Class Group

Object
   |
   +--Group

class Group

Defined in Group.js

Requires:

- Set

Field Detail

hasAssociativity

Boolean hasAssociativity

Whether or not the group is associative

hasClosure

Boolean hasClosure

Whether or not the group has closure

hasIdentity

Boolean hasIdentity

Whether or not the group has an identity element

hasInverse

Boolean hasInverse

Whether or not the group satisfies the inverse axiom

operation

Function operation

Either a function, or a string 'addition' or 'multiplication'

set

Object set

Group

Group(<Array> elements, <Function> operator)

Generator function for a new group (mathematical).

Parameters:
elements - the set of elements that defines the set in the group
operator - if a function, must take two parameters (elements of the set); if a string: 'addition' or 'multiplication'

Requires:
- Set

getIdentity

Object getIdentity()

Gets the identity element if it exists. Should be called after setIdentity() already has been.

Returns:
the identity element if it exists, false otherwise

isGroup

Boolean isGroup()

Tests to see whether the group satisfies all four axioms in the definition of a formal group.

Returns:
true if the group does, false otherwise

operand

Object operand(<Object> el1, <Object> el2)

The actual binary operation that is carried out for the group.

Parameters:
el1 - - the first element
el2 - - the second element

Returns:
(el1 operation el2)

setIdentity

void setIdentity()

Sets the identity element if it exists and hasIdentity to true.*

testAssociativity

Boolean testAssociativity()

Tests whether or not group is associative.

Returns:
true if group is associative, false otherwise

testClosure

Boolean testClosure()

Determines if the group does or does not have closure and sets the binary hasClosure.

Returns:
true if group has closure, false otherwise

testCycle

Boolean testCycle(<Array> array)

Tests if a given array (in this case, a permutation) is a cycle of the set.

Parameters:
array - - the array to test

Returns:
true if array is a cycle, false otherwise

testIdentity

Boolean testIdentity()

Tells whether or not group has identity element. Should be called after setIdentity() already has been.

Returns:
true if has identity element, false otherwise

testInverse

Boolean testInverse()

Tests for the existence of an inverse element for every element. Should be called after setIdentity().

Returns:
true if every element has an inverse, false otherwise