A B C D E F G H I J L M N O P Q R S T U V W Π Ω

A

add(PerisicFieldElement) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

agarwalAndSharir2002 - Static variable in class net.sf.oriented.omi.Bibliography

[Agarwal and Sharir, 2002] Agarwal, P.

all() - Static method in class net.sf.oriented.omi.Examples

all(int) - Static method in class net.sf.oriented.util.combinatorics.Permutation

Return all permutations of the sequence ( 0, 1, ...

Alternating - Class in net.sf.oriented.omi

Implements an alternating function over a non-alternating one.

Alternating(Chirotope) - Constructor for class net.sf.oriented.omi.Alternating

We pass in a map that is not necessarily alternating, and we get back one that is.

and(Permutation) - Method in class net.sf.oriented.util.combinatorics.Permutation

Permutation composition

asCollection() - Method in interface net.sf.oriented.omi.SetOf

asDrawing() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

Prepare to draw this arrangement of pseudolines.

asInt(Label) - Method in interface net.sf.oriented.omi.OM

The integer corresponding to this element (counting from 0).

asInt(String) - Method in interface net.sf.oriented.omi.OM

The integer corresponding to this element (counting from 0).

asInt(T...) - Method in interface net.sf.oriented.omi.OM

The integers corresponding to these elements (counting from 0).

asInt(UnsignedSet) - Method in interface net.sf.oriented.omi.OM

Gets the indexes of each element in u

asSet(int...) - Method in interface net.sf.oriented.omi.OM

Concerts integer indices of OM.elements() into an UnsignedSet.

automorphisms() - Method in interface net.sf.oriented.omi.Matroid

The automorphism group for this matroid.

automorphisms() - Method in interface net.sf.oriented.omi.OM

The automorphism group of this oriented matroid.

AxiomViolation - Exception in net.sf.oriented.omi

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

AxiomViolation(Object, String) - Constructor for exception net.sf.oriented.omi.AxiomViolation

Construct a new AxiomViolation.

B

background - Variable in class net.sf.oriented.pseudoline.ImageOptions

The color of the background to the rectangle, outside the picture

bases() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for matroids from bases.

Bibliography - Class in net.sf.oriented.omi

A somewhat disorganized list of references from the literature.

björnerEtAl1999 - Static variable in class net.sf.oriented.omi.Bibliography

[Björner et al., 1999] Björner, A., Las Vergnas, M., Sturmfels, B., White, N., and Ziegler, G.

border - Variable in class net.sf.oriented.pseudoline.ImageOptions

The width of the border in which line labels are shown.

bottom() - Method in interface net.sf.oriented.omi.FaceLattice

The bottom face of the lattice, labelled with the empty signed set.

C

carroll2000a - Static variable in class net.sf.oriented.omi.Bibliography

[Carroll, 2000a] Carroll, J.

carroll2000b - Static variable in class net.sf.oriented.omi.Bibliography

[Carroll, 2000b] — (2000b).

carroll2000c - Static variable in class net.sf.oriented.omi.Bibliography

[Carroll, 2000c] — (2000c).

carroll2000d - Static variable in class net.sf.oriented.omi.Bibliography

[Carroll, 2000d] — (2000d).

carroll2006 - Static variable in class net.sf.oriented.omi.Bibliography

[Carroll, 2006] — (2006).

carver1922 - Static variable in class net.sf.oriented.omi.Bibliography

[Carver, 1922] Carver, W.

ceva() - Static method in class net.sf.oriented.omi.Examples

An oriented matroid representing Ceva's theorem.

ceva1678 - Static variable in class net.sf.oriented.omi.Bibliography

[Ceva, 1678] Ceva, G.

chapter1() - Static method in class net.sf.oriented.omi.Examples

This is from the Oriented Matroid book Bibliography.björnerEtAl1999

chi(int...) - Method in class net.sf.oriented.omi.Alternating

chi(int...) - Method in interface net.sf.oriented.omi.Chirotope

This is only called when it has Chirotope.rank() arguments, and they are strictly monotonic increasing.

chi(int...) - Method in interface net.sf.oriented.omi.FullChirotope

The alternating map.

Chirotope - Interface in net.sf.oriented.omi

The base interface for implementing new chirotope sources.

chirotope() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for oriented matroids which uses the chirotope representation.

ChirotopeFactory - Interface in net.sf.oriented.omi

Create Oriented Matroids from their Chirotope.

circuits() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for oriented matroids which uses the circuit representation.

circularsaw3() - Static method in class net.sf.oriented.omi.Examples

The oriented matroid corresponding to the circular saw diagram of size three.

CoLexicographic - Class in net.sf.oriented.util.combinatorics

Iterate over colexicographic orderings of integers.

CoLexicographic(int, int) - Constructor for class net.sf.oriented.util.combinatorics.CoLexicographic

Construct a colexicographic ordering or r items chosen from 0 through n − 1.

CoLoopCannotBeDrawnException - Exception in net.sf.oriented.pseudoline

The representation of rank 3 oriented matroids as pseudoline drawings in the Euclidean plane can only draw co-loops as the line at infinity.

compose(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

Signed set composition.

conformsWith(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

Does this conform with x? i.e.

construct(Chirotope) - Method in interface net.sf.oriented.omi.ChirotopeFactory

Create an oriented matroid from a chirotope provided programmatically.

construct(Collection<? extends Label>, Chirotope) - Method in interface net.sf.oriented.omi.ChirotopeFactory

Create an oriented matroid from a chirotope provided programmatically, with given element labels.

construct(RationalMatrix) - Method in interface net.sf.oriented.omi.RealizedFactory

Construct an oriented matroid from a matrix, using default labels for the elements.

construct(Collection<? extends Label>, RationalMatrix) - Method in interface net.sf.oriented.omi.RealizedFactory

Construct an oriented matroid from a matrix, using given labels for the elements.

construct(UnsignedSet, UnsignedSet) - Method in interface net.sf.oriented.omi.SignedSetFactory

Build a signed set from two disjoint unsigned sets.

contains(ITEM) - Method in interface net.sf.oriented.omi.SetOf

copyBackingCollection(Iterable<? extends ITEM>) - Method in interface net.sf.oriented.omi.SetFactory

Create an immutable new set by copying a Java collection as the backing collection.

covector() - Method in interface net.sf.oriented.omi.Face

The covector labeling the face in the lattice (null for the Face.Type.Top element)

coxeter1995 - Static variable in class net.sf.oriented.omi.Bibliography

[Coxeter, 1995] Coxeter, H.

create(int) - Method in class net.sf.oriented.util.matrix.PerisicField

Map an integer into this field.

D

defaultBlackAndWhite() - Static method in class net.sf.oriented.pseudoline.ImageOptions

Get image options that generate a black and white image.

defaultColor() - Static method in class net.sf.oriented.pseudoline.ImageOptions

Get image options that generate a color image.

determinantFromColumns(int[]) - Method in class net.sf.oriented.util.matrix.RationalMatrix

Computes the determinant on the sub-matrix formed by the specified columns

dimension() - Method in interface net.sf.oriented.omi.Face

The dimension of this face, -1 for Face.Type.Bottom, 0 for points, etc.

divide(PerisicFieldElement) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

dual() - Method in interface net.sf.oriented.omi.Matroid

The dual of the matroid.

dual() - Method in interface net.sf.oriented.omi.OM

The dual oriented matroid.

E

elements() - Method in interface net.sf.oriented.omi.Matroid

The elements on which this matroid is defined.

elements() - Method in interface net.sf.oriented.omi.OM

The elements on which this oriented matroid is defined.

empty() - Method in interface net.sf.oriented.omi.MatroidFactory

This does not, and will not, work.

empty() - Method in interface net.sf.oriented.omi.OMSFactory

This does not, and will not, work.

empty() - Method in interface net.sf.oriented.omi.SetFactory

The (immutable) empty set.

emptyCollectionOf() - Method in interface net.sf.oriented.omi.Factory

A suggested Java Collection for gathering up some such items.

equals(Object) - Method in interface net.sf.oriented.omi.OM

An Oriented Matroid is equal to any other object implementing this interface, which represents the same underlying oriented matroid, including the OM.elements() being equal.

equals(Object) - Method in class net.sf.oriented.util.combinatorics.Permutation

equals(Object) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

equalsIgnoreSign(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

Either s is equal to this, or to the opposite of this.

equalsIsSameSetAs() - Method in interface net.sf.oriented.omi.SetOf

This indicates whether in the implementing class the notion of equality is set equality or not.

equalsOpposite(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

This is a short hand for s.equals(opposite()).

euclidC300BC - Static variable in class net.sf.oriented.omi.Bibliography

[Euclid, c300BC] Euclid (c300BC).

EuclideanPseudoLines - Class in net.sf.oriented.pseudoline

This class takes a rank 3 oriented matroid and prepares it for processing from a Euclidean perspective.

EuclideanPseudoLines(OM, String, String...) - Constructor for class net.sf.oriented.pseudoline.EuclideanPseudoLines

Prepare the given oriented matroid for Euclidean processing, with the given line at infinity, and a hint, which may or may not be followed, concerning which lines to re-orient.

EuclideanPseudoLines(OM, Label) - Constructor for class net.sf.oriented.pseudoline.EuclideanPseudoLines

Prepare the given oriented matroid for Euclidean processing, with the given line at infinity.

Examples - Class in net.sf.oriented.omi

Here are some 'interesting' oriented matroids.

Examples() - Constructor for class net.sf.oriented.omi.Examples

F

Face - Interface in net.sf.oriented.omi

A face in a FaceLattice

Face.Type - Enum in net.sf.oriented.omi

The types of faces in a FaceLattice

FaceLattice - Interface in net.sf.oriented.omi

The face lattice corresponding to an oriented matroid.

Factory<T> - Interface in net.sf.oriented.omi

Provides conversion to and from String for some class.

FactoryFactory - Class in net.sf.oriented.omi

This class generates Factory's and SetFactory's for the interfaces in the API.

FactoryFactory() - Constructor for class net.sf.oriented.omi.FactoryFactory

A new FactoryFactory with default options.

FactoryFactory(Options) - Constructor for class net.sf.oriented.omi.FactoryFactory

A new FactoryFactory with given Options.

felsner1997 - Static variable in class net.sf.oriented.omi.Bibliography

[Felsner, 1997] Felsner, S.

felsnerAndKriegel1999 - Static variable in class net.sf.oriented.omi.Bibliography

[Felsner and Kriegel, 1999] Felsner, S.

felsnerAndWeil1999 - Static variable in class net.sf.oriented.omi.Bibliography

[Felsner and Weil, 1999] Felsner, S.

felsnerAndZiegler2001 - Static variable in class net.sf.oriented.omi.Bibliography

[Felsner and Ziegler, 2001] Felsner, S.

ffactory() - Method in interface net.sf.oriented.omi.OM

The factory for making this oriented matroid and its various parts.

fill - Variable in class net.sf.oriented.pseudoline.ImageOptions

The color of the faces inside the picture

filter(Predicate<Permutation>) - Method in class net.sf.oriented.util.combinatorics.Group

Create a subgroup by accepting some of the elements in the group.

finschi2001 - Static variable in class net.sf.oriented.omi.Bibliography

[Finschi, 2001]

folkmanAndLawrence1978 - Static variable in class net.sf.oriented.omi.Bibliography

[Folkman and Lawrence, 1978] Folkman, J.

fontSizeRatio - Variable in class net.sf.oriented.pseudoline.ImageOptions

Any scaling that should be applied to the font size.

foreground - Variable in class net.sf.oriented.pseudoline.ImageOptions

The foregound color that is used for text, vertices, and the origin.

from0toN(int) - Static method in class net.sf.oriented.util.combinatorics.Permutation

fromCircuits(String) - Static method in class net.sf.oriented.omi.FactoryFactory

Given a string representation of a set of circuits create an oriented matroid.

fromCoLexicographic(int, String) - Method in interface net.sf.oriented.omi.ChirotopeFactory

Create an oriented matroid from its colexicographic representation as a series of +, -, 0s.

fromCoLexicographic(int, int, String) - Static method in class net.sf.oriented.omi.FactoryFactory

Gives an oriented matroid corresponding to a chirotope in colexicographic form.

fromCoLexicographic(int, int, String) - Static method in class net.sf.oriented.util.combinatorics.Lexicographic

Convert a colexicographic chirotope string into a lexicographic one

fromCrossings(String...) - Static method in class net.sf.oriented.omi.FactoryFactory

This method is for turning a pseudoline configuration into an oriented matroid.

fromEuclideanLines(int[][]...) - Static method in class net.sf.oriented.omi.FactoryFactory

Generate an OM from lines being specified as a pair of points (integer coordinates).

fromLexicographic(int, String) - Method in interface net.sf.oriented.omi.ChirotopeFactory

Create an oriented matroid from its lexicographic representation as a series of +, -, 0s.

fromLexicographic(int, int, String) - Static method in class net.sf.oriented.omi.FactoryFactory

Gives an oriented matroid corresponding to a chirotope in lexicographic form.

fromLexicographic(int, int, String) - Static method in class net.sf.oriented.util.combinatorics.CoLexicographic

Convert a lexicographic chirotope string into a colexicographic one

fromMatrix(int[][]) - Static method in class net.sf.oriented.omi.FactoryFactory

This method is for turning a simple matrix of integers into an oriented matroid over the columns.

fromMatrix(double, double[][]) - Static method in class net.sf.oriented.omi.FactoryFactory

This method is for turning a simple matrix of doubles into an oriented matroid over the columns.

fromSets(SetOfUnsignedSet) - Method in interface net.sf.oriented.omi.MatroidFactory

fromSignedSets(Label[], SetOfSignedSet) - Method in interface net.sf.oriented.omi.OMSFactory

FullChirotope - Interface in net.sf.oriented.omi

A true chirotope with an alternating map.

G

get(SignedSet) - Method in interface net.sf.oriented.omi.FaceLattice

The face labeled with the given covector.

get(int) - Method in class net.sf.oriented.util.combinatorics.Permutation

The ith slot from the permutation

getBases() - Method in interface net.sf.oriented.omi.Matroid

A view of the matroid as a set of bases.

getBasis() - Method in class net.sf.oriented.util.matrix.GramSchmidt

An orthogonal basis spanning the same space as the original matrix.

getChirotope() - Method in interface net.sf.oriented.omi.OM

Get the chirotope representation of the oriented matroid.

getCircuits() - Method in interface net.sf.oriented.omi.Matroid

A view of the matroid as a set of circuits.

getCircuits() - Method in interface net.sf.oriented.omi.OM

Get the circuit representation of the oriented matroid.

getDelegate() - Method in class net.sf.oriented.util.matrix.RationalMatrix

Access the underlying FieldMatrix

getDual() - Method in class net.sf.oriented.util.matrix.GramSchmidt

Continues the GramSchmidt process to compute a dual basis too.

getEquivalentOM() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

This is the oriented matroid which is actually being processed.

getFaceLattice() - Method in interface net.sf.oriented.omi.OM

Get the face lattice representation of the oriented matroid.

getField() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

getIndependentSets() - Method in interface net.sf.oriented.omi.Matroid

A view of the matroid as a set of independent sets.

getInfinity() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

This is the element at infinity as from the constructor.

getLabel(int) - Method in class net.sf.oriented.omi.Options

Get the ith label from the universe.

getMatrix() - Method in interface net.sf.oriented.omi.OMasRealized

An underlying matrix realizing this oriented matroid.

getMatroid() - Method in interface net.sf.oriented.omi.OM

The underlying matroid.

getMaxVectors() - Method in interface net.sf.oriented.omi.OM

Get the maximum vector representation of the oriented matroid.

getMessage() - Method in exception net.sf.oriented.omi.AxiomViolation

getOne() - Method in class net.sf.oriented.util.matrix.PerisicField

getPermutation() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

The elements of the original oriented matroid are permuted in the equivalent oriented matroid.

getPlusMinus() - Method in class net.sf.oriented.omi.Options

Are we using the +/- form.

getRealized() - Method in interface net.sf.oriented.omi.OM

Get the realized representation of the oriented matroid.

getReorientation() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

This is the set of elements which were reoriented in the processing of this class.

getRuntimeClass() - Method in class net.sf.oriented.util.matrix.PerisicField

getSingleChar() - Method in class net.sf.oriented.omi.Options

Are we using short labels or long labels?

getUniverse() - Method in interface net.sf.oriented.omi.LabelFactory

getUniverse() - Method in class net.sf.oriented.omi.Options

Returns all the known labels.

getVectors() - Method in interface net.sf.oriented.omi.OM

Get the vector representation of the oriented matroid.

getZero() - Method in class net.sf.oriented.util.matrix.PerisicField

gioanAndLasVergnas2004 - Static variable in class net.sf.oriented.omi.Bibliography

[Gioan and Las Vergnas, 2004] Gioan, E.

GramSchmidt<T extends FieldElement<T>> - Class in net.sf.oriented.util.matrix

The Gram–Schmidt process, but without normalizing.

GramSchmidt(FieldMatrix<T>) - Constructor for class net.sf.oriented.util.matrix.GramSchmidt

Initialize the GramSchmidt process over the given matrix.

Group - Class in net.sf.oriented.util.combinatorics

This is the mathematically concept of finite group, however we consider every group as a subgroup of a permutation group, and every group element is a Permutation.

grünbaum1969 - Static variable in class net.sf.oriented.omi.Bibliography

[Grünbaum, 1969] Grünbaum, B.

H

hashCode() - Method in interface net.sf.oriented.omi.OM

The hashCode of an Oriented Matroid is the hashCode of the circuit representation as a SetOfSignedSets.

hashCode() - Method in interface net.sf.oriented.omi.SetOf

Returns the hash code value for this set.

hashCode() - Method in class net.sf.oriented.util.combinatorics.Permutation

hashCode() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

height - Variable in class net.sf.oriented.pseudoline.ImageOptions

The width and height of the intended image.

height() - Method in class net.sf.oriented.util.matrix.RationalMatrix

The height or number of rows of the matrix.

higher() - Method in interface net.sf.oriented.omi.Face

The faces one dimension higher than this face.

I

identity() - Method in class net.sf.oriented.util.combinatorics.Group

The identity element of this group.

identityGroup(int) - Static method in class net.sf.oriented.util.combinatorics.Group

The group consisting of the identity permutation over 0, 1, ....

image() - Method in class net.sf.oriented.pseudoline.PseudoLineDrawing

Returns an image of the oriented matroid with default options.

image(ImageOptions) - Method in class net.sf.oriented.pseudoline.PseudoLineDrawing

Returns an image of the oriented matroid with the specified options.

Image - Class in oriented

Create a pseudoline picture corresponding to one of the example oriented matroids.

ImageOptions - Class in net.sf.oriented.pseudoline

Settings for drawing pseudoline diagrams.

independentSets() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for matroids from independent sets.

index(int...) - Static method in class net.sf.oriented.util.combinatorics.CoLexicographic

In a colexicographic ordering, what position is this index.

index(int, int[]) - Static method in class net.sf.oriented.util.combinatorics.Lexicographic

In a lexicographic ordering, what position is this index.

intersection(SET) - Method in interface net.sf.oriented.omi.SetOf

inverse() - Method in class net.sf.oriented.util.combinatorics.Permutation

The inverse permutation

isAcyclic() - Method in interface net.sf.oriented.omi.OM

This returns true if the oriented matroid contains no positive circuit, or equivalently, every edge is in a positive cocircuit.

isEmpty() - Method in interface net.sf.oriented.omi.SetOf

isRestrictionOf(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

Is this a restriction of x? i.e.

isSubsetOf(SET) - Method in interface net.sf.oriented.omi.SetOf

isSupersetOf(SET) - Method in interface net.sf.oriented.omi.SetOf

isUniform() - Method in interface net.sf.oriented.omi.OM

True if every set of OM.rank() elements is a basis for the underlying matroid.

iterator() - Method in interface net.sf.oriented.omi.FaceLattice

The faces in the lattice.

iterator() - Method in class net.sf.oriented.util.combinatorics.CoLexicographic

iterator() - Method in class net.sf.oriented.util.combinatorics.Lexicographic

J

jaudonAndParlier2006 - Static variable in class net.sf.oriented.omi.Bibliography

[Jaudon and Parlier, 2006] Jaudon, G.

JavaSet<X> - Interface in net.sf.oriented.omi

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.

javaSetFor(Class<T>) - Method in class net.sf.oriented.omi.Options

Not part of the API

L

Label - Interface in net.sf.oriented.omi

The base items in sets and signed sets are these, which essentially correspond to Strings.

label() - Method in interface net.sf.oriented.omi.Label

The corresponding String.

labelBorder - Variable in class net.sf.oriented.pseudoline.ImageOptions

An additional border around labels.

LabelFactory - Interface in net.sf.oriented.omi

A factory for producing labels, which are used as the points or elements on which our oriented matroids and matroids are defined.

labelPosition - Variable in class net.sf.oriented.pseudoline.ImageOptions

The position of the labels within the border.

labels() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for labels.

lasVergnas1986 - Static variable in class net.sf.oriented.omi.Bibliography

[Las Vergnas, 1986] Las Vergnas, M.

lawrence1983 - Static variable in class net.sf.oriented.omi.Bibliography

[Lawrence, 1983] Lawrence, J.

levi1926 - Static variable in class net.sf.oriented.omi.Bibliography

[Levi, 1926] Levi, F.

Lexicographic - Class in net.sf.oriented.util.combinatorics

Iterate over lexicographic orderings of integers.

Lexicographic(int, int) - Constructor for class net.sf.oriented.util.combinatorics.Lexicographic

Construct a lexicographic ordering or r items chosen from 0 through n − 1.

lineWidth - Variable in class net.sf.oriented.pseudoline.ImageOptions

The width of lines in the diagram.

lower() - Method in interface net.sf.oriented.omi.Face

The faces one dimension lower than this face.

M

main(String[]) - Static method in class net.sf.oriented.util.combinatorics.CoLexicographic

simple test code

main(String[]) - Static method in class net.sf.oriented.util.combinatorics.Lexicographic

simple test code

main(String[]) - Static method in class net.sf.oriented.util.combinatorics.Permutation

simple test

main(String[]) - Static method in class oriented.Image

main(String[]) - Static method in class oriented.MathOverflow129698

main(String[]) - Static method in class oriented.WebPage

map(String) - Method in class net.sf.oriented.util.matrix.PerisicField

Parse some string, and map it into this field

mapAll(int...) - Method in class net.sf.oriented.util.combinatorics.Permutation

For each of the arguments, which must be between 0 and Permutation.n() map it to the new value under this permutation.

MathOverflow129698 - Class in oriented

Run the main method to get some of the workings of my answer to the Realizability of extensions of a free oriented matroid by an independent set

Matroid - Interface in net.sf.oriented.omi

A minimal matroid interface, not intended as a useful part of this library.

MatroidAsSet - Interface in net.sf.oriented.omi

View a matroid also as a set.

MatroidFactory - Interface in net.sf.oriented.omi

Convert a set of sets of elements into a matroid.

maxVectors() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for oriented matroids which uses the maximum vector (co-tope) representation.

minus(SET) - Method in interface net.sf.oriented.omi.SetOf

minus(ITEM) - Method in interface net.sf.oriented.omi.SetOf

minus() - Method in interface net.sf.oriented.omi.SignedSet

The negative component.

mnev1988 - Static variable in class net.sf.oriented.omi.Bibliography

[Mnev, 1988] Mnev, N.

motzkin1933 - Static variable in class net.sf.oriented.omi.Bibliography

[Motzkin, 1933] Motzkin, T.

motzkin1983 - Static variable in class net.sf.oriented.omi.Bibliography

[Motzkin, 1983] Motzkin, T.

multiply(int) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

multiply(PerisicFieldElement) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

mutate(int, Label...) - Method in interface net.sf.oriented.omi.OMasChirotope

Produce a new oriented matroid by setting the value of the chirotope on the given basis to i This method does not check that the mutation is legal.

mutate(int, int...) - Method in interface net.sf.oriented.omi.OMasChirotope

Produce a new oriented matroid by setting the value of the chirotope on the given basis to i This method does not check that the mutation is legal.

N

n() - Method in class net.sf.oriented.omi.Alternating

n() - Method in interface net.sf.oriented.omi.Chirotope

The number of elements on which this Chirotope is defined

n() - Method in interface net.sf.oriented.omi.OM

The size of OM.elements()

n() - Method in class net.sf.oriented.util.combinatorics.Group

The permutations in this group permute the numbers 0, 1, ....

n() - Method in class net.sf.oriented.util.combinatorics.Permutation

The number of items being permuted by this permutation.

negate() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

net.sf.oriented.omi - package net.sf.oriented.omi

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

net.sf.oriented.pseudoline - package net.sf.oriented.pseudoline

This package is for representing rank 3 oriented matroids as pseudoline drawings, particularly in the Euclidean plane.

net.sf.oriented.util.combinatorics - package net.sf.oriented.util.combinatorics

A few additional combinatoric related classes and functions needed for this library.

net.sf.oriented.util.matrix - package net.sf.oriented.util.matrix

Minimal extension over the Apache Commons Math Library required for this library.

NotRank3Exception - Exception in net.sf.oriented.pseudoline

An algorithm that only applies to rank 3 oriented matroids was applied to an oriented matroid of a different rank.

O

OM - Interface in net.sf.oriented.omi

An Oriented Matroid.

OMasChirotope - Interface in net.sf.oriented.omi

The chirotope view of an oriented matroid.

OMasFaceLattice - Interface in net.sf.oriented.omi

The face lattice view of an oriented matroid.

OMasRealized - Interface in net.sf.oriented.omi

For an oriented matroid which was produced, or whose dual was produced, from a rational matrix, retrieve that view.

OMasSignedSet - Interface in net.sf.oriented.omi

An oriented matroid viewed as a set of signed sets: a set of circuits, a set of vectors, or a set of maximum vectors.

omega14(int) - Static method in class net.sf.oriented.omi.Examples

Richter-Gebert's interesting oriented matroids.

OMSFactory - Interface in net.sf.oriented.omi

An interface for producing oriented matroids from sets of signed sets (cicruits, vectors, maximum vectors).

opposite() - Method in interface net.sf.oriented.omi.SignedSet

Swaps the positive and negative components

options() - Method in class net.sf.oriented.omi.FactoryFactory

The options used by this factory.

Options - Class in net.sf.oriented.omi

Provide the options for String representations.

Options() - Constructor for class net.sf.oriented.omi.Options

Default options (32 bit implementation).

Options(Options.Impl) - Constructor for class net.sf.oriented.omi.Options

Allows using the non-default implementation.

Options.Impl - Enum in net.sf.oriented.omi

The choices of underlying implementation.

order() - Method in class net.sf.oriented.util.combinatorics.Group

The number of elements in this group.

oriented - package oriented

Command line tools.

originArrowLength - Variable in class net.sf.oriented.pseudoline.ImageOptions

The length of the arrow used to show the origin.

originArrowSize - Variable in class net.sf.oriented.pseudoline.ImageOptions

The size of the arrowhead used to show the origin.

P

pappus() - Static method in class net.sf.oriented.omi.Examples

The oriented matroid corresponding to the arrangement in Pappus's theorm

parse(String) - Method in interface net.sf.oriented.omi.Factory

Create a new T.

parse(String...) - Method in interface net.sf.oriented.omi.Factory

PerisicField - Class in net.sf.oriented.util.matrix

Combine the perisic library with the apache commons math library.

PerisicFieldElement - Class in net.sf.oriented.util.matrix

Implements the FieldElement interface, for PerisicField

Permutation - Class in net.sf.oriented.util.combinatorics

A permutation of integers

Permutation(int...) - Constructor for class net.sf.oriented.util.combinatorics.Permutation

Create a new permutations which maps i to map[i] for each i.

Permutation(int, int[][]) - Constructor for class net.sf.oriented.util.combinatorics.Permutation

Use the notation (0 1) (4 5 6)to represent the permutation (1 0 2 3 5 6 4)

permute(Permutation) - Method in interface net.sf.oriented.omi.OM

Permute the Oriented Matroid, the ground set is not permuted.

permute(T...) - Method in class net.sf.oriented.util.combinatorics.Permutation

This method returns the permuted arguments, which must be of number Permutation.n()

permuteGround(Permutation) - Method in interface net.sf.oriented.omi.OM

Permute the ground set.

plus() - Method in interface net.sf.oriented.omi.SignedSet

The positive component.

plücker1835 - Static variable in class net.sf.oriented.omi.Bibliography

[Plücker, 1835] Plücker, J.

Polynomials - Static variable in class net.sf.oriented.util.matrix.PerisicField

A universal polynomial field over the rationals.

powerSet() - Method in interface net.sf.oriented.omi.SetOf

PseudoLineDrawing - Class in net.sf.oriented.pseudoline

This class is for generating images of pseudolines as Euclidean pictures of the projective plane.

Q

Q - Static variable in class net.sf.oriented.util.matrix.PerisicField

Imports the rationals.

QPolynomials - Static variable in class net.sf.oriented.util.matrix.PerisicField

A universal polynomial field, with quotient polynomials over the rationals.

R

rank() - Method in class net.sf.oriented.omi.Alternating

rank() - Method in interface net.sf.oriented.omi.Chirotope

Must be a positive integer, which is constant for each object implementing this interface.

rank() - Method in interface net.sf.oriented.omi.Matroid

The rank of the matroid.

rank() - Method in interface net.sf.oriented.omi.OM

The rank of this oriented matroid.

rational(String) - Static method in class net.sf.oriented.util.matrix.PerisicField

Parse some string as a rational, and map it into this field

RationalMatrix - Class in net.sf.oriented.util.matrix

A class implementing matrixes of rationals via FieldMatrix and PerisicField.

RationalMatrix(int[][]) - Constructor for class net.sf.oriented.util.matrix.RationalMatrix

Initialize a matrix from integers.

RationalMatrix(FieldMatrix<PerisicFieldElement>) - Constructor for class net.sf.oriented.util.matrix.RationalMatrix

Wraps a delegate.

RationalMatrix(List<List<PerisicFieldElement>>) - Constructor for class net.sf.oriented.util.matrix.RationalMatrix

Initialize a matrix from lists of lists of PerisicFieldElement.

realized() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for oriented matroids which uses a realization of the OM as the representation.

RealizedFactory - Interface in net.sf.oriented.omi

An interface for producing oriented matroids from rational matrixes which realize them.

reciprocal() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

remake(T) - Method in interface net.sf.oriented.omi.Factory

reorient(Label...) - Method in interface net.sf.oriented.omi.OM

Reorients (i.e.

respectingEquals() - Method in interface net.sf.oriented.omi.SetOf

Return a set s such that: s.sameSetSetAs(this) && s.equalsIsSameSetAs().

restriction(UnsignedSet) - Method in interface net.sf.oriented.omi.SignedSet

The restriction of this to x.

richterGebert1996 - Static variable in class net.sf.oriented.omi.Bibliography

[Richter-Gebert, 1996] Richter-Gebert, J.

richterGebertAndSturmfels1991 - Static variable in class net.sf.oriented.omi.Bibliography

[Richter-Gebert and Sturmfels, 1991] Richter-Gebert, J.

ringel() - Static method in class net.sf.oriented.omi.Examples

The oriented matroid corresponding to Ringel's uniform non-realizable, non-Pappus configuration.

ringel1956 - Static variable in class net.sf.oriented.omi.Bibliography

[Ringel, 1956] Ringel, G.

S

sameSetAs(SET) - Method in interface net.sf.oriented.omi.SetOf

This is mathematically set equality, except for empty sets - which respect type as well.

sendov1995 - Static variable in class net.sf.oriented.omi.Bibliography

[Sendov, 1995] Sendov, B.

separation(SignedSet) - Method in interface net.sf.oriented.omi.SignedSet

The set of elements that have different sign in this and b.

setColor(Label, Color) - Method in class net.sf.oriented.pseudoline.ImageOptions

Provides the color for a line.

setColorOfInfinity(Color) - Method in class net.sf.oriented.pseudoline.ImageOptions

Provides the color for the line at infinity, if null then the color is chosen like any other line.

SetFactory<ITEM,SET> - Interface in net.sf.oriented.omi

Provides conversion to and from String for some Set class.

setLongLabels() - Method in class net.sf.oriented.omi.Options

Some of the Label's used may consist of more than one character.

SetOf<ITEM,SET extends SetOf<ITEM,SET>> - Interface in net.sf.oriented.omi

Immutable mathematical sets.

setOfElements() - Method in interface net.sf.oriented.omi.Matroid

This is the same as Matroid.elements(), except it is unordered.

setOfElements() - Method in interface net.sf.oriented.omi.OM

This is the same as OM.elements(), except it is unordered.

setOfElements() - Method in interface net.sf.oriented.omi.SetOfSignedSet

This is the union over this set of the support of each member.

SetOfSignedSet - Interface in net.sf.oriented.omi

Mathematical sets of signed sets, as defined in Oriented Matroid literature.

SetOfUnsignedSet - Interface in net.sf.oriented.omi

Mathematical sets SetOf of mathematical sets SetOf of Labels.

setPlusMinus(boolean) - Method in class net.sf.oriented.omi.Options

Use 0 + - as the representation.

setShortLabels() - Method in class net.sf.oriented.omi.Options

All the Label's used consist of a single character (unicode code point).

setShowLabels(boolean) - Method in class net.sf.oriented.pseudoline.ImageOptions

Either show labels or not.

setsOfSignedSet() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for sets of signed sets.

setsOfUnsignedSet() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for sets of unsigned sets.

setStroke(Label, float...) - Method in class net.sf.oriented.pseudoline.ImageOptions

Provides the dash array for a line.

setStrokeOfInfinity(float...) - Method in class net.sf.oriented.pseudoline.ImageOptions

Provides the dashes for the line at infinity, if null then the dashes are chosen like any other line.

setUniverse(String[]) - Method in class net.sf.oriented.omi.Options

Provide all the Labels to be used, as Strings.

sharirAndSmorodinsky2001 - Static variable in class net.sf.oriented.omi.Bibliography

[Sharir and Smorodinsky, 2001] Sharir, M.

shor1991 - Static variable in class net.sf.oriented.omi.Bibliography

[Shor, 1991] Shor, P.

showOrigin - Variable in class net.sf.oriented.pseudoline.ImageOptions

Whether to show the origin or not.

showVertices - Variable in class net.sf.oriented.pseudoline.ImageOptions

Whether to high light vertices with a circle around them

sign(int...) - Static method in class net.sf.oriented.omi.Alternating

What is the sign of the permutation that sorts the values in x.

sign(Label) - Method in interface net.sf.oriented.omi.SignedSet

Returns 1, -1 or 0 depending on whether e is in the positive, the negative or neither component respectively.

sign() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

compare this value with 0.

SignedSet - Interface in net.sf.oriented.omi

A signed set is defined by disjoint positive SignedSet.plus() and negative SignedSet.minus() components, both of which are UnsignedSets.

SignedSetFactory - Interface in net.sf.oriented.omi

A factory for producing signed sets.

signedSetPermuter(Permutation) - Method in interface net.sf.oriented.omi.OM

Convert a permutation of the OM.elements() into a function that will map a signed set to the permuted signed set.

signedSets() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for signed sets.

size() - Method in interface net.sf.oriented.omi.SetOf

size() - Method in interface net.sf.oriented.omi.SignedSet

The number of elements which have a sign in this signed set.

size() - Method in class net.sf.oriented.util.combinatorics.CoLexicographic

size() - Method in class net.sf.oriented.util.combinatorics.Lexicographic

subsetsOfSize(int) - Method in interface net.sf.oriented.omi.SetOf

subtract(PerisicFieldElement) - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

support() - Method in interface net.sf.oriented.omi.SignedSet

The union of the positive and negative components.

suvorov14() - Static method in class net.sf.oriented.omi.Examples

Suvorov's non-isotopic Oriented Matroid, (as presented in Bibliography.björnerEtAl1999

suvorov1988 - Static variable in class net.sf.oriented.omi.Bibliography

[Suvorov, 1988]

switchFaceLattice() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

This method impacts performance.

symmetric(int) - Static method in class net.sf.oriented.util.combinatorics.Group

The symmetric group of permutations over 0, 1, ....

symmetricSetsOfSignedSet() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for symmetric sets of signed sets.

T

toArray() - Method in interface net.sf.oriented.omi.SetOf

An array of the members of this set.

toArray() - Method in class net.sf.oriented.util.combinatorics.Permutation

The permutation as an array of integers.

toCoLexicographicString() - Method in interface net.sf.oriented.omi.OMasChirotope

The simplest form of the chirotope: in colexicographic ordering.

toCrossingsString() - Method in class net.sf.oriented.pseudoline.EuclideanPseudoLines

Gives a representation of the modified oriented matroid as a list of crossings strings that can be used in FactoryFactory.fromCrossings(String...)

toLexicographicString() - Method in interface net.sf.oriented.omi.OMasChirotope

The simplest form of the chirotope: in lexicographic ordering.

top() - Method in interface net.sf.oriented.omi.FaceLattice

The (artificial) top face of the lattice.

toString(T) - Method in interface net.sf.oriented.omi.Factory

Convert a T into a String

toString() - Method in class net.sf.oriented.pseudoline.PseudoLineDrawing

toString() - Method in class net.sf.oriented.util.combinatorics.Permutation

toString() - Method in class net.sf.oriented.util.matrix.PerisicFieldElement

toString() - Method in class net.sf.oriented.util.matrix.RationalMatrix

tsukamoto13(int) - Static method in class net.sf.oriented.omi.Examples

Tsukamoto's non-isotopic Oriented Matroid

tsukamoto2013 - Static variable in class net.sf.oriented.omi.Bibliography

[Tsukamoto, 2013]

type() - Method in interface net.sf.oriented.omi.Face

The type, ie the position of the face in the lattice.

U

uniform3() - Static method in class net.sf.oriented.omi.Examples

The uniform oriented matroid of 3 points of rank 3

uniform4() - Static method in class net.sf.oriented.omi.Examples

The uniform oriented matroid of 4 points of rank 3

union(SET) - Method in interface net.sf.oriented.omi.SetOf

Set union.

union(ITEM) - Method in interface net.sf.oriented.omi.SetOf

Set union with the singleton set containing b

union() - Method in interface net.sf.oriented.omi.SetOfUnsignedSet

The union over this set of the members of this set.

unsignedCircuits() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for matroids from circuits.

UnsignedSet - Interface in net.sf.oriented.omi

This class represents mathematical sets of Labels which are the base elements in our universe of discourse.

unsignedSets() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for unsigned sets.

V

valueOf(String) - Static method in enum net.sf.oriented.omi.Face.Type

Returns the enum constant of this type with the specified name.

valueOf(String) - Static method in enum net.sf.oriented.omi.Options.Impl

Returns the enum constant of this type with the specified name.

values() - Static method in enum net.sf.oriented.omi.Face.Type

Returns an array containing the constants of this enum type, in the order they are declared.

values() - Static method in enum net.sf.oriented.omi.Options.Impl

Returns an array containing the constants of this enum type, in the order they are declared.

vectors() - Method in class net.sf.oriented.omi.FactoryFactory

A factory for oriented matroids which uses the vector representation.

verify() - Method in interface net.sf.oriented.omi.SetOf

Check invariants of the object, in particular check that Object.hashCode() satisfies its contract.

Verify - Interface in net.sf.oriented.omi

This interface is implemented by classes which represent mathematical concepts that have certain axioms, and/or by java classes that have invariants.

verify() - Method in interface net.sf.oriented.omi.Verify

Check invariants of the object.

verify() - Method in class net.sf.oriented.pseudoline.PseudoLineDrawing

verify() - Method in class net.sf.oriented.util.matrix.GramSchmidt

vertexSize - Variable in class net.sf.oriented.pseudoline.ImageOptions

The size of the vertex circle if shown.

W

WebPage - Class in oriented

wheel12() - Static method in class net.sf.oriented.omi.Examples

This is from the Oriented Matroid book Bibliography.björnerEtAl1999

width - Variable in class net.sf.oriented.pseudoline.ImageOptions

The width and height of the intended image.

width() - Method in class net.sf.oriented.util.matrix.RationalMatrix

The width or number of columns of the matrix.

withDimension(int) - Method in interface net.sf.oriented.omi.FaceLattice

The grade of the face lattice with faces of a given dimension.

withDimensions(int, int) - Method in interface net.sf.oriented.omi.FaceLattice

An iterable of the grades of the lattice between lower and upper inclusive.

Π

πάππος() - Static method in class net.sf.oriented.omi.Examples

The oriented matroid corresponding to the arrangement in Pappus's theorm

πάπποςAndJones1986a - Static variable in class net.sf.oriented.omi.Bibliography

[Pappus and Jones, 1986a] Pappus and Jones, A.

πάπποςAndJones1986b - Static variable in class net.sf.oriented.omi.Bibliography

[Pappus and Jones, 1986b] — (1986b).

πάπποςC340 - Static variable in class net.sf.oriented.omi.Bibliography

[Pappus, c340] Pappus (c340).

Ω

Ω14(int) - Static method in class net.sf.oriented.omi.Examples

Richter-Gebert's interesting oriented matroids.

A B C D E F G H I J L M N O P Q R S T U V W Π Ω