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Public Types | Public Member Functions | Data Fields
QField< Rational > Class Referenceabstract

Rational Domain. More...

#include <qfield.h>

+ Inheritance diagram for QField< Rational >:
+ Collaboration diagram for QField< Rational >:

Public Types

using Self_t = QField< Element >
 
typedef Rational Element
 
typedef Rational Rep
 
typedef int64_t Residu_t
 
typedef GeneralRingRandIter< Self_t > RandIter
 
typedef GeneralRingNonZeroRandIter< Self_t > NonZeroRandIter
 
typedef Element * Element_ptr
 
typedef const Element ConstElement
 
typedef const Element * ConstElement_ptr
 

Public Member Functions

 QField ()
 
template<class X >
 QField (const X &x)
 
int operator== (const QField< Element > &) const
 
int operator!= (const QField< Element > &) const
 
Residu_t characteristic () const
 
Residu_t cardinality () const
 
template<typename T >
T & cardinality (T &c) const
 
template<typename T >
T & characteristic (T &c) const
 
Rep & init (Rep &a) const
 
Rep & init (Rep &a, const Integer &n, const Integer &d) const
 
template<class XXX >
Rep & init (Rep &r, const XXX &x) const
 
template<class XXX >
XXX & convert (XXX &x, const Rep &a) const
 
Rep & assign (Rep &a, const Rep &b) const
 
Integer & get_num (Integer &n, const Element &r) const
 
Integer & get_den (Integer &d, const Element &r) const
 
Rep & mul (Rep &r, const Rep &a, const Rep &b) const
 
Rep & div (Rep &r, const Rep &a, const Rep &b) const
 
Rep & add (Rep &r, const Rep &a, const Rep &b) const
 
Rep & sub (Rep &r, const Rep &a, const Rep &b) const
 
Rep & mulin (Rep &r, const Rep &a) const
 
Rep & divin (Rep &r, const Rep &a) const
 
Rep & addin (Rep &r, const Rep &a) const
 
Rep & subin (Rep &r, const Rep &a) const
 
Rep & axpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
 
Rep & axpyin (Rep &r, const Rep &a, const Rep &b) const
 
Rep & maxpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
 
Rep & axmy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
 
Rep & axmyin (Rep &r, const Rep &a, const Rep &b) const
 
Rep & maxpyin (Rep &r, const Rep &a, const Rep &b) const
 
Rep & neg (Rep &r, const Rep &a) const
 
Rep & negin (Rep &r) const
 
Rep & inv (Rep &r, const Rep &a) const
 
Rep & invin (Rep &r) const
 
Rep & pow (Rep &r, const Rep &n, const uint64_t l) const
 
Rep & pow (Rep &r, const Rep &n, const uint32_t l) const
 
Rep & ratrecon (Rep &r, const Integer &f, const Integer &m, const Integer &k, bool recurs=false) const
 
Rep & ratrecon (Rep &r, const Integer &f, const Integer &m, bool recurs=true) const
 
size_t length (const Rep &a) const
 
int sign (const Rep &a) const
 
bool isOne (const Rep &a) const
 
bool isMOne (const Rep &a) const
 
bool isUnit (const Rep &a) const
 
bool isZero (const Rep &a) const
 
bool areEqual (const Rep &a, const Rep &b) const
 
int areNEqual (const Rep &a, const Rep &b) const
 
template<class MyRandIter >
Rep & random (MyRandIter &g, Rep &r, int64_t s=1) const
 
template<class MyRandIter >
Rep & random (MyRandIter &g, Rep &r, const Rep &b) const
 
template<class MyRandIter >
Rep & nonzerorandom (MyRandIter &g, Rep &r, int64_t s=1) const
 
template<class MyRandIter >
Rep & nonzerorandom (MyRandIter &g, Rep &r, const Rep &b) const
 
std::istream & read (std::istream &i)
 
std::ostream & write (std::ostream &o) const
 
std::istream & read (std::istream &i, Rep &n) const
 
std::ostream & write (std::ostream &o, const Rep &n) const
 
virtual bool isZero (const Element &a) const =0
 
virtual bool isOne (const Element &a) const =0
 
virtual bool isMOne (const Element &a) const =0
 
virtual bool isUnit (const Element &a) const =0
 
virtual bool areEqual (const Element &a, const Element &b) const =0
 
virtual Element & init (Element &r) const =0
 
virtual Element & assign (Element &r, const Element &a) const =0
 
virtual Element & mul (Element &r, const Element &a, const Element &b) const =0
 
virtual Element & add (Element &r, const Element &a, const Element &b) const =0
 
virtual Element & sub (Element &r, const Element &a, const Element &b) const =0
 
virtual Element & neg (Element &r, const Element &a) const =0
 
virtual Element & mulin (Element &r, const Element &a) const =0
 
virtual Element & addin (Element &r, const Element &a) const =0
 
virtual Element & subin (Element &r, const Element &a) const =0
 
virtual Element & negin (Element &r) const =0
 
virtual Element & axpy (Element &r, const Element &a, const Element &x, const Element &y) const =0
 
virtual Element & axpyin (Element &r, const Element &a, const Element &x) const =0
 
virtual Element & axmy (Element &r, const Element &a, const Element &x, const Element &y) const =0
 
virtual Element & axmyin (Element &r, const Element &a, const Element &x) const =0
 
virtual Element & maxpy (Element &r, const Element &a, const Element &x, const Element &y) const =0
 
virtual Element & maxpyin (Element &r, const Element &a, const Element &x) const =0
 
virtual std::ostream & write (std::ostream &s, const Element &a) const =0
 
virtual std::istream & read (std::istream &s, Element &a) const =0
 

Data Fields

const Element one
 
const Element mOne
 
const Element zero
 

Detailed Description

Rational Domain.

Member Typedef Documentation

◆ Self_t

using Self_t = QField<Element>

◆ Element

typedef Rational Element

◆ Rep

typedef Rational Rep

◆ Residu_t

typedef int64_t Residu_t

◆ RandIter

typedef GeneralRingRandIter<Self_t> RandIter

◆ NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

◆ Element_ptr

typedef Element* Element_ptr
inherited

◆ ConstElement

typedef const Element ConstElement
inherited

◆ ConstElement_ptr

typedef const Element* ConstElement_ptr
inherited

Constructor & Destructor Documentation

◆ QField() [1/2]

QField ( )
inline

◆ QField() [2/2]

QField ( const X &  x)
inline

Member Function Documentation

◆ operator==()

int operator== ( const QField< Element > &  ) const
inline

◆ operator!=()

int operator!= ( const QField< Element > &  ) const
inline

◆ characteristic() [1/2]

Residu_t characteristic ( ) const
inline

◆ cardinality() [1/2]

Residu_t cardinality ( ) const
inline

◆ cardinality() [2/2]

T& cardinality ( T &  c) const
inline

◆ characteristic() [2/2]

T& characteristic ( T &  c) const
inline

◆ init() [1/4]

Rep& init ( Rep &  a) const
inline

◆ init() [2/4]

Rep& init ( Rep &  a,
const Integer &  n,
const Integer &  d 
) const
inline

◆ init() [3/4]

Rep& init ( Rep &  r,
const XXX &  x 
) const
inline

◆ convert()

XXX& convert ( XXX &  x,
const Rep &  a 
) const
inline

◆ assign() [1/2]

Rep& assign ( Rep &  a,
const Rep &  b 
) const
inline

◆ get_num()

Integer& get_num ( Integer &  n,
const Element &  r 
) const
inline

◆ get_den()

Integer& get_den ( Integer &  d,
const Element &  r 
) const
inline

◆ mul() [1/2]

Rep& mul ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ div()

Rep& div ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inlinevirtual

Implements FieldInterface< Rational >.

◆ add() [1/2]

Rep& add ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ sub() [1/2]

Rep& sub ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ mulin() [1/2]

Rep& mulin ( Rep &  r,
const Rep &  a 
) const
inline

◆ divin()

Rep& divin ( Rep &  r,
const Rep &  a 
) const
inlinevirtual

Implements FieldInterface< Rational >.

◆ addin() [1/2]

Rep& addin ( Rep &  r,
const Rep &  a 
) const
inline

◆ subin() [1/2]

Rep& subin ( Rep &  r,
const Rep &  a 
) const
inline

◆ axpy() [1/2]

Rep& axpy ( Rep &  r,
const Rep &  a,
const Rep &  b,
const Rep &  c 
) const
inline

◆ axpyin() [1/2]

Rep& axpyin ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ maxpy() [1/2]

Rep& maxpy ( Rep &  r,
const Rep &  a,
const Rep &  b,
const Rep &  c 
) const
inline

◆ axmy() [1/2]

Rep& axmy ( Rep &  r,
const Rep &  a,
const Rep &  b,
const Rep &  c 
) const
inline

◆ axmyin() [1/2]

Rep& axmyin ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ maxpyin() [1/2]

Rep& maxpyin ( Rep &  r,
const Rep &  a,
const Rep &  b 
) const
inline

◆ neg() [1/2]

Rep& neg ( Rep &  r,
const Rep &  a 
) const
inline

◆ negin() [1/2]

Rep& negin ( Rep &  r) const
inline

◆ inv()

Rep& inv ( Rep &  r,
const Rep &  a 
) const
inlinevirtual

Implements FieldInterface< Rational >.

◆ invin()

Rep& invin ( Rep &  r) const
inlinevirtual

Implements FieldInterface< Rational >.

◆ pow() [1/2]

Rep& pow ( Rep &  r,
const Rep &  n,
const uint64_t  l 
) const
inline

◆ pow() [2/2]

Rep& pow ( Rep &  r,
const Rep &  n,
const uint32_t  l 
) const
inline

◆ ratrecon() [1/2]

Rep& ratrecon ( Rep &  r,
const Integer &  f,
const Integer &  m,
const Integer &  k,
bool  recurs = false 
) const
inline

◆ ratrecon() [2/2]

Rep& ratrecon ( Rep &  r,
const Integer &  f,
const Integer &  m,
bool  recurs = true 
) const
inline

◆ length()

size_t length ( const Rep &  a) const
inline

◆ sign()

int sign ( const Rep &  a) const
inline

◆ isOne() [1/2]

bool isOne ( const Rep &  a) const
inline

◆ isMOne() [1/2]

bool isMOne ( const Rep &  a) const
inline

◆ isUnit() [1/2]

bool isUnit ( const Rep &  a) const
inline

◆ isZero() [1/2]

bool isZero ( const Rep &  a) const
inline

◆ areEqual() [1/2]

bool areEqual ( const Rep &  a,
const Rep &  b 
) const
inline

◆ areNEqual()

int areNEqual ( const Rep &  a,
const Rep &  b 
) const
inline

◆ random() [1/2]

Rep& random ( MyRandIter &  g,
Rep &  r,
int64_t  s = 1 
) const
inline

◆ random() [2/2]

Rep& random ( MyRandIter &  g,
Rep &  r,
const Rep &  b 
) const
inline

◆ nonzerorandom() [1/2]

Rep& nonzerorandom ( MyRandIter &  g,
Rep &  r,
int64_t  s = 1 
) const
inline

◆ nonzerorandom() [2/2]

Rep& nonzerorandom ( MyRandIter &  g,
Rep &  r,
const Rep &  b 
) const
inline

◆ read() [1/3]

std::istream& read ( std::istream &  i)
inline

◆ write() [1/3]

std::ostream& write ( std::ostream &  o) const
inlinevirtual

Implements RingInterface< _Element >.

◆ read() [2/3]

std::istream& read ( std::istream &  i,
Rep &  n 
) const
inline

◆ write() [2/3]

std::ostream& write ( std::ostream &  o,
const Rep &  n 
) const
inline

◆ isZero() [2/2]

virtual bool isZero ( const Element &  a) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

◆ isOne() [2/2]

virtual bool isOne ( const Element &  a) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

◆ isMOne() [2/2]

virtual bool isMOne ( const Element &  a) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

◆ isUnit() [2/2]

virtual bool isUnit ( const Element &  a) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

◆ areEqual() [2/2]

virtual bool areEqual ( const Element &  a,
const Element &  b 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ init() [4/4]

virtual Element& init ( Element &  r) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, UnparametricZRing< Integer >, and UnparametricOperations< _Element >.

◆ assign() [2/2]

virtual Element& assign ( Element &  r,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, UnparametricZRing< Integer >, and UnparametricOperations< _Element >.

◆ mul() [2/2]

virtual Element& mul ( Element &  r,
const Element &  a,
const Element &  b 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ add() [2/2]

virtual Element& add ( Element &  r,
const Element &  a,
const Element &  b 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ sub() [2/2]

virtual Element& sub ( Element &  r,
const Element &  a,
const Element &  b 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ neg() [2/2]

virtual Element& neg ( Element &  r,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ mulin() [2/2]

virtual Element& mulin ( Element &  r,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ addin() [2/2]

virtual Element& addin ( Element &  r,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ subin() [2/2]

virtual Element& subin ( Element &  r,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ negin() [2/2]

virtual Element& negin ( Element &  r) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ axpy() [2/2]

virtual Element& axpy ( Element &  r,
const Element &  a,
const Element &  x,
const Element &  y 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ axpyin() [2/2]

virtual Element& axpyin ( Element &  r,
const Element &  a,
const Element &  x 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ axmy() [2/2]

virtual Element& axmy ( Element &  r,
const Element &  a,
const Element &  x,
const Element &  y 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ axmyin() [2/2]

virtual Element& axmyin ( Element &  r,
const Element &  a,
const Element &  x 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ maxpy() [2/2]

virtual Element& maxpy ( Element &  r,
const Element &  a,
const Element &  x,
const Element &  y 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ maxpyin() [2/2]

virtual Element& maxpyin ( Element &  r,
const Element &  a,
const Element &  x 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >.

◆ write() [3/3]

virtual std::ostream& write ( std::ostream &  s,
const Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >, UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

◆ read() [3/3]

virtual std::istream& read ( std::istream &  s,
Element &  a 
) const
pure virtualinherited

Implemented in UnparametricOperations< _Element >, UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Integer >.

Field Documentation

◆ one

const Element one

◆ mOne

const Element mOne

◆ zero

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