ringzp.h File Reference

Elements of the ring Z_p. More...

#include <istream>
#include <ostream>
#include <sstream>
#include <string>
#include "chomp/system/config.h"

Go to the source code of this file.

Classes
class	IntFeatures< intType >
	A collection of selected features of integer numbers. More...
class	IntFeatures< int >
	Specific features of the type 'int'. More...
class	IntFeatures< short >
	Specific features of the type 'short'. More...
class	IntFeatures< char >
	Specific features of the type 'char' (use with caution!). More...
class	tZp< intType >
	An element of the ring Z_p, where p is globally set. More...
class	tZp< intType >
	An element of the ring Z_p, where p is globally set. More...

Functions
template<class intType >
intType	invertModuloLargeP (const intType &n, const intType &q)
	Inverts a number in the modulo 'p' arithmetic, provided that 'p' is a prime number. More...
template<class intType >
intType	invertModuloSmallP (const intType &n, const intType &q)
	Inverts a number in the modulo 'p' arithmetic, provided that 'p' is a prime number. More...
template<class intType >
bool	numberIsPrime (const intType &n)
	Verifies if the given number is a positive prime number. More...
template<class intType >
bool	divide (const tZp< intType > &a, const tZp< intType > &b, tZp< intType > &quotient, tZp< intType > &remainder)
template<class intType >
int_t	hashkey1 (const tZp< intType > &n)
	Generates a hashing key no. More...
template<class intType >
int_t	hashkey2 (const tZp< intType > &n)
	Generates a hashing key no. More...
template<class intType >
std::istream &	operator>> (std::istream &in, tZp< intType > &n)
	Reads an element from an input stream. More...
template<class intType >
std::ostream &	operator<< (std::ostream &out, const tZp< intType > &n)
	Writes an element to an output stream. More...
template<class intType1 , class intType2 >
bool	operator== (const tZp< intType1 > &n1, const tZp< intType2 > &n2)
	Operator == for checking whether two elements of possibly different rings are equal. More...
template<class intType1 , class intType2 >
bool	operator== (const tZp< intType1 > &n1, const intType2 &n2)
	Operator == for checking whether a ring element is equivalent to an integer number. More...
template<class intType1 , class intType2 >
bool	operator== (const intType1 &n1, const tZp< intType2 > &n2)
	Operator == for checking whether a ring element is equivalent to an integer number. More...

Detailed Description

Elements of the ring Z_p.

Definition in file ringzp.h.

Function Documentation

divide()

template<class intType >

bool divide ( const tZp< intType > &  a, const tZp< intType > &  b, tZp< intType > &  quotient, tZp< intType > &  remainder  )

inline

Returns true if the remainer is zero, false otherwise.

Definition at line 182 of file ringzp.h.

References tZp< intType >::_n, and tZp< intType >::invert().

Referenced by tEuclWrap< CoefT >::operator%(), and tEuclWrap< CoefT >::operator/().

hashkey1()

template<class intType >

int_t hashkey1 ( const tZp< intType > &  n )

inline

Generates a hashing key no.

1 for an element of the Zp ring. This key is to be used in a hashed set.

Definition at line 455 of file ringzp.h.

hashkey2()

template<class intType >

int_t hashkey2 ( const tZp< intType > &  n )

inline

Generates a hashing key no.

2 for a general pair of elements, based on hashing keys of the elements. This key is to be used in a hashed set.

Definition at line 464 of file ringzp.h.

invertModuloLargeP()

template<class intType >

intType invertModuloLargeP	(	const intType &	n,
		const intType &	q
	)

Inverts a number in the modulo 'p' arithmetic, provided that 'p' is a prime number.

This procedure is good for large values of 'p' and uses a longer type of integers for multiplication.

Definition at line 95 of file ringzp.h.

invertModuloSmallP()

template<class intType >

intType invertModuloSmallP	(	const intType &	n,
		const intType &	q
	)

Inverts a number in the modulo 'p' arithmetic, provided that 'p' is a prime number.

This procedure is good for small values of 'p', such that 'p' squared still fits in the same integer type.

Definition at line 127 of file ringzp.h.

Referenced by tZp< intType >::invert().

numberIsPrime()

template<class intType >

bool numberIsPrime

(

const intType &

n

)

Verifies if the given number is a positive prime number.

Definition at line 155 of file ringzp.h.

Referenced by tZp< intType >::setp().

operator<<()

template<class intType >

std::ostream& operator<< ( std::ostream &  out, const tZp< intType > &  n  )

inline

Writes an element to an output stream.

Definition at line 483 of file ringzp.h.

operator==() [1/3]

template<class intType1 , class intType2 >

bool operator== ( const tZp< intType1 > &  n1, const tZp< intType2 > &  n2  )

inline

Operator == for checking whether two elements of possibly different rings are equal.

Definition at line 494 of file ringzp.h.

operator==() [2/3]

template<class intType1 , class intType2 >

bool operator== ( const tZp< intType1 > &  n1, const intType2 &  n2  )

inline

Operator == for checking whether a ring element is equivalent to an integer number.

Intended to compare with 0 and 1 only.

Definition at line 502 of file ringzp.h.

operator==() [3/3]

template<class intType1 , class intType2 >

bool operator== ( const intType1 &  n1, const tZp< intType2 > &  n2  )

inline

Operator == for checking whether a ring element is equivalent to an integer number.

Intended to compare with 0 and 1 only.

Definition at line 510 of file ringzp.h.

operator>>()

template<class intType >

std::istream& operator>> ( std::istream &  in, tZp< intType > &  n  )

inline

Reads an element from an input stream.

Definition at line 473 of file ringzp.h.