net.sf.oriented.omi

Class Examples

java.lang.Object

net.sf.oriented.omi.Examples

public class Examples
extends Object

Here are some 'interesting' oriented matroids. Of course, all we mean by interesting is interesting to me, and my projects of pseudoline stretching.

Author:

jeremycarroll

Constructor Summary

Constructors

Constructor and Description
Examples()

Method Summary

Methods

Modifier and Type	Method and Description
static Map<String,OM>	all()
static OM	ceva() An oriented matroid representing Ceva's theorem.
static OM	chapter1() This is from the Oriented Matroid book Bibliography.björnerEtAl1999
static OM	circularsaw3() The oriented matroid corresponding to the circular saw diagram of size three.
static OM	omega14(int i) Richter-Gebert's interesting oriented matroids.
static OM	pappus() The oriented matroid corresponding to the arrangement in Pappus's theorm
static OM	ringel() The oriented matroid corresponding to Ringel's uniform non-realizable, non-Pappus configuration.
static OM	suvorov14() Suvorov's non-isotopic Oriented Matroid, (as presented in Bibliography.björnerEtAl1999
static OM	tsukamoto13(int i) Tsukamoto's non-isotopic Oriented Matroid
static OM	uniform3() The uniform oriented matroid of 3 points of rank 3
static OM	uniform4() The uniform oriented matroid of 4 points of rank 3
static OM	wheel12() This is from the Oriented Matroid book Bibliography.björnerEtAl1999
static OM	Ω14(int i) Richter-Gebert's interesting oriented matroids.
static OM	πάππος() The oriented matroid corresponding to the arrangement in Pappus's theorm

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Examples

public Examples()

Method Detail

chapter1

public static OM chapter1()

This is from the Oriented Matroid book Bibliography.björnerEtAl1999

uniform3

public static OM uniform3()

The uniform oriented matroid of 3 points of rank 3

uniform4

public static OM uniform4()

The uniform oriented matroid of 4 points of rank 3

wheel12

public static OM wheel12()

This is from the Oriented Matroid book Bibliography.björnerEtAl1999

ceva

public static OM ceva()

An oriented matroid representing Ceva's theorem. See Bibliography.ceva1678

pappus

public static OM pappus()

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

See Also:

Bibliography.πάπποςC340, Bibliography.πάπποςAndJones1986b

πάππος

public static OM πάππος()

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

See Also:

Bibliography.πάπποςC340, Bibliography.πάπποςAndJones1986b

ringel

public static OM ringel()

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

See Also:

Bibliography.ringel1956

circularsaw3

public static OM circularsaw3()

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

See Also:

Bibliography.carroll2000d

suvorov14

public static OM suvorov14()

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

See Also:

Bibliography.suvorov1988

tsukamoto13

public static OM tsukamoto13(int i)

Tsukamoto's non-isotopic Oriented Matroid

Parameters:

i - 1, 0 or -1 giving the chirotope χ(8,11,12) (counting from 0)

See Also:

Bibliography.tsukamoto2013

omega14

public static OM omega14(int i)

Richter-Gebert's interesting oriented matroids.

Parameters:

i - 1, 0 or -1 giving the chirotope χ(11,12,13) (counting from 0)

See Also:

Bibliography.richterGebert1996

Ω14

public static OM Ω14(int i)

Richter-Gebert's interesting oriented matroids.

Parameters:

i - 1, 0 or -1 giving the chirotope χ(11,12,13) (counting from 0)

See Also:

Bibliography.richterGebert1996

all

public static Map<String,OM> all()