org.lsmp.djep.groupJep.groups

Class Zn

java.lang.Object

org.lsmp.djep.groupJep.groups.Group

org.lsmp.djep.groupJep.groups.Zn

All Implemented Interfaces:

GroupI, AbelianGroupI, FieldI, HasDivI, HasModI, HasPowerI, IntegralDomainI, OrderedSetI, RingI

public class Zn
extends Group
implements FieldI, OrderedSetI, HasModI, HasPowerI

The group of integers mod n. For prime values of n this is a field, with some nice division tables. i.e. for Z5

* | 1 2 3 4
 ------------
 1 | 1 2 3 4
 2 | 2 4 1 3
 3 | 3 1 4 2
 4 | 4 3 2 1
 

/ | 1 2 3 4
 ------------
 1 | 1 2 3 4
 2 | 3 1 4 2
 3 | 2 4 1 3
 4 | 4 3 2 1
 

Constructor Summary

Constructors

Constructor and Description
Zn(BigInteger modulus)

Method Summary

Modifier and Type	Method and Description
Number	add(Number num1, Number num2) Get sum of the numbers
int	compare(Number a, Number b) Returns -1,0,1 depending on whether a is less than, equal to or greater than b.
Number	div(Number num1, Number num2) get division of two numbers.
boolean	equals(Number a, Number b) whether two numbers are equal
Number	getInverse(Number num) Get Inverse of a number
Number	getMulInverse(Number num) get mul inverse
Number	getONE() Get multiplicative identity i.e.
Number	getZERO() Returns the identity element under +
Number	mod(Number num1, Number num2)
Number	mul(Number num1, Number num2) Returns the product of two numbers, a*b
Number	pow(Number num1, Number num2)
Number	sub(Number num1, Number num2) Get the difference of the numbers.
String	toString()
Number	valueOf(String str) returns number given by the string

Methods inherited from class org.lsmp.djep.groupJep.groups.Group

addStandardConstants, addStandardFunctions, getNumberFactory, isConstantPoly

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.lsmp.djep.groupJep.GroupI

addStandardConstants, addStandardFunctions, getNumberFactory, isConstantPoly

Constructor Detail

Zn

public Zn(BigInteger modulus)

Method Detail

getZERO

public Number getZERO()

Description copied from interface: GroupI

Returns the identity element under +

Specified by:

getZERO in interface GroupI

getONE

public Number getONE()

Description copied from interface: RingI

Get multiplicative identity i.e. 1. Strictly speaking a ring need not have a mul indentity. However most useful ones do, and they are not all integral domains.

Specified by:

getONE in interface RingI

getInverse

public Number getInverse(Number num)

Description copied from interface: GroupI

Get Inverse of a number

Specified by:

getInverse in interface GroupI

getMulInverse

public Number getMulInverse(Number num)

Description copied from interface: FieldI

get mul inverse

Specified by:

getMulInverse in interface FieldI

add

public Number add(Number num1,
                  Number num2)

Description copied from interface: GroupI

Get sum of the numbers

Specified by:

add in interface GroupI

sub

public Number sub(Number num1,
                  Number num2)

Description copied from interface: GroupI

Get the difference of the numbers. i.e. a + (-b)

Specified by:

sub in interface GroupI

mul

public Number mul(Number num1,
                  Number num2)

Description copied from interface: RingI

Returns the product of two numbers, a*b

Specified by:

mul in interface RingI

div

public Number div(Number num1,
                  Number num2)

Description copied from interface: HasDivI

get division of two numbers. i.e. a * ( b^-1). Strictly speeking

Specified by:

div in interface HasDivI

mod

public Number mod(Number num1,
                  Number num2)

Specified by:

mod in interface HasModI

pow

public Number pow(Number num1,
                  Number num2)

Specified by:

pow in interface HasPowerI

equals

public boolean equals(Number a,
                      Number b)

Description copied from interface: GroupI

whether two numbers are equal

Specified by:

equals in interface GroupI

compare

public int compare(Number a,
                   Number b)

Description copied from interface: OrderedSetI

Returns -1,0,1 depending on whether a is less than, equal to or greater than b.

Specified by:

compare in interface OrderedSetI

valueOf

public Number valueOf(String str)

Description copied from interface: GroupI

returns number given by the string

Specified by:

valueOf in interface GroupI

toString

public String toString()

Overrides:

toString in class Group