UnparametricZRing< _Element > Class Template Reference

Generic Class ZRing. More...

#include <zring.h>

Inheritance diagram for UnparametricZRing< _Element >:

Public Types
enum	{ size_rep = sizeof(Element) }
using	Element = _Element
using	Rep = _Element
using	Self_t = UnparametricZRing<Element>
using	Parent_t = UnparametricOperations<Element>
using	Residu_t = _Element
using	Element_ptr = Element*
using	ConstElement_ptr = const Element*
typedef DomainRandIter< Self_t >::RandIter	RandIter
typedef GeneralRingNonZeroRandIter< Self_t >	NonZeroRandIter
typedef const Element	ConstElement

Public Member Functions
	UnparametricZRing ()
	UnparametricZRing (const UnparametricZRing &F)
template<class T>
	UnparametricZRing (const T &)
Residu_t	residu () const
Residu_t	size () const
Residu_t	cardinality () const
Residu_t	characteristic () const
template<typename T>
T &	cardinality (T &c) const
template<typename T>
T &	characteristic (T &c) const
bool	operator== (const Self_t &F) const
bool	operator!= (const Self_t &F) const
UnparametricZRing< Element > &	operator= (const UnparametricZRing< Element > &)
bool	isZero (const Element &a) const
bool	isOne (const Element &a) const
bool	isMOne (const Element &a) const
bool	isUnit (const Element &a) const
Element &	abs (Element &x, const Element &a) const
Element	abs (const Element &a) const
long	compare (const Element &a, const Element &b) const
Element &	init (Element &x) const
template<typename T>
Element &	init (Element &x, const T &s) const
Element &	assign (Element &x, const Element &y) const
template<typename T>
T &	convert (T &x, const Element &y) const
Element &	reduce (Element &x, const Element &y) const
Element &	reduce (Element &x) const
Element	minElement () const
Element	maxElement () const
template<class Random>
Element &	random (const Random &g, Element &r) const
template<class Random>
Element &	nonzerorandom (Random &g, Element &a) const
std::ostream &	write (std::ostream &os) const
	Print field.
std::ostream &	write (std::ostream &os, const Element &a) const
	Print field element.
std::istream &	read (std::istream &is, Element &a) const
	Read field element.
Comparison Predicates
bool	areEqual (const Element &x, const Element &y) const
	x == y
Arithmetic Operations
The first argument is set and is also the return value.
Element &	add (Element &x, const Element &y, const Element &z) const
	x := y + z
Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z
Element &	mul (Element &x, const Element &y, const Element &z) const
	x := y*z
Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z
Element &	mod (Element &x, const Element &y, const Element &z) const
	x := y mod z
Element &	neg (Element &x, const Element &y) const
	x := -y
Element &	inv (Element &x, const Element &y) const
	x := 1/y
Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y
Element &	axpyin (Element &z, const Element &a, const Element &x) const
	z := a*x + z
Element &	axmy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x - y
Element &	axmyin (Element &z, const Element &a, const Element &x) const
	z := a*x - z
Element &	maxpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := y - a*x
Element &	maxpyin (Element &z, const Element &a, const Element &x) const
	z := z - a*x
Inplace Arithmetic Operations
The first argument is modified and the result is the return value.
Element &	addin (Element &x, const Element &y) const
	x := x + y
Element &	subin (Element &x, const Element &y) const
	x := x - y
Element &	mulin (Element &x, const Element &y) const
	x := x*y
Element &	divin (Element &x, const Element &y) const
	x := x/y
Element &	modin (Element &x, const Element &y) const
	x := x mod y
Element &	negin (Element &x) const
	x := -x
Element &	invin (Element &x) const
	x := 1/x
Input/Output Operations
std::ostream &	write (std::ostream &os, std::string F) const
	Read field.
std::istream &	read (std::istream &is) const
	Read field.

Static Public Member Functions
static Residu_t	maxCardinality ()
static Residu_t	minCardinality ()
static const std::string	type_string ()

Data Fields
const Element	one = 1
const Element	zero = 0
const Element	mOne = -1

Detailed Description

template<class _Element>
class Givaro::UnparametricZRing< _Element >

Generic Class ZRing.

Ring of integers, using the unparametric _Element base type. Provide unparametric with domain features ZRing<Element> is a sugar name for UnparametricZRing<Element> Also, there is a specialization, below, for ZRing<Integer>

Member Typedef Documentation

Element

template<class _Element>

using Element = _Element

Rep

template<class _Element>

using Rep = _Element

Self_t

template<class _Element>

using Self_t = UnparametricZRing<Element>

Parent_t

template<class _Element>

using Parent_t = UnparametricOperations<Element>

Residu_t

template<class _Element>

using Residu_t = _Element

Element_ptr

template<class _Element>

using Element_ptr = Element*

ConstElement_ptr

template<class _Element>

using ConstElement_ptr = const Element*

RandIter

template<class _Element>

typedef DomainRandIter<Self_t>::RandIter RandIter

NonZeroRandIter

template<class _Element>

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

ConstElement

template<class _Element>

typedef const Element ConstElement

inherited

Member Enumeration Documentation

anonymous enum

template<class _Element>

anonymous enum

Enumerator
size_rep

Constructor & Destructor Documentation

UnparametricZRing() [1/3]

template<class _Element>

UnparametricZRing ( )

inline

UnparametricZRing() [2/3]

template<class _Element>

UnparametricZRing ( const UnparametricZRing< _Element > & F )

inline

UnparametricZRing() [3/3]

template<class _Element>

template<class T>

UnparametricZRing ( const T & )

inline

Member Function Documentation

residu()

template<class _Element>

Residu_t residu ( ) const

inline

size()

template<class _Element>

Residu_t size ( ) const

inline

cardinality() [1/2]

template<class _Element>

Residu_t cardinality ( ) const

inline

characteristic() [1/2]

template<class _Element>

Residu_t characteristic ( ) const

inline

cardinality() [2/2]

template<class _Element>

template<typename T>

T & cardinality ( T & c ) const

inline

characteristic() [2/2]

template<class _Element>

template<typename T>

T & characteristic ( T & c ) const

inline

maxCardinality()

template<class _Element>

static Residu_t maxCardinality ( )

inlinestatic

minCardinality()

template<class _Element>

static Residu_t minCardinality ( )

inlinestatic

operator==()

template<class _Element>

bool operator== ( const Self_t & F ) const

inline

operator!=()

template<class _Element>

bool operator!= ( const Self_t & F ) const

inline

operator=()

template<class _Element>

UnparametricZRing< Element > & operator= ( const UnparametricZRing< Element > & )

inline

isZero()

template<class _Element>

bool isZero ( const Element & a ) const

inlinevirtual

Implements RingInterface< _Element >.

isOne()

template<class _Element>

bool isOne ( const Element & a ) const

inlinevirtual

Implements RingInterface< _Element >.

isMOne()

template<class _Element>

bool isMOne ( const Element & a ) const

inlinevirtual

Implements RingInterface< _Element >.

isUnit()

template<class _Element>

bool isUnit ( const Element & a ) const

inlinevirtual

Implements RingInterface< _Element >.

abs() [1/2]

template<class _Element>

Element & abs ( Element & x, const Element & a ) const

inline

abs() [2/2]

template<class _Element>

Element abs ( const Element & a ) const

inline

compare()

template<class _Element>

long compare ( const Element & a, const Element & b ) const

inline

init() [1/2]

template<class _Element>

Element & init ( Element & x ) const

inlinevirtual

Reimplemented from UnparametricOperations< _Element >.

init() [2/2]

template<class _Element>

template<typename T>

Element & init ( Element & x, const T & s ) const

inline

assign()

template<class _Element>

Element & assign ( Element & x, const Element & y ) const

inlinevirtual

Reimplemented from UnparametricOperations< _Element >.

convert()

template<class _Element>

template<typename T>

T & convert ( T & x, const Element & y ) const

inline

reduce() [1/2]

template<class _Element>

Element & reduce ( Element & x, const Element & y ) const

inline

reduce() [2/2]

template<class _Element>

Element & reduce ( Element & x ) const

inline

minElement()

template<class _Element>

Element minElement ( ) const

inline

maxElement()

template<class _Element>

Element maxElement ( ) const

inline

random()

template<class _Element>

template<class Random>

Element & random ( const Random & g, Element & r ) const

inline

nonzerorandom()

template<class _Element>

template<class Random>

Element & nonzerorandom ( Random & g, Element & a ) const

inline

type_string()

template<class _Element>

static const std::string type_string ( )

inlinestatic

write() [1/3]

template<class _Element>

std::ostream & write ( std::ostream & os ) const

inlinevirtual

Print field.

Returns

output stream to which field is written.

Parameters

os	output stream to which field is written.

Reimplemented from UnparametricOperations< _Element >.

write() [2/3]

template<class _Element>

std::ostream & write ( std::ostream & os, const Element & x ) const

inlinevirtual

Print field element.

Returns

output stream to which field element is written.

Parameters

os	output stream to which field element is written.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

read() [1/2]

template<class _Element>

std::istream & read ( std::istream & is, Element & x ) const

inlinevirtual

Read field element.

Returns

input stream from which field element is read.

Parameters

is	input stream from which field element is read.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

areEqual()

template<class _Element>

bool areEqual ( const Element & x, const Element & y ) const

inlinevirtualinherited

x == y

Implements RingInterface< _Element >.

add()

template<class _Element>

Element & add ( Element & x, const Element & y, const Element & z ) const

inlinevirtualinherited

x := y + z

Implements RingInterface< _Element >.

sub()

template<class _Element>

Element & sub ( Element & x, const Element & y, const Element & z ) const

inlinevirtualinherited

x := y - z

Implements RingInterface< _Element >.

mul()

template<class _Element>

Element & mul ( Element & x, const Element & y, const Element & z ) const

inlinevirtualinherited

x := y*z

Implements RingInterface< _Element >.

div()

template<class _Element>

Element & div ( Element & x, const Element & y, const Element & z ) const

inlineinherited

x := y/z

mod()

template<class _Element>

Element & mod ( Element & x, const Element & y, const Element & z ) const

inlineinherited

x := y mod z

neg()

template<class _Element>

Element & neg ( Element & x, const Element & y ) const

inlinevirtualinherited

x := -y

Implements RingInterface< _Element >.

inv()

template<class _Element>

Element & inv ( Element & x, const Element & y ) const

inlineinherited

x := 1/y

axpy()

template<class _Element>

Element & axpy ( Element & z, const Element & a, const Element & x, const Element & y ) const

inlinevirtualinherited

z := a*x + y

Implements RingInterface< _Element >.

axpyin()

template<class _Element>

Element & axpyin ( Element & z, const Element & a, const Element & x ) const

inlinevirtualinherited

z := a*x + z

Implements RingInterface< _Element >.

axmy()

template<class _Element>

Element & axmy ( Element & z, const Element & a, const Element & x, const Element & y ) const

inlinevirtualinherited

z := a*x - y

Implements RingInterface< _Element >.

axmyin()

template<class _Element>

Element & axmyin ( Element & z, const Element & a, const Element & x ) const

inlinevirtualinherited

z := a*x - z

Implements RingInterface< _Element >.

maxpy()

template<class _Element>

Element & maxpy ( Element & z, const Element & a, const Element & x, const Element & y ) const

inlinevirtualinherited

z := y - a*x

Implements RingInterface< _Element >.

maxpyin()

template<class _Element>

Element & maxpyin ( Element & z, const Element & a, const Element & x ) const

inlinevirtualinherited

z := z - a*x

Implements RingInterface< _Element >.

addin()

template<class _Element>

Element & addin ( Element & x, const Element & y ) const

inlinevirtualinherited

x := x + y

Implements RingInterface< _Element >.

subin()

template<class _Element>

Element & subin ( Element & x, const Element & y ) const

inlinevirtualinherited

x := x - y

Implements RingInterface< _Element >.

mulin()

template<class _Element>

Element & mulin ( Element & x, const Element & y ) const

inlinevirtualinherited

x := x*y

Implements RingInterface< _Element >.

divin()

template<class _Element>

Element & divin ( Element & x, const Element & y ) const

inlineinherited

x := x/y

modin()

template<class _Element>

Element & modin ( Element & x, const Element & y ) const

inlineinherited

x := x mod y

negin()

template<class _Element>

Element & negin ( Element & x ) const

inlinevirtualinherited

x := -x

Implements RingInterface< _Element >.

invin()

template<class _Element>

Element & invin ( Element & x ) const

inlineinherited

x := 1/x

write() [3/3]

template<class _Element>

std::ostream & write ( std::ostream & os, std::string F ) const

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

read() [2/2]

template<class _Element>

std::istream & read ( std::istream & is ) const

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

Field Documentation

one

template<class _Element>

const Element one = 1

zero

template<class _Element>

const Element zero = 0

mOne

template<class _Element>

const Element mOne = -1

---

The documentation for this class was generated from the following file:

• zring.h