Rational Class Reference

Rationals. No doc. More...

#include <givrational.h>

Collaboration diagram for Rational:

Public Types
enum	ReduceFlag { Reduce = 0x1 , NoReduce = 0x0 }

Public Member Functions
	Rational (Neutral n=Neutral::zero)
	Rational (int32_t n)
	Rational (uint32_t n)
	Rational (int64_t n)
	Rational (uint64_t n)
	Rational (int64_t n, int64_t d)
	Rational (uint64_t n, uint64_t d)
	Rational (int32_t n, int32_t d)
	Rational (uint32_t n, uint32_t d)
	Rational (double x)
	Rational (const char *s)
	Rational (const Integer &n)
	Rational (const Integer &n, const Integer &d, int red=1)
	Rational (const Integer &f, const Integer &m, const Integer &k, bool recurs=false)
	Rational number reconstruction. More...
	Rational (const Rational &)
Rational &	operator= (const Rational &)
Rational &	logcpy (const Rational &)
Rational &	copy (const Rational &)
Rational	operator+ (const Rational &r) const
Rational	operator- (const Rational &r) const
Rational	operator- () const
Rational	operator+ () const
Rational	operator* (const Rational &r) const
Rational	operator/ (const Rational &r) const
Rational &	operator+= (const Rational &r)
Rational &	operator-= (const Rational &r)
Rational &	operator*= (const Rational &r)
Rational &	operator/= (const Rational &r)
Integer	operator% (const Integer &r) const
const Integer	nume () const
const Integer	deno () const
std::ostream &	print (std::ostream &o) const
Rational	reduce (const Rational &R) const
	operator short () const
	operator uint16_t () const
	operator uint8_t () const
	operator uint32_t () const
	operator int () const
	operator signed char () const
	operator uint64_t () const
	operator int64_t () const
	operator std::string () const
	operator float () const
	operator double () const
	Rational (givNoInit)

Static Public Member Functions
static void	SetReduce ()
static void	SetNoReduce ()
static bool	ratrecon (Integer &num, Integer &den, const Integer &f, const Integer &m, const Integer &k, bool forcereduce=true, bool recurs=true)
static bool	RationalReconstruction (Integer &num, Integer &den, const Integer &f, const Integer &m)
static bool	RationalReconstruction (Integer &num, Integer &den, const Integer &f, const Integer &m, const Integer &numbound, bool forcereduce=true, bool recursive=true)
static bool	RationalReconstruction (Integer &num, Integer &den, const Integer &f, const Integer &m, const Integer &numbound, const Integer &denbound)

Static Public Attributes
static const Rational	zero
static const Rational	one
static const Rational	mOne
static GivModule	Module

Protected Member Functions
Rational &	reduce ()
bool	ratrecon (const Integer &f, const Integer &m, const Integer &k, bool forcereduce=true, bool recurs=false)
	num/den \equiv f modulo m, with a bound k on num forcereduce : must return a reduced fraction num/den recurs : tries to augment the given bound k if failure More...

Static Protected Member Functions
static void	Init (int *argc, char ***argv)
static void	End ()

Protected Attributes
Integer	num
Integer	den

Static Protected Attributes
static ReduceFlag	flags = Rational::Reduce

Friends
class	GivModule
class	QField< Rational >
int	compare (const Rational &a, const Rational &b)
int	absCompare (const Rational &a, const Rational &b)
const Rational	pow (const Rational &r, const int64_t l)
const Integer	floor (const Rational &r)
const Integer	ceil (const Rational &r)
const Integer	round (const Rational &r)
const Integer	trunc (const Rational &r)
const Rational	abs (const Rational &r)
const Rational	pow (const Rational &n, uint32_t l)
const Rational	pow (const Rational &n, uint64_t l)
uint64_t	length (const Rational &r)
int	sign (const Rational &r)
int	isZero (const Rational &r)
int	isOne (const Rational &r)
int	isMOne (const Rational &r)
int	isInteger (const Rational &r)

Detailed Description

Rationals. No doc.

Member Enumeration Documentation

ReduceFlag

enum ReduceFlag

Enumerator
Reduce
NoReduce

Constructor & Destructor Documentation

Rational() [1/16]

Rational

(

Neutral

n = Neutral::zero

)

Rational() [2/16]

Rational

(

int32_t

n

)

Rational() [3/16]

Rational

(

uint32_t

n

)

Rational() [4/16]

Rational

(

int64_t

n

)

Rational() [5/16]

Rational

(

uint64_t

n

)

Rational() [6/16]

Rational	(	int64_t	n,
		int64_t	d
	)

Rational() [7/16]

Rational	(	uint64_t	n,
		uint64_t	d
	)

Rational() [8/16]

Rational	(	int32_t	n,
		int32_t	d
	)

Rational() [9/16]

Rational	(	uint32_t	n,
		uint32_t	d
	)

Rational() [10/16]

Rational

(

double

x

)

Rational() [11/16]

Rational

(

const char *

s

)

Rational() [12/16]

Rational

(

const Integer &

n

)

Rational() [13/16]

Rational	(	const Integer &	n,
		const Integer &	d,
		int	red = 1
	)

Rational() [14/16]

Rational	(	const Integer &	f,
		const Integer &	m,
		const Integer &	k,
		bool	recurs = false
	)

Rational number reconstruction.

, with and

Bibliography:

• von zur Gathen & Gerhard Modern Computer Algebra, 5.10, Cambridge Univ. Press 1999]

Rational() [15/16]

Rational

(

const Rational &

r

)

Rational() [16/16]

Rational

(

givNoInit

)

Member Function Documentation

operator=()

Rational & operator=

(

const Rational &

r

)

logcpy()

Rational & logcpy

(

const Rational &

r

)

copy()

Rational & copy

(

const Rational &

r

)

operator+() [1/2]

Rational operator+

(

const Rational &

r

)

const

operator-() [1/2]

Rational operator-

(

const Rational &

r

)

const

operator-() [2/2]

Rational operator-

(

)

const

operator+() [2/2]

Rational operator+ ( ) const

inline

operator*()

Rational operator*

(

const Rational &

r

)

const

operator/()

Rational operator/

(

const Rational &

r

)

const

operator+=()

Rational & operator+=

(

const Rational &

r

)

operator-=()

Rational & operator-=

(

const Rational &

r

)

operator*=()

Rational & operator*=

(

const Rational &

r

)

operator/=()

Rational & operator/=

(

const Rational &

r

)

operator%()

Integer operator%

(

const Integer &

r

)

const

nume()

const Integer nume ( ) const

inline

deno()

const Integer deno ( ) const

inline

print()

std::ostream & print

(

std::ostream &

o

)

const

reduce() [1/2]

Rational reduce ( const Rational &  R ) const

inline

SetReduce()

void SetReduce ( )

static

SetNoReduce()

void SetNoReduce ( )

static

Examples

examples/Rational/polydouble.C.

operator short()

operator short ( ) const

inline

operator uint16_t()

operator uint16_t ( ) const

inline

operator uint8_t()

operator uint8_t ( ) const

inline

operator uint32_t()

operator uint32_t ( ) const

inline

operator int()

operator int ( ) const

inline

operator signed char()

operator signed char ( ) const

inline

operator uint64_t()

operator uint64_t ( ) const

inline

operator int64_t()

operator int64_t ( ) const

inline

operator std::string()

operator std::string ( ) const

inline

operator float()

operator float ( ) const

inline

operator double()

operator double ( ) const

inline

reduce() [2/2]

Rational & reduce ( )

protected

Init()

void Init ( int *  argc, char ***  argv  )

staticprotected

End()

void End ( )

staticprotected

ratrecon() [1/2]

bool ratrecon ( const Integer &  f, const Integer &  m, const Integer &  k, bool  forcereduce = true, bool  recurs = false  )

protected

num/den \equiv f modulo m, with a bound k on num forcereduce : must return a reduced fraction num/den recurs : tries to augment the given bound k if failure

ratrecon() [2/2]

bool ratrecon ( Integer &  num, Integer &  den, const Integer &  f, const Integer &  m, const Integer &  k, bool  forcereduce = true, bool  recurs = true  )

static

RationalReconstruction() [1/3]

bool RationalReconstruction ( Integer &  num, Integer &  den, const Integer &  f, const Integer &  m  )

static

RationalReconstruction() [2/3]

bool RationalReconstruction ( Integer &  num, Integer &  den, const Integer &  f, const Integer &  m, const Integer &  numbound, bool  forcereduce = true, bool  recursive = true  )

static

RationalReconstruction() [3/3]

bool RationalReconstruction ( Integer &  num, Integer &  den, const Integer &  f, const Integer &  m, const Integer &  numbound, const Integer &  denbound  )

static

Friends And Related Function Documentation

GivModule

friend class GivModule

friend

QField< Rational >

friend class QField< Rational >

friend

compare

int compare ( const Rational &  a, const Rational &  b  )

friend

absCompare

int absCompare ( const Rational &  a, const Rational &  b  )

friend

pow [1/3]

const Rational pow ( const Rational &  r, const int64_t  l  )

friend

floor

const Integer floor ( const Rational &  r )

friend

ceil

const Integer ceil ( const Rational &  r )

friend

round

const Integer round ( const Rational &  r )

friend

trunc

const Integer trunc ( const Rational &  r )

friend

abs

const Rational abs ( const Rational &  r )

friend

pow [2/3]

const Rational pow ( const Rational &  n, uint32_t  l  )

friend

pow [3/3]

const Rational pow ( const Rational &  n, uint64_t  l  )

friend

length

uint64_t length ( const Rational &  r )

friend

sign

int sign ( const Rational &  r )

friend

isZero

int isZero ( const Rational &  r )

friend

isOne

int isOne ( const Rational &  r )

friend

isMOne

int isMOne ( const Rational &  r )

friend

isInteger

int isInteger ( const Rational &  r )

friend

Field Documentation

zero

const Rational zero

static

one

const Rational one

static

mOne

const Rational mOne

static

num

Integer num

protected

den

Integer den

protected

flags

Rational::ReduceFlag flags = Rational::Reduce

staticprotected

Module

GivModule Module

static

---

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

• givrational.h
• givrataddsub.C
• givratcpy.C
• givratcstor.C
• givratio.C
• givrational.inl
• givratmisc.C
• givratmuldiv.C
• givratreconstruct.C