net.sf.oriented.omi

Interface SignedSet

public interface SignedSet

A signed set is defined by disjoint positive plus() and negative minus() components, both of which are UnsignedSets. A signed set can be seen as a partial map from the universe of elements to a sign { −, + }, see sign(Label). These are a key concept in the Oriented Matroid literature. These are immutable.

Author:

jeremycarroll

See Also:

Bibliography.björnerEtAl1999

Method Summary

Methods

Modifier and Type	Method and Description
SignedSet	compose(SignedSet b) Signed set composition.
boolean	conformsWith(SignedSet x) Does this conform with x? i.e.
boolean	equalsIgnoreSign(SignedSet s) Either s is equal to this, or to the opposite of this.
boolean	equalsOpposite(SignedSet s) This is a short hand for s.equals(opposite()).
boolean	isRestrictionOf(SignedSet x) Is this a restriction of x? i.e.
UnsignedSet	minus() The negative component.
SignedSet	opposite() Swaps the positive and negative components
UnsignedSet	plus() The positive component.
SignedSet	restriction(UnsignedSet x) The restriction of this to x.
UnsignedSet	separation(SignedSet b) The set of elements that have different sign in this and b.
int	sign(Label e) Returns 1, -1 or 0 depending on whether e is in the positive, the negative or neither component respectively.
int	size() The number of elements which have a sign in this signed set.
UnsignedSet	support() The union of the positive and negative components.

Method Detail

opposite

SignedSet opposite()

Swaps the positive and negative components

Returns:

The opposite signed set

plus

UnsignedSet plus()

The positive component.

Returns:

The positive component.

minus

UnsignedSet minus()

The negative component.

Returns:

The negative component.

equalsIgnoreSign

boolean equalsIgnoreSign(SignedSet s)

Either s is equal to this, or to the opposite of this. This is short hand for equals(s) || equalsOpposite(s).

Parameters:

s - The signed set to compare with.

Returns:

true if this is equal to s or its opposite.

equalsOpposite

boolean equalsOpposite(SignedSet s)

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

Parameters:

s - The signed set to compare with

Returns:

true if this is equal to the opposite of s

separation

UnsignedSet separation(SignedSet b)

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

Parameters:

b - The signed set to compare with

Returns:

The unsigned set of elements differing in sign

compose

SignedSet compose(SignedSet b)

Signed set composition. The composition takes the sign of each element from this, and if none, then from b

Parameters:

b - The signed set to compose with

Returns:

The composition of this with b.

size

int size()

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

Returns:

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

conformsWith

boolean conformsWith(SignedSet x)

Does this conform with x? i.e. is the positive part of this disjoint with the negative part of x, and the negative part of this disjoint with the positive part of x,

Parameters:

x - The signed set to compare with.

Returns:

true if this conforms with x.

See Also:

isRestrictionOf(SignedSet)

support

UnsignedSet support()

The union of the positive and negative components.

Returns:

The union of the positive and negative components.

sign

int sign(Label e)

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

Parameters:

e - the label to look up

Returns:

the sign of e in this signed set.

isRestrictionOf

boolean isRestrictionOf(SignedSet x)

Is this a restriction of x? i.e. is the positive part of this a subset of the positive part of x, and the negative part of this a subset of the negative part of x,

Parameters:

x - The signed set to compare with.

Returns:

true if this is a restriction of x.

See Also:

conformsWith(SignedSet)

restriction

SignedSet restriction(UnsignedSet x)

The restriction of this to x. We retain only the positive and negative elements that are in x.

Parameters:

x - The unsigned set to intersect with.

Returns:

The restriction of this to x