- 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.
- 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.
- 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
-
- 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.
- 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.