ZRing< Element > Class Template Reference

#include <zring.h>

Inheritance diagram for ZRing< Element >:

Collaboration diagram for ZRing< Element >:

Public Types
enum
using	Element = Element
using	Rep = 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
Residu_t	residu () const
Residu_t	size () const
Residu_t	cardinality () const
T &	cardinality (T &c) const
Residu_t	characteristic () const
T &	characteristic (T &c) const
bool	operator== (const Self_t &F) const
bool	operator!= (const Self_t &F) const
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
Element &	init (Element &x, const T &s) const
Element &	assign (Element &x, const Element &y) const
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
Element &	random (const Random &g, Element &r) const
Element &	nonzerorandom (const Random &g, Element &a) const
std::ostream &	write (std::ostream &os) const
	Print field. More...
std::ostream &	write (std::ostream &os, const Element &a) const
	Print field element. More...
std::istream &	read (std::istream &is, Element &a) const
	Read field element. More...
Input/Output Operations
std::ostream &	write (std::ostream &os, std::string F) const
	Read field. More...
std::istream &	read (std::istream &is) const
	Read field. More...
Comparison Predicates
bool	areEqual (const Element &x, const Element &y) const
	x == y More...
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 More...
Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z More...
Element &	mul (Element &x, const Element &y, const Element &z) const
	x := y*z More...
Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z More...
Element &	mod (Element &x, const Element &y, const Element &z) const
	x := y mod z More...
Element &	neg (Element &x, const Element &y) const
	x := -y More...
Element &	inv (Element &x, const Element &y) const
	x := 1/y More...
Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y More...
Element &	axpyin (Element &z, const Element &a, const Element &x) const
	z := a*x + z More...
Element &	axmy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x - y More...
Element &	axmyin (Element &z, const Element &a, const Element &x) const
	z := a*x - z More...
Element &	maxpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := y - a*x More...
Element &	maxpyin (Element &z, const Element &a, const Element &x) const
	z := z - a*x More...
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 More...
Element &	subin (Element &x, const Element &y) const
	x := x - y More...
Element &	mulin (Element &x, const Element &y) const
	x := x*y More...
Element &	divin (Element &x, const Element &y) const
	x := x/y More...
Element &	modin (Element &x, const Element &y) const
	x := x mod y More...
Element &	negin (Element &x) const
	x := -x More...
Element &	invin (Element &x) const
	x := 1/x More...

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

Data Fields
const Element	one
const Element	zero
const Element	mOne

Member Typedef Documentation

Element

using Element = Element

inherited

Rep

using Rep = Element

inherited

Residu_t

using Residu_t = Element

inherited

Element_ptr

using Element_ptr = Element*

inherited

ConstElement_ptr

using ConstElement_ptr = const Element*

inherited

RandIter

typedef DomainRandIter<Self_t>::RandIter RandIter

inherited

NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

inherited

ConstElement

typedef const Element ConstElement

inherited

Member Enumeration Documentation

anonymous enum

anonymous enum

inherited

Member Function Documentation

residu()

Residu_t residu ( ) const

inlineinherited

size()

Residu_t size ( ) const

inlineinherited

cardinality() [1/2]

Residu_t cardinality ( ) const

inlineinherited

cardinality() [2/2]

T& cardinality ( T &  c ) const

inlineinherited

characteristic() [1/2]

Residu_t characteristic ( ) const

inlineinherited

characteristic() [2/2]

T& characteristic ( T &  c ) const

inlineinherited

maxCardinality()

static Residu_t maxCardinality ( )

inlinestaticinherited

minCardinality()

static Residu_t minCardinality ( )

inlinestaticinherited

operator==()

bool operator== ( const Self_t &  F ) const

inlineinherited

operator!=()

bool operator!= ( const Self_t &  F ) const

inlineinherited

isZero()

bool isZero ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isOne()

bool isOne ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isMOne()

bool isMOne ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isUnit()

bool isUnit ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

abs() [1/2]

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

inlineinherited

abs() [2/2]

Element abs ( const Element &  a ) const

inlineinherited

compare()

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

inlineinherited

init() [1/2]

Element& init ( Element &  x ) const

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

init() [2/2]

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

inlineinherited

assign()

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

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

convert()

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

inlineinherited

reduce() [1/2]

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

inlineinherited

reduce() [2/2]

Element& reduce ( Element &  x ) const

inlineinherited

minElement()

Element minElement ( ) const

inlineinherited

maxElement()

Element maxElement ( ) const

inlineinherited

random()

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

inlineinherited

nonzerorandom()

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

inlineinherited

type_string()

static const std::string type_string ( )

inlinestaticinherited

write() [1/3]

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

inlinevirtualinherited

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]

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

inlinevirtualinherited

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 >.

write() [3/3]

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() [1/2]

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

inlinevirtualinherited

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 >.

read() [2/2]

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.

areEqual()

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

inlinevirtualinherited

x == y

Implements RingInterface< _Element >.

add()

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

inlinevirtualinherited

x := y + z

Implements RingInterface< _Element >.

sub()

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

inlinevirtualinherited

x := y - z

Implements RingInterface< _Element >.

mul()

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

inlinevirtualinherited

x := y*z

Implements RingInterface< _Element >.

div()

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

inlineinherited

x := y/z

mod()

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

inlineinherited

x := y mod z

neg()

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

inlinevirtualinherited

x := -y

Implements RingInterface< _Element >.

inv()

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

inlineinherited

x := 1/y

axpy()

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

inlinevirtualinherited

z := a*x + y

Implements RingInterface< _Element >.

axpyin()

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

inlinevirtualinherited

z := a*x + z

Implements RingInterface< _Element >.

axmy()

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

inlinevirtualinherited

z := a*x - y

Implements RingInterface< _Element >.

axmyin()

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

inlinevirtualinherited

z := a*x - z

Implements RingInterface< _Element >.

maxpy()

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

inlinevirtualinherited

z := y - a*x

Implements RingInterface< _Element >.

maxpyin()

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

inlinevirtualinherited

z := z - a*x

Implements RingInterface< _Element >.

addin()

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

inlinevirtualinherited

x := x + y

Implements RingInterface< _Element >.

subin()

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

inlinevirtualinherited

x := x - y

Implements RingInterface< _Element >.

mulin()

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

inlinevirtualinherited

x := x*y

Implements RingInterface< _Element >.

divin()

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

inlineinherited

x := x/y

modin()

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

inlineinherited

x := x mod y

negin()

Element& negin ( Element &  x ) const

inlinevirtualinherited

x := -x

Implements RingInterface< _Element >.

invin()

Element& invin ( Element &  x ) const

inlineinherited

x := 1/x

Field Documentation

one

const Element one

inherited

zero

const Element zero

inherited

mOne

const Element mOne

inherited

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

• random-integer.h
• zring.h