An arbitrary-precision rational number. More...

#include <RationalNumber.hpp>

Simplified semantic inheritance diagram for RationalNumber:

Full inheritance diagram for RationalNumber:

Public Member Functions
	RationalNumber (int a, int b=1)

	RationalNumber (const std::string &digits, int base=10)

	RationalNumber (const mpq_t &q)

	RationalNumber (const mpq_class &a)

	RationalNumber (const mpz_class &a, const mpz_class &b=mpz_class(1))

	RationalNumber (const RationalNumber &a)

	RationalNumber (const Integer &a)

	RationalNumber (const ComplexRationalNumber &a)

	RationalNumber (const SmallPrimeField &a)

	RationalNumber (const BigPrimeField &a)

	RationalNumber (const GeneralizedFermatPrimeField &a)

	RationalNumber (const DenseUnivariateIntegerPolynomial &a)

	RationalNumber (const DenseUnivariateRationalPolynomial &a)

	RationalNumber (const SparseUnivariatePolynomial< Integer > &a)

	RationalNumber (const SparseUnivariatePolynomial< RationalNumber > &a)

	RationalNumber (const SparseUnivariatePolynomial< ComplexRationalNumber > &a)

	RationalNumber (const SparseMultivariateRationalPolynomial &a)

template<class Ring >
	RationalNumber (const SparseUnivariatePolynomial< Ring > &a)

RationalNumber *	RNpointer (RationalNumber *a)

RationalNumber *	RNpointer (SmallPrimeField *a)

RationalNumber *	RNpointer (BigPrimeField *a)

RationalNumber *	RNpointer (GeneralizedFermatPrimeField *a)

RationalNumber &	set (int a, int b)

mpq_class	get_mpq () const

mpq_class &	get_mpq_ref ()

const mpq_class &	get_mpq_ref () const

mpq_ptr	get_mpq_t ()

mpq_srcptr	get_mpq_t () const

Integer	get_num () const

double	get_d () const

Integer	get_den () const

bool	isZero () const
	Is a zero. More...

void	zero ()
	Assign to zero. More...

bool	isOne () const
	Is a 1. More...

void	one ()
	Assign to one. More...

bool	isNegativeOne () const
	Is a -1. More...

void	negativeOne ()
	Assign to negative one. More...

int	isConstant () const
	Is a constant. More...

RationalNumber	unitCanonical (RationalNumber u=NULL, RationalNumber v=NULL) const
	Obtain the unit normal (a.k.a canonical associate) of an element. More...

RationalNumber &	operator= (const RationalNumber &a)
	Copy assignment.

RationalNumber	operator+ (const RationalNumber &i) const
	Addition.

RationalNumber &	operator+= (const RationalNumber &i)
	Addition assignment.

RationalNumber	operator- (const RationalNumber &i) const
	Subtraction.

RationalNumber &	operator-= (const RationalNumber &i)
	Subtraction assignment.

RationalNumber	operator- () const
	Negation.

RationalNumber	operator* (const RationalNumber &i) const
	Multiplication.

RationalNumber &	operator*= (const RationalNumber &i)
	Multiplication assignment.

bool	operator== (const RationalNumber &i) const
	Equality test,. More...

bool	operator!= (const RationalNumber &i) const
	Inequality test,. More...

ExpressionTree	convertToExpressionTree () const
	Convert this to an expression tree. More...

RationalNumber	operator/ (const RationalNumber &i) const
	Exact division.

RationalNumber &	operator/= (const RationalNumber &i)
	Exact division assignment.

bool	operator< (const RationalNumber &r) const

bool	operator<= (const RationalNumber &r) const

bool	operator> (const RationalNumber &r) const

bool	operator>= (const RationalNumber &r) const

RationalNumber	gcd (const RationalNumber &b) const
	GCD(a, b) More...

Factors< RationalNumber >	squareFree () const
	Compute squarefree factorization of *this.

RationalNumber	euclideanSize () const
	Get the euclidean size of *this.

RationalNumber	euclideanDivision (const RationalNumber &b, RationalNumber *q=NULL) const
	Perform the eucldiean division of *this and b. More...

RationalNumber	extendedEuclidean (const RationalNumber &b, RationalNumber s=NULL, RationalNumber t=NULL) const
	Perform the extended euclidean division on *this and b. More...

RationalNumber	quotient (const RationalNumber &b) const
	Get the quotient of *this and b.

RationalNumber	remainder (const RationalNumber &b) const
	Get the remainder of *this and b.

RationalNumber	operator^ (long long int e) const
	Overload operator ^ replace xor operation by exponentiation. More...

RationalNumber &	operator^= (long long int e)
	Exponentiation assignment.

RationalNumber	operator% (const RationalNumber &r) const
	Get the remainder of *this and b;.

RationalNumber &	operator%= (const RationalNumber &r)
	Assign this to be the remainder of this and b.

RationalNumber	inverse () const
	Get the inverse of *this.

Static Public Attributes
static mpz_class	characteristic

static RingProperties	properties

Friends
RationalNumber	operator+ (int a, const RationalNumber &r)

RationalNumber	operator- (int a, const RationalNumber &r)

RationalNumber	operator* (int a, const RationalNumber &r)

RationalNumber	operator/ (int a, const RationalNumber &r)

RationalNumber	operator+ (long int a, const RationalNumber &r)

RationalNumber	operator- (long int a, const RationalNumber &r)

RationalNumber	operator* (long int a, const RationalNumber &r)

RationalNumber	operator/ (long int a, const RationalNumber &r)

RationalNumber	abs (const RationalNumber &i)

Detailed Description

An arbitrary-precision rational number.

Member Function Documentation

◆ convertToExpressionTree()

ExpressionTree RationalNumber::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ euclideanDivision()

RationalNumber RationalNumber::euclideanDivision	(	const RationalNumber &	b,
		RationalNumber *	q = `NULL`
	)		const

virtual

Perform the eucldiean division of *this and b.

Returns the remainder. If q is not NULL, then returns the quotient in q.

Implements BPASEuclideanDomain< RationalNumber >.

◆ extendedEuclidean()

RationalNumber RationalNumber::extendedEuclidean	(	const RationalNumber &	b,
		RationalNumber *	s = `NULL`,
		RationalNumber *	t = `NULL`
	)		const

virtual

Perform the extended euclidean division on *this and b.

Returns the GCD. If s and t are not NULL, returns the bezout coefficients in them.

Implements BPASEuclideanDomain< RationalNumber >.

◆ gcd()

RationalNumber RationalNumber::gcd ( const RationalNumber & b ) const

inlinevirtual

GCD(a, b)

Parameters

b	The other rational number

Implements BPASGCDDomain< RationalNumber >.

◆ isConstant()

int RationalNumber::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isNegativeOne()

bool RationalNumber::isNegativeOne ( ) const

inline

Is a -1.

Parameters

◆ isOne()

bool RationalNumber::isOne ( ) const

inlinevirtual

Is a 1.

Parameters

Implements BPASRing< RationalNumber >.

◆ isZero()

bool RationalNumber::isZero ( ) const

inlinevirtual

Is a zero.

Parameters

Implements BPASRing< RationalNumber >.

◆ negativeOne()

void RationalNumber::negativeOne ( )

inline

Assign to negative one.

Parameters

◆ one()

void RationalNumber::one ( )

inlinevirtual

Assign to one.

Parameters

Implements BPASRing< RationalNumber >.

◆ operator!=()

bool RationalNumber::operator!= ( const RationalNumber & i ) const

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< RationalNumber >.

◆ operator==()

bool RationalNumber::operator== ( const RationalNumber & i ) const

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< RationalNumber >.

◆ operator^()

RationalNumber RationalNumber::operator^ ( long long int e ) const

inlinevirtual

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation

Implements BPASRing< RationalNumber >.

◆ unitCanonical()

RationalNumber RationalNumber::unitCanonical	(	RationalNumber *	u = `NULL`,
		RationalNumber *	v = `NULL`
	)		const

virtual

Obtain the unit normal (a.k.a canonical associate) of an element.

If either parameters u, v, are non-NULL then the units are returned such that b = ua, v = u^-1. Where b is the unit normal of a, and is the returned value.

Implements BPASRing< RationalNumber >.

◆ zero()

void RationalNumber::zero ( )

inlinevirtual

Assign to zero.

Parameters

Implements BPASRing< RationalNumber >.

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

include/Ring/RationalNumber.hpp

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

◆ convertToExpressionTree()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ isConstant()

◆ isNegativeOne()

◆ isOne()

◆ isZero()

◆ negativeOne()

◆ one()

◆ operator!=()

◆ operator==()

◆ operator^()

◆ unitCanonical()

◆ zero()