net.sf.oriented.omi

Interface Summary
Interface	Description
Chirotope	The base interface for implementing new chirotope sources.
ChirotopeFactory	Create Oriented Matroids from their Chirotope.
Face	A face in a `FaceLattice`
FaceLattice	The face lattice corresponding to an oriented matroid.
Factory<T>	Provides conversion to and from String for some class.
FullChirotope	A true chirotope with an alternating map.
JavaSet<X>	This interface adds nothing to the java.util.Set interface, but is used in preference, to clarify the distinction with the more mathematically pure set interfaces.
Label	The base items in sets and signed sets are these, which essentially correspond to Strings.
LabelFactory	A factory for producing labels, which are used as the points or elements on which our oriented matroids and matroids are defined.
Matroid	A minimal matroid interface, not intended as a useful part of this library.
MatroidAsSet	View a matroid also as a set.
MatroidFactory	Convert a set of sets of elements into a matroid.
OM	An Oriented Matroid.
OMasChirotope	The chirotope view of an oriented matroid.
OMasFaceLattice	The face lattice view of an oriented matroid.
OMasRealized	For an oriented matroid which was produced, or whose dual was produced, from a rational matrix, retrieve that view.
OMasSignedSet	An oriented matroid viewed as a set of signed sets: a set of circuits, a set of vectors, or a set of maximum vectors.
OMSFactory	An interface for producing oriented matroids from sets of signed sets (cicruits, vectors, maximum vectors).
RealizedFactory	An interface for producing oriented matroids from rational matrixes which realize them.
SetFactory<ITEM,SET>	Provides conversion to and from String for some Set class.
SetOf<ITEM,SET extends SetOf<ITEM,SET>>	Immutable mathematical sets.
SetOfSignedSet	Mathematical sets of signed sets, as defined in Oriented Matroid literature.
SetOfUnsignedSet	Mathematical sets `SetOf` of mathematical sets `SetOf` of `Label`s.
SignedSet	A signed set is defined by disjoint positive `SignedSet.plus()` and negative `SignedSet.minus()` components, both of which are `UnsignedSet`s.
SignedSetFactory	A factory for producing signed sets.
UnsignedSet	This class represents mathematical sets of `Label`s which are the base elements in our universe of discourse.
Verify	This interface is implemented by classes which represent mathematical concepts that have certain axioms, and/or by java classes that have invariants.

Class Summary
Class	Description
Alternating	Implements an alternating function over a non-alternating one.
Bibliography	A somewhat disorganized list of references from the literature.
Examples	Here are some 'interesting' oriented matroids.
FactoryFactory	This class generates `Factory`'s and `SetFactory`'s for the interfaces in the API.
Options	Provide the options for String representations.

Enum Summary
Enum Description

Face.Type
The types of faces in a FaceLattice

Options.Impl
The choices of underlying implementation.
Exception Summary
Exception Description

AxiomViolation
An object does not satisfy its invariants and/or axioms.

Enum Summary
Enum	Description
Face.Type	The types of faces in a `FaceLattice`
Options.Impl	The choices of underlying implementation.

Exception Summary
Exception	Description
AxiomViolation	An object does not satisfy its invariants and/or axioms.

Package net.sf.oriented.omi Description

This package is the public interface, with OM as the key interface defining oriented matroids.

Use Options and FactoryFactory to get started. There is support for: mathematical sets SetOf, UnsignedSet; signed sets SignedSet, and sets of such sets SetOfSignedSet, SetOfUnsignedSet, SetOf.powerSet(),SetOf.subsetsOfSize(int).

Oriented Matroids can be viewed as circuits, vectors or maximum vectors via the OMasSignedSet interface, or as chirotopes via the OMasChirotope interface. The OM.dual() method gives the cocircuits, covectors and topes. Oriented Matroids can be entered as matrixes, in which ase the OMasRealized interface applies.