor for class homology.f2homology.F2OrderComplexQuotient
Creates a new instance of F2OrderComplexQuotient
F2OrderComplexQuotient(FiniteSpace<E>, FiniteSpace<E>) - Constructor for class homology.f2homology.F2OrderComplexQuotient
Creates the quotient complex of space1 and space2 if space1 is specially submersed in space2
F2Vector<K> - Class in homology.f2homology
This class represents a vector over the field F2 of two elements.
F2Vector() - Constructor for class homology.f2homology.F2Vector
Creates a new empty F2Vector.
F2Vector(Map<K, F2>) - Constructor for class homology.f2homology.F2Vector
Creates an F2Vector from a Map to F2.
fatPoints() - Method in class topology.FiniteSpace
Returns the set of fat points of this finite topological space.
FiniteSpace<E extends java.lang.Comparable<E>> - Class in topology
Implements the mathematical object named Finite Topological Space.
FiniteSpace() - Constructor for class topology.FiniteSpace
Creates an empty space.
FiniteSpace(Set<E>, BinaryRelation<E>) - Constructor for class topology.FiniteSpace
Creates a space with given point set and binary relation.
FiniteSpace(FiniteSpace<E>) - Constructor for class topology.FiniteSpace
Creates a new finite topological space from a given finite space.

G

getBoundaryOperator() - Method in class homology.f2homology.F2ChainComplex
Returns the boundary operator of this chain complex.
getComponentList() - Method in class topology.PrimMST
Returns a list of connected components.
getComponentSetList() - Method in class topology.PrimMST
Returns a list of the point sets underlying the connected components of the space.
getCore() - Method in class homology.Betti
Returns the core of this space.
getDimension() - Method in class homology.f2homology.F2ChainComplex
Returns the length of this chain complex.
getF2ChainComplex() - Method in class homology.f2homology.F2OrderComplexQuotient
Returns the quotient complex over the finite field F2.
getGeneratingSystem() - Method in class homology.f2homology.F2Module
Returns the generating system of this F2Module.
getKey() - Method in class topology.ComparablePair
Returns the key (= first element) of a ComparablePair.
getKey() - Method in interface topology.Pair
 
getMatrix() - Method in class homology.f2homology.F2Module
Returns the F2Matrix associated with the generating system of this F2Module.
getMaximalChains() - Method in class homology.OrderComplex
Returns the set of maximal chains as a set of linked lists.
getMst() - Method in class topology.PrimMST
Returns the spanning forest as a finite space.
getMstRelation() - Method in class topology.PrimMST
Returns the binary relation defining the spanning forest.
getNumber() - Method in class homology.f2homology.F2
Returns an integer number corresponding to this element modulo 2.
getPairs() - Method in class topology.BinaryRelation
Returns the pairs of this BinaryRelation.
getPointSet() - Method in class topology.FiniteSpace
Returns the point set underlying the topological space.
getPointSet() - Method in interface topology.TopologicalSpace
Returns the point set underlying the topological space.
getPreOrder() - Method in class topology.FiniteSpace
Returns the reflexive and transitive closure of the topology-defining relation.
getRank() - Method in class homology.f2homology.F2Module
Returns the rank of the module.
getRelation() - Method in class topology.FiniteSpace
Returns the topology-defining relation.
getRelation() - Method in interface topology.TopologicalSpace
Returns the relation which defines the topology.
getSpace() - Method in class homology.Betti
Returns this space.
getValue() - Method in class topology.ComparablePair
Returns the value (= second element) of a ComparablePair.
getValue() - Method in interface topology.Pair
 

H

HasseDiagram() - Method in class topology.FiniteSpace
Returns the Hasse diagram of the Kolmogorov quotient of this finite topological space.
homologicalDimension() - Method in class homology.f2homology.F2ChainComplex
Returns the homological dimension of the chain complex.
homology - package homology
 
homology.f2homology - package homology.f2homology
 

I

imageBasis() - Method in class homology.f2homology.F2Matrix
Returns a basis of F2Vectors for the image of this F2Matrix.
imageBasisListOfArray() - Method in class homology.f2homology.F2Matrix
Returns a basis of the image of this F2Matrix as a list of arrays.
indexMap() - Method in class homology.OrderComplex
Returns a bijective map between the set of all simplices and a set of integers.
inLink(E) - Method in class topology.BinaryRelation
Returns all elements in this BinaryRelation to a given element.
InvalidOperationException - Exception in homology.f2homology
This class provides a run-time exception that gets thrown whenever an invalid operation is attempted.
InvalidOperationException(String) - Constructor for exception homology.f2homology.InvalidOperationException
 
inverseMap() - Method in class homology.OrderComplex
 
isAntiSymmetric() - Method in class topology.BinaryRelation
Returns true if BinaryRelation is anti-symmetric.
isDownBeatPoint(FiniteSpace<E>, E) - Static method in class topology.PointReductions
Returns true if the given point is a down beat point of the Kolmogorov quotient of a given finite topological space.
isDownWeakPoint(FiniteSpace<E>, E) - Static method in class topology.PointReductions
Returns true if the given point is a down weak point of the Kolmogorov quotient of a given finite topological space.
isSpecialSubmersion() - Method in class homology.f2homology.F2OrderComplexQuotient
Returns true iff there is a special submersion from space1 into space2.
isTzero() - Method in class topology.FiniteSpace
Returns true iff pre-order is antisymmetric.
isTzero() - Method in interface topology.TopologicalSpace
Returns true if the space is T0-separable.
isUpBeatPoint(FiniteSpace<E>, E) - Static method in class topology.PointReductions
Returns true if the given point is an up beat point of the Kolmogorov quotient of a given finite topological space.
isUpWeakPoint(FiniteSpace<E>, E) - Static method in class topology.PointReductions
Returns true if the given point is an up weak point of the Kolmogorov quotient of a given finite topological space.

K

kernelBasis() - Method in class homology.f2homology.F2Matrix
Returns a basis for the kernel of this F2Matrix as a list of F2Vectors.
kernelBasisListOfArray() - Method in class homology.f2homology.F2Matrix
Returns a basis for the kernel of this F2Matrix as a list of arrays over F2.
KolmogorovQuotient() - Method in class topology.FiniteSpace
Returns the Kolmogorov Quotient of this finite topological space by removing points.
KOpenPoints() - Method in class topology.FiniteSpace
Returns the set of maximal elements of the Kolmogorov quotient of a finite topological space.
KVertices() - Method in class topology.FiniteSpace
Returns the set of minimal elements of the Kolmogorov quotient of this finite topological space.

L

length() - Method in class homology.f2homology.F2Vector
Returns the length of this F2Vector.
ListComparator<E extends java.lang.Comparable<E>> - Class in topology
This class provides for a comparator of lists.
ListComparator() - Constructor for class topology.ListComparator
 
listOfSimplexSets() - Method in class homology.f2homology.F2OrderComplexQuotient
Returns the list of simplex sets.
listOfSimplexSets() - Method in class homology.OrderComplex
Returns a list of sets of simplex indices.

M

maximalSimplices() - Method in class homology.OrderComplex
Returns the set of maximal simplices as a set of sets.
multiply(F2) - Method in class homology.f2homology.F2
Returns the product of this element and another one.
mySpace() - Static method in class topology.TopologyExamples
Returns my space.

N

neighbourhood(E) - Method in class topology.FiniteSpace
Returns the minimal open neighbourhood of a point in this finite topological space.
noBeatPoint(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns true if the Kolmogorov quotient of a finite topological space has no beat point.
nonHausdorffJoin(FiniteSpace<Integer>, FiniteSpace<Integer>) - Static method in class topology.TopoCollection
Returns the non-Hausdorff join of two finite topological spaces of Integer type.
noWeakPoint(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns true if the Kolmogorov quotient of a finite topological space has no weak point.

O

orderComplex() - Method in class homology.Betti
Returns the order complex of the core of this space.
OrderComplex<K extends java.lang.Comparable<K>> - Class in homology
This class represents the order complex associated to a finite topological space.
OrderComplex() - Constructor for class homology.OrderComplex
Constructs a new empty order complex.
OrderComplex(FiniteSpace<K>) - Constructor for class homology.OrderComplex
Constructs an order complex from a finite topological space.
outLink(E) - Method in class topology.BinaryRelation
Returns all elements to which a given element is in this BinaryRelation with.

P

Pair<K,V> - Interface in topology
Interface for pairs of elements.
pClosure(E) - Method in class topology.FiniteSpace
Returns the punctured closure of a point in this finite topological space.
pNeighbourhood(E) - Method in class topology.FiniteSpace
Returns the punctured minimal open neighbourhood of a point in this finite topological space.
PointReductions - Class in topology
The class PointReductions consists of some point-reduction methods for finite topological spaces which yield weakly homotopy equivalent spaces.
PointReductions() - Constructor for class topology.PointReductions
 
pointSpace(E) - Static method in class topology.TopologyExamples
Returns a parametrised singleton space.
power(BinaryRelation<E>, int) - Static method in class topology.RelationCollection
Returns the n-th power of a binary relation.
PrimMST<E extends java.lang.Comparable<E>> - Class in topology
This class computes a spanning forest for a finite topological space using Prim's algorithm.
PrimMST() - Constructor for class topology.PrimMST
Creates a new PrimMST object.
PrimMST(FiniteSpace<E>) - Constructor for class topology.PrimMST
Creates a spanning forest for the given finite space
product(F2Matrix<L, M>) - Method in class homology.f2homology.F2Matrix
Returns the product AB of this matrix A with another matrix B.
product(BinaryRelation<E>, BinaryRelation<E>) - Static method in class topology.RelationCollection
Returns the product of two binary relations.

R

randomSpace(int) - Static method in class topology.TopologyExamples
Returns a random finite space with n points.
rank() - Method in class homology.f2homology.F2Matrix
Returns the rank of this F2Matrix.
readOffNF() - Method in class homology.f2homology.F2Matrix
Returns the normal form for reading off a basis for the kernel of this F2Matrix.
RelationCollection - Class in topology
The class RelationCollections consists of some methods for BinaryRelations.
RelationCollection() - Constructor for class topology.RelationCollection
 
remove(Pair<E, E>) - Method in class topology.BinaryRelation
Removes a pair from the pairs of this BinaryRelation.
removeAll(Set<Pair<E, E>>) - Method in class topology.BinaryRelation
Removes a set of pairs from the pairs of this BinaryRelation.
removeAllPair(Set<Pair<E, E>>) - Method in class topology.FiniteSpace
Removes a set of pairs from the topology-defining relation.
removeAllPoint(Set<E>) - Method in class topology.FiniteSpace
Removes a set of points and updates the relation.
removeBeatPoints(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns a 0-core of a the Kolmogorov quotient of a finite topological space, i.e.
removePair(Pair<E, E>) - Method in class topology.FiniteSpace
Removes a pair from the topology-defining relation.
removePoint(E) - Method in class topology.FiniteSpace
Removes a point from the point set, and updates the relation.
removeWeakPoints(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns a 1-core of the Kolmogorov quotient of a finite topological space, i.e.
rowEchelon() - Method in class homology.f2homology.F2Matrix
Returns a row echelon form of this F2Matrix.
rowEchelonArray() - Method in class homology.f2homology.F2Matrix
Returns an array which is a row echelon form of this F2Matrix.
rowList() - Method in class homology.f2homology.F2Matrix
Returns a list of row indices of this F2Matrix.
rows() - Method in class homology.f2homology.F2Matrix
Returns the row set of this F2Matrix.

S

simplices() - Method in class homology.OrderComplex
Returns the set of all simplices as a set of sets.
someSpace() - Static method in class topology.TopologyExamples
Returns some space.
spanningTreeList() - Method in class topology.PrimMST
Returns a list of trees making up the spanning forest.

T

T0Space() - Method in class topology.FiniteSpace
Returns the Kolmogorov quotient of this finite topological space, where the relation is the Hasse diagram.
toArray() - Method in class homology.f2homology.F2Matrix
Returns the array associated with this F2Matrix.
toArray() - Method in class homology.f2homology.F2Vector
Returns the array associated with this F2Vector.
TopoCollection - Class in topology
The class TopoCollection consists of some methods for finite topological spaces.
TopoCollection() - Constructor for class topology.TopoCollection
 
TopologicalSpace<E> - Interface in topology
This interface models finite topological spaces.
topology - package topology
 
TopologyExamples - Class in topology
Some examples of finite topological spaces.
TopologyExamples() - Constructor for class topology.TopologyExamples
 
toString() - Method in class homology.f2homology.F2
Returns a String representation of this element.
toString() - Method in class topology.ComparablePair
Returns a string representation of this ComparablePair.
transitiveClosure(BinaryRelation<E>) - Static method in class topology.RelationCollection
Returns the transitive closure of a relation.
TreeSetComparator<E extends java.lang.Comparable<E>> - Class in topology
This class provides for a comparator of TreeSets.
TreeSetComparator() - Constructor for class topology.TreeSetComparator
 
twoSphere() - Static method in class topology.TopologyExamples
Returns a 2-sphere.

U

upBeatPoints(FiniteSpace<E>) - Static method in class topology.PointReductions
Returns the set of up beat points of the Kolmogorov quotient of a finite topological space.
upperTriangArray() - Method in class homology.f2homology.F2Matrix
Returns an upper triangular array by partial Gaussian elimination of this F2Matrix.
upperTriangular() - Method in class homology.f2homology.F2Matrix
Returns an upper triangular matrix by partial Gaussian elimination of this F2Matrix.

W

wallet() - Static method in class topology.TopologyExamples
Returns the wallet.

Y

yas() - Static method in class topology.TopologyExamples
Returns yet another finite space.
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