lima.mathematical.utilities
Class BigIntegerFunctions

java.lang.Object
  |
  +--lima.mathematical.utilities.BigIntegerFunctions

public class BigIntegerFunctions

extends java.lang.Object

A class to provide extra functions performed on BigInteger's

See Also:

BigInteger

Field Summary

static java.math.BigInteger	EIGHT
static java.math.BigInteger	FIVE
static java.math.BigInteger	FOUR
static java.math.BigInteger	ONE
static int	PRIME_CERTAINTY The degree of certainty that this big integer is actually prime.
static java.math.BigInteger	SEVEN
static java.math.BigInteger	SIX
static java.math.BigInteger	SIXTEEN
static java.math.BigInteger	THREE
static java.math.BigInteger	TWO
static java.math.BigInteger	ZERO

Constructor Summary

BigIntegerFunctions()

Method Summary

static int	doJacobi(int sign, java.math.BigInteger m, java.math.BigInteger n)
static boolean	isPrime(java.math.BigInteger n) Determine whether (or not) the specified * BigInteger is prime, with high certainty.
static int	jacobiSymbol(java.math.BigInteger n, java.math.BigInteger p)
static long	legendreSymbol(java.math.BigInteger n, java.math.BigInteger p) Calculate the Legendre symbol (n/p)
static double	log(java.math.BigInteger z) Calculate the logarithm of a BigInteger.
static java.math.BigInteger	sqrt(java.math.BigInteger i) Calculate square root of a BigInteger, rounding down
static java.math.BigInteger	sqrtMod(java.math.BigInteger a, java.math.BigInteger q) Calculate the sqaure root of a BigInteger with respect to a certain modulo

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

ZERO

public static final java.math.BigInteger ZERO

ONE

public static final java.math.BigInteger ONE

TWO

public static final java.math.BigInteger TWO

THREE

public static final java.math.BigInteger THREE

FOUR

public static final java.math.BigInteger FOUR

FIVE

public static final java.math.BigInteger FIVE

SIX

public static final java.math.BigInteger SIX

SEVEN

public static final java.math.BigInteger SEVEN

EIGHT

public static final java.math.BigInteger EIGHT

SIXTEEN

public static final java.math.BigInteger SIXTEEN

PRIME_CERTAINTY

public static final int PRIME_CERTAINTY

The degree of certainty that this big integer is actually prime.

See Also:

Constant Field Values

Constructor Detail

BigIntegerFunctions

public BigIntegerFunctions()

Method Detail

isPrime

public static boolean isPrime(java.math.BigInteger n)

Determine whether (or not) the specified * BigInteger is prime, with high certainty.

legendreSymbol

public static long legendreSymbol(java.math.BigInteger n,
                                  java.math.BigInteger p)

Calculate the Legendre symbol (n/p)

jacobiSymbol

public static int jacobiSymbol(java.math.BigInteger n,
                               java.math.BigInteger p)

doJacobi

public static int doJacobi(int sign,
                           java.math.BigInteger m,
                           java.math.BigInteger n)

sqrt

public static java.math.BigInteger sqrt(java.math.BigInteger i)

Calculate square root of a BigInteger, rounding down

log

public static double log(java.math.BigInteger z)

Calculate the logarithm of a BigInteger.

sqrtMod

public static java.math.BigInteger sqrtMod(java.math.BigInteger a,
                                           java.math.BigInteger q)
                                    throws java.lang.Exception

Calculate the sqaure root of a BigInteger with respect to a certain modulo

Parameters:

a - - the big integer to be square rooted

q - - the modulo which this is to be done in respect of

java.lang.Exception