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Class Set

class Set
A mathematical set, essentially nothing but a collection of objects. The class is essentially a wrapper for an array which defines some traditional operations done on sets, such as cartesianProduct.
Defined in Set.js

Variable Summary
int cardinality
the cardinality ("dimension") of the set
Array elements
the elements of the set
public static Set empty
the empty set {}

Constructor Summary
Set ([Array elements])
Set ([Set set])
Constructor function for a new set.

Function Summary
public Set addElement (Object el)
Adds a new element to the set and updates the cardinality.
public Set cartesianProduct (Set set)
Calculates the Cartesian product of two sets (the set of all ordered pairs, which are here treated as subsets).
public Set complement (Set set)
Creates a new set that is the relative complement of two sets.
public boolean equalTo (Set set)
Tests whether or not two sets (including subsets, which must be defined as sets and not simply arrays) are equal.
public boolean inSet()
Determines if a specified element is in the set of this group.
public int indexOf (Object el)
Finds the index of the first occurence of the specified element.
public Set intersection (Set set)
Creates a new set out of the intersection (shared elements) of two sets.
public boolean properSubsetOf (Set set)
Tests if this set is a proper subset of a given set (i.e.
public boolean properSupersetOf (Set set)
Tests whether or not this set is a proper superset of a given set.
public Set removeElement (Object el)
Removes ALL OCCURENCES of an element from the set and updates the cardinality.
public boolean subsetOf (Set set)
Tests to see if a set is a subset (not necessarily a proper subset; i.e.
public boolean supersetOf (Set set)
Tests if the set is a superset of a given set.
public String toString()
Returns a string representation of the set (and subsets).
public Set union (Set set)
Creates a new set that is the union of two sets.
public static Set zero (int n)
Creates a set with n zero elements

Variable Details

variable int cardinality

the cardinality ("dimension") of the set

variable Array elements

the elements of the set

variable public static Set empty

the empty set {}

Constructor Details

constructor Set

Set([Array elements])
Set([Set set])
Constructor function for a new set. If no parameters supplied, constructs an empty (null) set
Parameters:
fromArray
[elements] - the elements of your set
clone
[set] - the set to clone

Function Details

function addElement

public Set addElement(Object el)
Adds a new element to the set and updates the cardinality.
Parameters:
el - the element to be added
Returns:
this set, updated

function cartesianProduct

public Set cartesianProduct(Set set)
Calculates the Cartesian product of two sets (the set of all ordered pairs, which are here treated as subsets).
Parameters:
set - the set with which to compute the product
Returns:
a new set that is the Cartesian product of the other two

function complement

public Set complement(Set set)
Creates a new set that is the relative complement of two sets. This operation is analogous to subtracting the specified set from the original set.
Parameters:
set - the set to which to find the complement
Returns:
a new set that is the specified complement

function equalTo

public boolean equalTo(Set set)
Tests whether or not two sets (including subsets, which must be defined as sets and not simply arrays) are equal.
Parameters:
set - the set to compare to
Returns:
true if the two sets are equal, false otherwise

function inSet

public boolean inSet()
Determines if a specified element is in the set of this group.
Returns:
true if element is in set, false otherwise

function indexOf

public int indexOf(Object el)
Finds the index of the first occurence of the specified element. Should suffice since most sets should be in order and have no recurring elements.
Parameters:
el - the element for which to find the index
Returns:
the index of the element in the set (NOT in the array of the set object)

function intersection

public Set intersection(Set set)
Creates a new set out of the intersection (shared elements) of two sets.
Parameters:
set - the set with which to find the intersection
Returns:
the intersection of the two sets as a new set

function properSubsetOf

public boolean properSubsetOf(Set set)
Tests if this set is a proper subset of a given set (i.e. there is at least one element in the superset not in the subset).
Parameters:
set - the set which may or may not be a strict superset
Returns:
true if this is a proper subset of set, false otherwise

function properSupersetOf

public boolean properSupersetOf(Set set)
Tests whether or not this set is a proper superset of a given set.
Parameters:
set - the set which may or may not be a proper subset
Returns:
true if this is proper superset of set, false if not

function removeElement

public Set removeElement(Object el)
Removes ALL OCCURENCES of an element from the set and updates the cardinality.
Parameters:
el - the element to be removed
Returns:
this set, updated

function subsetOf

public boolean subsetOf(Set set)
Tests to see if a set is a subset (not necessarily a proper subset; i.e. by this method, a set is a subset of itself) of a given set.
Parameters:
set - the set that may or may not be a superset of the original
Returns:
true if this is a subset of set, false otherwise

function supersetOf

public boolean supersetOf(Set set)
Tests if the set is a superset of a given set. Note: not strict definition of superset; any set is also a superset of itself by this definition.
Parameters:
set - the set which may or may not be a subset of the original
Returns:
true if this is a superset of set, false otherwise

function toString

public String toString()
Returns a string representation of the set (and subsets).
Returns:
the string representatoin of the set.

function union

public Set union(Set set)
Creates a new set that is the union of two sets.
Parameters:
set - the set to join with the current set
Returns:
a new set that is the union of the calling and given sets

function zero

public static Set zero(int n)
Creates a set with n zero elements
Parameters:
n - the number of elements in the zero set
Returns:
a set of n elements all equal to 0