OM

All Superinterfaces:

Verify

All Known Subinterfaces:

OMasChirotope, OMasFaceLattice, OMasRealized, OMasSignedSet
```
public interface OM
extends Verify
```
An Oriented Matroid. This interface represents operations on and between oriented matroids independently of the cryptomorphic representations available. These are accessor methods to get a representation specific view of the oriented matroid. For example, to get the circuits of an oriented matroid use getCircuits(). This returns an oriented matroid that is equal to this one, and also implements the SetOfSignedSet interface giving the circuits. Each of five cryptomorphisms is similarly implemented.
Many methods return an OM. In practice it might be found that the returned OM is always the circuit representation: this is not part of the contract, and should not be relied on - call getCircuits() if that is the representation you need.

Author:

jeremycarroll

Method Summary

Methods
Modifier and Type	Method and Description
`int`	`asInt(Label e)` The integer corresponding to this element (counting from 0).
`int`	`asInt(String label)` The integer corresponding to this element (counting from 0).
`<T extends Label> int[]`	`asInt(T... e)` The integers corresponding to these elements (counting from 0).
`int[]`	`asInt(UnsignedSet u)` Gets the indexes of each element in `u`
`UnsignedSet`	`asSet(int... ix)` Concerts integer indices of `elements()` into an UnsignedSet.
`Group`	`automorphisms()` The automorphism group of this oriented matroid.
`OM`	`dual()` The dual oriented matroid.
`Label[]`	`elements()` The elements on which this oriented matroid is defined.
`boolean`	`equals(Object om)` An Oriented Matroid is equal to any other object implementing this interface, which represents the same underlying oriented matroid, including the `elements()` being equal.
`FactoryFactory`	`ffactory()` The factory for making this oriented matroid and its various parts.
`OMasChirotope`	`getChirotope()` Get the chirotope representation of the oriented matroid.
`OMasSignedSet`	`getCircuits()` Get the circuit representation of the oriented matroid.
`OMasFaceLattice`	`getFaceLattice()` Get the face lattice representation of the oriented matroid.
`Matroid`	`getMatroid()` The underlying matroid.
`OMasSignedSet`	`getMaxVectors()` Get the maximum vector representation of the oriented matroid.
`OMasRealized`	`getRealized()` Get the realized representation of the oriented matroid.
`OMasSignedSet`	`getVectors()` Get the vector representation of the oriented matroid.
`int`	`hashCode()` The hashCode of an Oriented Matroid is the hashCode of the circuit representation as a `SetOfSignedSet`s.
`boolean`	`isAcyclic()` This returns true if the oriented matroid contains no positive circuit, or equivalently, every edge is in a positive cocircuit.
`boolean`	`isUniform()` True if every set of `rank()` elements is a basis for the underlying matroid.
`int`	`n()` The size of `elements()`
`OM`	`permute(Permutation p)` Permute the Oriented Matroid, the ground set is not permuted.
`OM`	`permuteGround(Permutation p)` Permute the ground set.
`int`	`rank()` The rank of this oriented matroid.
`OM`	`reorient(Label... reorientationSet)` Reorients (i.e.
`UnsignedSet`	`setOfElements()` This is the same as `elements()`, except it is unordered.
`Function<SignedSet,SignedSet>`	`signedSetPermuter(Permutation p)` Convert a permutation of the `elements()` into a function that will map a signed set to the permuted signed set.

Methods inherited from interface net.sf.oriented.omi.Verify
verify

- Method Detail
  - getChirotope
```
OMasChirotope getChirotope()
```
    Get the chirotope representation of the oriented matroid. equals(getChirotope()) is true.
    
    Returns:
    The chirotope representation.
  - getCircuits
```
OMasSignedSet getCircuits()
```
    Get the circuit representation of the oriented matroid. equals(getCircuits()) is true.
    
    Returns:
    The circuit representation.
  - getVectors
```
OMasSignedSet getVectors()
```
    Get the vector representation of the oriented matroid. equals(getVectors()) is true.
    
    Returns:
    The vector representation.
  - getMaxVectors
```
OMasSignedSet getMaxVectors()
```
    Get the maximum vector representation of the oriented matroid. equals(getMaxVectors()) is true.
    
    Returns:
    The maximum vector representation.
  - getRealized
```
OMasRealized getRealized()
```
    Get the realized representation of the oriented matroid. equals(getRealized()) is true. This is (currently) only implemented for oriented matroids that were initially created from matrices; i.e. the original realization of this oriented matroid or its dual is remembered.
    The principal goal of the Java Oriented Matroid project is to improve the implementation of this method.
    
    Returns:
    The remembered realization
    
    Throws:
    
    UnsupportedOperationException - Realization not implemented in most cases.
    See Also:
    Bibliography.shor1991
  - getFaceLattice
```
OMasFaceLattice getFaceLattice()
```
    Get the face lattice representation of the oriented matroid. equals(getFaceLattice()) is true. Note that in some sense this is a property of the dual. The labels on the faces of the return face lattice are covectors.
    
    Returns:
    The face lattice representation of this oriented matroid.
  - dual
```
OM dual()
```
    The dual oriented matroid.
    
    Returns:
    The dual oriented matroid.
  - reorient
```
OM reorient(Label... reorientationSet)
```
    Reorients (i.e. swaps the signs in circuits) of the given set.
    
    Parameters:
    reorientationSet - The elements to reorient
    
    Returns:
    a reoriented oriented matroid
  - elements
```
Label[] elements()
```
    The elements on which this oriented matroid is defined. The order is significant with respect to some representations (e.g. getChirotope() and getRealized()
    
    Returns:
    The ordered elements on which this oriented matroid is defined.
  - setOfElements
```
UnsignedSet setOfElements()
```
    This is the same as elements(), except it is unordered.
    
    Returns:
    The unordered elements on which this oriented matroid is defined.
  - getMatroid
```
Matroid getMatroid()
```
    The underlying matroid.
    
    Returns:
    The underlying matroid.
  - rank
```
int rank()
```
    The rank of this oriented matroid.
    
    Returns:
    The rank of this oriented matroid.
  - hashCode
```
int hashCode()
```
    The hashCode of an Oriented Matroid is the hashCode of the circuit representation as a SetOfSignedSets.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    the hashCode
  - equals
```
boolean equals(Object om)
```
    An Oriented Matroid is equal to any other object implementing this interface, which represents the same underlying oriented matroid, including the elements() being equal.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    om -
    
    Returns:
    true if these both represent the same Oriented Matroid
  - asInt
```
int asInt(Label e)
```
    The integer corresponding to this element (counting from 0).
    
    Parameters:
    e - An element in elements()
    
    Returns:
    The index of e in elements()
  - asInt
```
int asInt(String label)
```
    The integer corresponding to this element (counting from 0).
    
    Parameters:
    label - The label of the element
    
    Returns:
    The index of e in elements(), where e.label() = label
  - asInt
```
<T extends Label> int[] asInt(T... e)
```
    The integers corresponding to these elements (counting from 0).
    
    Parameters:
    e - Elements in elements()
    
    Returns:
    The corresponding indexes of e in elements()
  - asSet
```
UnsignedSet asSet(int... ix)
```
    Concerts integer indices of elements() into an UnsignedSet.
    
    Parameters:
    ix - The indices
    
    Returns:
    The set of elements corresponding to the indices ix
    See Also:
    asInt(UnsignedSet)
  - asInt
```
int[] asInt(UnsignedSet u)
```
    Gets the indexes of each element in u
    
    Parameters:
    u - a subset of setOfElements()
    
    Returns:
    The increasing corresponding indexes
    See Also:
    asSet(int...)
  - isAcyclic
```
boolean isAcyclic()
```
    This returns true if the oriented matroid contains no positive circuit, or equivalently, every edge is in a positive cocircuit.
  - permuteGround
```
OM permuteGround(Permutation p)
```
    Permute the ground set. Returns an oriented matroid om s.t. om.equals(this) and Arrays.equals(p.permute(this.ground()),om.ground() are the same.
    
    Parameters:
    p - The permutation to apply.
    
    Returns:
    An equal oriented matroid with permuted ground set
  - permute
```
OM permute(Permutation p)
```
    Permute the Oriented Matroid, the ground set is not permuted. So in general, this.equals(this.permute(p)) is false.
    
    Parameters:
    p - The permutation to apply.
    
    Returns:
    An oriented matroid after the action of the permutation
  - n
```
int n()
```
    The size of elements()
    
    Returns:
    The size of elements().
  - automorphisms
```
Group automorphisms()
```
    The automorphism group of this oriented matroid. For each permutation π ∈ automorphisms() we have this.equals(this.permute(π))
    
    Returns:
    The automorphism group of this oriented matroid.
  - signedSetPermuter
```
Function<SignedSet,SignedSet> signedSetPermuter(Permutation p)
```
    Convert a permutation of the elements() into a function that will map a signed set to the permuted signed set.
    
    Parameters:
    p - This is a permutation of elements()
    
    Returns:
    A function that invokes the action of the permutation on signed sets
  - ffactory
```
FactoryFactory ffactory()
```
    The factory for making this oriented matroid and its various parts.
    
    Returns:
    The underlying factory.
  - isUniform
```
boolean isUniform()
```
    True if every set of rank() elements is a basis for the underlying matroid.
    
    Returns:
    true if this oriented matroid is uniform

Interface OM

Method Summary

Methods inherited from interface net.sf.oriented.omi.Verify

Method Detail

getChirotope

getCircuits

getVectors

getMaxVectors

getRealized

getFaceLattice

dual

reorient

elements

setOfElements

getMatroid

rank

hashCode

equals

asInt

asInt

asInt

asSet

asInt

isAcyclic

permuteGround

permute

n

automorphisms

signedSetPermuter

ffactory

isUniform