ElementCollection Public Fields

ElementCollection Public Enumerations

ElementCollection Constructors

New The Plain-Vanilla Constructor Public Sub New() Remarks: Parameters:

ElementCollection Public Properties

Item Default Property of this Collection; the Order.Element at a given 0-based position in the Collection Category: Default Public ReadOnly Property Item(ByVal Index As Int32) As Element Remarks: IndexParameters: ByVal Index As Int32 Return Value: Element

ElementCollection Public Methods

Add Adds an Element to this ElementCollection and Returns its Position in the Collection Public Overloads Function Add(ByVal NewEGWorld As Element) As Int32 Remarks: Parameters: ByVal NewEGWorld As Element Return Value: Int32

AddIfNew Adds an Element to this Collection and returns its Index provided it is not already a member; if it is a member, returns its Index Public Overloads Function AddIfNew(ByVal Candidate As Element) As Int32 Remarks: Parameters: ByVal Candidate As Element Return Value: Int32

AddIfNewRange Adds to this Collection the members of a given ElementCollection which are new to this Collection and returns the number of Elements added Public Overloads Function AddIfNewRange(ByVal Range As ElementCollection) As Int32 Remarks: Parameters: ByVal Range As ElementCollection Return Value: Int32

AddRange Adds the members of a given ElementCollection to this Collection and returns the number of EGWorlds added Public Overloads Function AddRange(ByVal Range As ElementCollection) As Int32 Remarks: Parameters: ByVal Range As ElementCollection Return Value: Int32

AddRange Adds the members of a given Array of Element Objects to this Collection and returns the number of Elements added Public Overloads Function AddRange(ByVal Range As Element[]) As Int32 Remarks: Parameters: ByVal Range As Element[] Return Value: Int32

Complements Returns True iff a given pair of Elements are Complements in THIS ElementCollection Public Function Complements(ByVal EltX As Element, ByVal EltY As Element) As Boolean Remarks: A Complement of X is an Element Y such that Join(X, Y) = Supremum And Meet(X, Y) = Infimum Parameters: ByVal EltX As Element ByVal EltY As Element Return Value: Boolean

Contains Returns True iff a given Element belongs to this Collection Public Overloads Function Contains(ByVal EGW As Element) As Boolean Remarks: Parameters: ByVal EGW As Element Return Value: Boolean

GetLowerBoundsOf Returns the ElementCollection of Lower Bounds in a given ElementCollection (ContextElts) of the Elements in a given ElementCollection (TargetElts - ordinarily a sub-collection of the first-mentioned ElementCollection); returns empty Collection if there are none such Public Shared Function GetLowerBoundsOf(ByVal TargetElts As ElementCollection, ByVal ContextElts As ElementCollection) As ElementCollection Remarks: Parameters: ByVal TargetElts As ElementCollection ByVal ContextElts As ElementCollection Return Value: ElementCollection

GetLowerBoundsOf Returns the ElementCollection of Lower Bounds of a given pair of Elements in THIS ElementCollection; returns empty Collection if there are none such Public Function GetLowerBoundsOf(ByVal EltX As Element, ByVal EltY As Element) As ElementCollection Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element Return Value: ElementCollection

GetLowerBoundsOf Returns the ElementCollection of Lower Bounds in THIS ElementCollection of the Elements in a given ElementCollection (TargetElts - ordinarily a sub-collection of the first-mentioned ElementCollection); returns empty Collection if there are none such Public Function GetLowerBoundsOf(ByVal TargetElts As ElementCollection) As ElementCollection Remarks: Parameters: ByVal TargetElts As ElementCollection Return Value: ElementCollection

GetLowerBoundsOf Returns the ElementCollection of Lower Bounds of a given pair of Elements in a given ElementCollection; returns empty Collection if there are none such Public Shared Function GetLowerBoundsOf(ByVal EltX As Element, ByVal EltY As Element, ByVal InCollection As ElementCollection) As ElementCollection Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element ByVal InCollection As ElementCollection Return Value: ElementCollection

GetMaximalElements Returns the ElementCollection of Maximal Elements of THIS ElementCollection Public Function GetMaximalElements() As ElementCollection Remarks: Parameters: Return Value: ElementCollection

GetMaximalElements Returns the ElementCollection of Maximal Elements of a given ElementCollection Public Shared Function GetMaximalElements(ByVal OfCollection As ElementCollection) As ElementCollection Remarks: Parameters: ByVal OfCollection As ElementCollection Return Value: ElementCollection

GetMinimalElements Returns the ElementCollection of Minimal Elements of THIS ElementCollection Public Function GetMinimalElements() As ElementCollection Remarks: Parameters: Return Value: ElementCollection

GetMinimalElements Returns the ElementCollection of Minimal Elements of a given ElementCollection Public Shared Function GetMinimalElements(ByVal OfCollection As ElementCollection) As ElementCollection Remarks: Parameters: ByVal OfCollection As ElementCollection Return Value: ElementCollection

GetUpperBoundsOf Returns the ElementCollection of Upper Bounds in THIS ElementCollection of the Elements in a given ElementCollection (TargetElts - ordinarily a sub-collection of the first-mentioned ElementCollection); returns empty Collection if there are none such Public Function GetUpperBoundsOf(ByVal TargetElts As ElementCollection) As ElementCollection Remarks: Parameters: ByVal TargetElts As ElementCollection Return Value: ElementCollection

GetUpperBoundsOf Returns the ElementCollection of Upper Bounds of a given pair of Elements in a given ElementCollection; returns empty Collection if there are none such Public Shared Function GetUpperBoundsOf(ByVal EltX As Element, ByVal EltY As Element, ByVal InCollection As ElementCollection) As ElementCollection Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element ByVal InCollection As ElementCollection Return Value: ElementCollection

GetUpperBoundsOf Returns the ElementCollection of Upper Bounds in a given ElementCollection (ContextElts) of the Elements in a given ElementCollection (TargetElts - ordinarily a sub-collection of the first-mentioned ElementCollection); returns empty Collection if there are none such Public Shared Function GetUpperBoundsOf(ByVal TargetElts As ElementCollection, ByVal ContextElts As ElementCollection) As ElementCollection Remarks: Parameters: ByVal TargetElts As ElementCollection ByVal ContextElts As ElementCollection Return Value: ElementCollection

GetUpperBoundsOf Returns the ElementCollection of Upper Bounds of a given pair of Elements in THIS ElementCollection; returns empty Collection if there are none such Public Function GetUpperBoundsOf(ByVal EltX As Element, ByVal EltY As Element) As ElementCollection Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element Return Value: ElementCollection

HasInfimum Returns True and passes the Infimum iff this ElementCollection has a Lowest Member; else passes Null Public Function HasInfimum(ByRef Inf As Element) As Boolean Remarks: Parameters: ByRef Inf As Element Return Value: Boolean

HasInfimum Returns True iff this ElementCollection has a Lowest Member Public Function HasInfimum() As Boolean Remarks: Parameters: Return Value: Boolean

HasSupremum Returns True and passes the Supremum iff this ElementCollection has a Lowest Member; else passes Null Public Function HasSupremum(ByRef Sup As Element) As Boolean Remarks: Parameters: ByRef Sup As Element Return Value: Boolean

HasSupremum Returns True iff this ElementCollection has a Highest Member Public Function HasSupremum() As Boolean Remarks: Parameters: Return Value: Boolean

IndexOf Returns the Index of a given Element if it is in this Collection; else returns -1 Public Overloads Function IndexOf(ByVal EGW As Element) As Int32 Remarks: Parameters: ByVal EGW As Element Return Value: Int32

Infimum Returns the Infimum of this ElementCollection, if it exists; else returns Null Public Function Infimum() As Element Remarks: Parameters: Return Value: Element

IsComplemented Returns True iff the poset defined by this ElementCollection is Complemented Public Function IsComplemented() As Boolean Remarks: A Complement of X is an Element Y such that Join(X, Y) = Supremum And Meet(X, Y) = Infimum; a poset is complemented iff every one of its Elements has a Complement Parameters: Return Value: Boolean

IsJoinSemilattice Returns True iff a given ElementCollection is a Join Semilattice Public Shared Function IsJoinSemilattice(ByVal Candidate As ElementCollection) As Boolean Remarks: Parameters: ByVal Candidate As ElementCollection Return Value: Boolean

IsJoinSemilattice Returns True iff the present ElementCollection is a Join Semilattice Public Function IsJoinSemilattice() As Boolean Remarks: Parameters: Return Value: Boolean

IsLattice Returns True iff a THIS ElementCollection is a Lattice Public Function IsLattice() As Boolean Remarks: Parameters: Return Value: Boolean

IsLattice Returns True iff a given ElementCollection is a Lattice Public Shared Function IsLattice(ByVal Candidate As ElementCollection) As Boolean Remarks: Parameters: ByVal Candidate As ElementCollection Return Value: Boolean

IsMaximal Returns True iff a given Element is a Maximal Element in THIS ElementCollection Public Function IsMaximal(ByVal Elt As Element) As Boolean Remarks: Parameters: ByVal Elt As Element Return Value: Boolean

IsMaximal Returns True iff a given Element is a Maximal Element in a given ElementCollection Public Shared Function IsMaximal(ByVal Elt As Element, ByVal InCollection As ElementCollection) As Boolean Remarks: Parameters: ByVal Elt As Element ByVal InCollection As ElementCollection Return Value: Boolean

IsMeetSemilattice Returns True iff the present ElementCollection is a Meet Semilattice Public Function IsMeetSemilattice() As Boolean Remarks: Parameters: Return Value: Boolean

IsMeetSemilattice Returns True iff a given ElementCollection is a Meet Semilattice Public Shared Function IsMeetSemilattice(ByVal Candidate As ElementCollection) As Boolean Remarks: Parameters: ByVal Candidate As ElementCollection Return Value: Boolean

IsMinimal Returns True iff a given Element is a Minimal Element in THIS ElementCollection Public Function IsMinimal(ByVal Elt As Element) As Boolean Remarks: Parameters: ByVal Elt As Element Return Value: Boolean

IsMinimal Returns True iff a given Element is a Minimal Element in a given ElementCollection Public Shared Function IsMinimal(ByVal Elt As Element, ByVal InCollection As ElementCollection) As Boolean Remarks: Parameters: ByVal Elt As Element ByVal InCollection As ElementCollection Return Value: Boolean

Join Returns the Least Upper Bound, if it exists, IN a given ElementCollection of the members OF THIS ElementCollection; if Join does not exist, returns Null Public Function Join(ByVal OfCollection As ElementCollection) As Element Remarks: Parameters: ByVal OfCollection As ElementCollection Return Value: Element

Join Returns the Least Upper Bound, if it exists, in THIS ElementCollection of the Elements EltX and EltY; if Join does not exist, returns Null Public Function Join(ByVal EltX As Element, ByVal EltY As Element) As Element Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element Return Value: Element

Join Returns the Least Upper Bound, if it exists, IN a given ElementCollection of the members OF a given ElementCollection; if Join does not exist, returns Null Public Shared Function Join(ByVal OfCollection As ElementCollection, ByVal InCollection As ElementCollection) As Element Remarks: Parameters: ByVal OfCollection As ElementCollection ByVal InCollection As ElementCollection Return Value: Element

Join Returns the Least Upper Bound, if it exists, in a given ElementCollection of the Elements EltX and EltY; if Join does not exist, returns Null Public Shared Function Join(ByVal EltX As Element, ByVal EltY As Element, ByVal InCollection As ElementCollection) As Element Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element ByVal InCollection As ElementCollection Return Value: Element

Meet Returns the Greatest Lower Bound, if it exists, IN a given ElementCollection of the members OF a given ElementCollection; if Meet does not exist, returns Null Public Shared Function Meet(ByVal OfCollection As ElementCollection, ByVal InCollection As ElementCollection) As Element Remarks: Parameters: ByVal OfCollection As ElementCollection ByVal InCollection As ElementCollection Return Value: Element

Meet Returns the Greatest Lower Bound, if it exists, in a given ElementCollection of the Elements EltX and EltY; if Meet does not exist, returns Null Public Shared Function Meet(ByVal EltX As Element, ByVal EltY As Element, ByVal InCollection As ElementCollection) As Element Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element ByVal InCollection As ElementCollection Return Value: Element

Meet Returns the Greatest Lower Bound, if it exists, IN a given ElementCollection of the members OF THIS ElementCollection; if Meet does not exist, returns Null Public Function Meet(ByVal OfCollection As ElementCollection) As Element Remarks: Parameters: ByVal OfCollection As ElementCollection Return Value: Element

Meet Returns the Greatest Lower Bound, if it exists, in THIS ElementCollection of the Elements EltX and EltY; if Meet does not exist, returns Null Public Function Meet(ByVal EltX As Element, ByVal EltY As Element) As Element Remarks: Parameters: ByVal EltX As Element ByVal EltY As Element Return Value: Element

Remove Removes a given Element from this Collection Public Overloads Sub Remove(ByVal Removee As Element) Remarks: Parameters: ByVal Removee As Element Return Value: Void

Supremum Returns the Supremum of this ElementCollection, if it exists; else returns Null Public Function Supremum() As Element Remarks: Parameters: Return Value: Element

ToString A String representation of this ElementCollection Public Overrides Function ToString() As String Remarks: Parameters: Return Value: String

ElementCollection Public Operators

ElementCollection Public Events