it.unimi.dsi.lama4j

Interface Element

All Known Implementing Classes:

AbstractElement, IntervalAntichains.Antichain, NamedElement

public interface Element

An element of a lattice.

Each lattice element has a reference to the containing lattice, and provides a number of utility methods that make it easy to write down expressions and perform computations.

Method Summary

Modifier and Type	Method and Description
boolean	comp(Element element) Return whether this element is comparable with the provided element.
Element	join(Element... element) Return the join of this element and of the provided elements.
Element	join(Element element) Return the join of this element and of the provided element.
Lattice	lattice() Return the lattice containing this element.
boolean	leq(Element element) Return whether this element is less than or equal to the provided element in the order of the containing lattice.
Element	meet(Element... element) Return the meet of this element and of the provided elements.
Element	meet(Element element) Return the meet of this element and of the provided element.
Element	pscomp(Element element) Return the pseudocomplement of this element relative to another element (optional operation).
Element	psdiff(Element element) Return the difference of this element with another element (optional operation).
Element	symdiff(Element element) Return the symmetric difference between this element and another element (optional operation).

Method Detail

meet

Element meet(Element... element)

Return the meet of this element and of the provided elements. In particular, upon the empty list of arguments returns this element.

Parameters:

element - the elements whose meet, together with this element, has to be computed.

Returns:

the meet of the provided elements and of this element.

meet

Element meet(Element element)

Return the meet of this element and of the provided element.

Parameters:

element - the element whose meet, together with this element, has to be computed.

Returns:

the meet of the provided element and of this element.

join

Element join(Element... element)

Return the join of this element and of the provided elements. In particular, upon the empty list of arguments returns this element.

Parameters:

element - the elements whose join, together with this element, has to be computed.

Returns:

the join of the provided elements and of this element.

join

Element join(Element element)

Return the join of this element and of the provided element.

Parameters:

element - the element whose join, together with this element, has to be computed.

Returns:

the join of the provided element and of this element.

comp

boolean comp(Element element)

Return whether this element is comparable with the provided element.

Parameters:

element - an element.

Returns:

true if this element is comparable with element, false otherwise.

leq

boolean leq(Element element)

Return whether this element is less than or equal to the provided element in the order of the containing lattice.

Parameters:

element - an element.

Returns:

true if this element is less than or equal to element, false otherwise.

psdiff

Element psdiff(Element element)

Return the difference of this element with another element (optional operation).

Parameters:

element - an element.

Returns:

the difference between this element and element.

See Also:

Lattice.psdiff(Element, Element)

pscomp

Element pscomp(Element element)

Return the pseudocomplement of this element relative to another element (optional operation).

Parameters:

element - an element.

Returns:

the pseudocomplement of this element relative to element.

See Also:

Lattice.pscomp(Element, Element)

symdiff

Element symdiff(Element element)

Return the symmetric difference between this element and another element (optional operation).

Parameters:

element - an element.

Returns:

the symmetric difference of this element with element.

See Also:

Lattice.symdiff(Element, Element)

lattice

Lattice lattice()

Return the lattice containing this element.

Returns:

the lattice containing this element.