A field of fractions templated by an arbitrary BPASGCDDomain. More...

#include <Fraction.hpp>

Simplified semantic inheritance diagram for Fraction< Domain >:

Full inheritance diagram for Fraction< Domain >:

Public Member Functions
	Fraction ()
	Construct the zero fraction function. More...

	Fraction (const Fraction< Domain > &b)
	Copy constructor. More...

	Fraction (Domain a, Domain b)
	constructor with two parameter More...

	~Fraction ()
	Deconstructor for fraction. More...

void	setNumerator (const Domain &b)

void	setDenominator (const Domain &b)

void	set (const Domain &a, const Domain &b)

Domain	numerator () const
	Get the fraction's numerator. More...

Domain	denominator () const
	Get the fraction's denominator. More...

bool	operator!= (const Fraction< Domain > &b) const
	Inequality test,. More...

bool	operator== (const Fraction< Domain > &b) const
	Equality test,. More...

Fraction< Domain >	operator+ (const Fraction< Domain > &b) const
	Addition.

Fraction< Domain > &	operator+= (const Fraction< Domain > &b)
	Addition assignment.

Fraction< Domain >	operator- (const Fraction< Domain > &b) const
	Subtraction.

Fraction< Domain > &	operator-= (const Fraction< Domain > &b)
	Subtraction assignment.

Fraction< Domain >	operator* (const Fraction< Domain > &b) const
	Multiplication.

Fraction< Domain > &	operator*= (const Fraction< Domain > &b)
	Multiplication assignment.

Fraction< Domain >	operator/ (const Fraction< Domain > &b) const
	Exact division. More...

Fraction< Domain > &	operator/= (const Fraction< Domain > &b)
	Exact division assignment. More...

Fraction< Domain >	operator- () const
	Negation.

Fraction< Domain >	operator^ (long long int e) const
	Overload operator ^ replace xor operation by exponentiation. More...

Fraction< Domain > &	operator^= (long long int e)
	Overload operator ^= replace xor operation by exponentiation. More...

Fraction< Domain >	inverse () const
	Get the inverse of *this. More...

bool	isZero () const
	Determine if *this ring element is zero, that is the additive identity. More...

void	zero ()
	Make *this ring element zero.

bool	isOne () const
	Determine if *this ring element is one, that is the multiplication identity. More...

void	one ()
	Make *this ring element one.

bool	isNegativeOne () const

void	negativeOne ()

int	isConstant () const

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

Fraction< Domain > &	operator= (const Fraction< Domain > &b)
	Overload operator =. More...

void	print (std::ostream &ostream) const
	Print the Ring element. More...

Fraction< Domain >	quotient (const Fraction< Domain > &b) const
	Get the quotient of *this and b. More...

Fraction< Domain >	remainder (const Fraction< Domain > &b) const
	Get the remainder of *this and b. More...

Fraction< Domain >	operator% (const Fraction< Domain > &b) const
	Get the remainder of *this and b;. More...

Fraction< Domain > &	operator%= (const Fraction< Domain > &b)
	Assign this to be the remainder of this and b. More...

void	canonicalize ()
	Canonicalize this fraction, reducing terms as needed.

void	differentiate ()

void	normalize ()

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

Fraction< Domain >	gcd (const Fraction< Domain > &b) const
	Get GCD of *this and other. More...

Factors< Fraction< Domain > >	squareFree () const
	Compute squarefree factorization of *this. More...

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

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

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

Detailed Description

template<class Domain>
class Fraction< Domain >

A field of fractions templated by an arbitrary BPASGCDDomain.

Constructor & Destructor Documentation

◆ Fraction() [1/3]

template<class Domain>

Fraction< Domain >::Fraction ( )

inline

Construct the zero fraction function.

Parameters

◆ Fraction() [2/3]

template<class Domain>

Fraction< Domain >::Fraction ( const Fraction< Domain > & b )

inline

Copy constructor.

Parameters

b	A rational function

◆ Fraction() [3/3]

template<class Domain>

Fraction< Domain >::Fraction	(	Domain	a,
		Domain	b
	)

inline

constructor with two parameter

Parameters

a	the numerator
b	the denominator

◆ ~Fraction()

template<class Domain>

Fraction< Domain >::~Fraction ( )

inline

Deconstructor for fraction.

Parameters

Member Function Documentation

◆ convertToExpressionTree()

template<class Domain>

ExpressionTree Fraction< Domain >::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ denominator()

template<class Domain>

Domain Fraction< Domain >::denominator ( ) const

virtual

Get the fraction's denominator.

Returns: the denominator

Implements BPASFieldOfFractions< Domain, Fraction< Domain > >.

◆ euclideanDivision()

template<class Domain>

Fraction<Domain> Fraction< Domain >::euclideanDivision	(	const Fraction< Domain > &	b,
		Fraction< Domain > *	q = `NULL`
	)		const

inlinevirtual

Perform the eucldiean division of *this and b.

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

Parameters

	b	the divisor.
[out]	q	a pointer to store the quotient in.

Returns: the remainder.

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ extendedEuclidean()

template<class Domain>

Fraction<Domain> Fraction< Domain >::extendedEuclidean	(	const Fraction< Domain > &	b,
		Fraction< Domain > *	s = `NULL`,
		Fraction< Domain > *	t = `NULL`
	)		const

inlinevirtual

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.

Parameters

	b	the divisor.
[out]	s	the bezout coefficient of this.
[out]	t	the bezout coefficient of b.

Returns: the remainder.

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ gcd()

template<class Domain>

Fraction<Domain> Fraction< Domain >::gcd ( const Fraction< Domain > & other ) const

inlinevirtual

Get GCD of *this and other.

Parameters

other the other element to get a gcd with.

Returns: the gcd.

Implements BPASGCDDomain< Fraction< Domain > >.

◆ inverse()

template<class Domain>

Fraction<Domain> Fraction< Domain >::inverse ( ) const

virtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< Fraction< Domain > >.

◆ isOne()

template<class Domain>

bool Fraction< Domain >::isOne ( ) const

virtual

Determine if *this ring element is one, that is the multiplication identity.

returns true iff *this is one.

Implements BPASRing< Fraction< Domain > >.

◆ isZero()

template<class Domain>

bool Fraction< Domain >::isZero ( ) const

virtual

Determine if *this ring element is zero, that is the additive identity.

returns true iff *this is zero.

Implements BPASRing< Fraction< Domain > >.

◆ numerator()

template<class Domain>

Domain Fraction< Domain >::numerator ( ) const

virtual

Get the fraction's numerator.

Returns: the numerator.

Implements BPASFieldOfFractions< Domain, Fraction< Domain > >.

◆ operator!=()

template<class Domain>

bool Fraction< Domain >::operator!= ( const Fraction< Domain > & ) const

virtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< Fraction< Domain > >.

◆ operator%()

template<class Domain>

Fraction<Domain> Fraction< Domain >::operator% ( const Fraction< Domain > & b ) const

virtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ operator%=()

template<class Domain>

Fraction<Domain>& Fraction< Domain >::operator%= ( const Fraction< Domain > & b )

virtual

Assign *this to be the remainder of *this and b.

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ operator/()

template<class Domain>

Fraction<Domain> Fraction< Domain >::operator/ ( const Fraction< Domain > & d ) const

virtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< Fraction< Domain > >.

◆ operator/=()

template<class Domain>

Fraction<Domain>& Fraction< Domain >::operator/= ( const Fraction< Domain > & d )

virtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< Fraction< Domain > >.

◆ operator=()

template<class Domain>

Fraction<Domain>& Fraction< Domain >::operator= ( const Fraction< Domain > & b )

virtual

Overload operator =.

Parameters

b	A rational function

Implements BPASRing< Fraction< Domain > >.

◆ operator==()

template<class Domain>

bool Fraction< Domain >::operator== ( const Fraction< Domain > & ) const

virtual

Equality test,.

returns true iff equal

Implements BPASRing< Fraction< Domain > >.

◆ operator^()

template<class Domain>

Fraction<Domain> Fraction< Domain >::operator^ ( long long int e ) const

virtual

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

Implements BPASRing< Fraction< Domain > >.

◆ operator^=()

template<class Domain>

Fraction<Domain>& Fraction< Domain >::operator^= ( long long int e )

virtual

Overload operator ^= replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

Implements BPASRing< Fraction< Domain > >.

◆ print()

template<class Domain>

void Fraction< Domain >::print ( std::ostream & ostream ) const

virtual

Print the Ring element.

Derived classes may override this to get custom printing that may be more expressive (and prettier) than expression tree printing.

Reimplemented from BPASRing< Fraction< Domain > >.

◆ quotient()

template<class Domain>

Fraction<Domain> Fraction< Domain >::quotient ( const Fraction< Domain > & b ) const

virtual

Get the quotient of *this and b.

Parameters

b	the divisor

Returns: the quotient

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ remainder()

template<class Domain>

Fraction<Domain> Fraction< Domain >::remainder ( const Fraction< Domain > & b ) const

virtual

Get the remainder of *this and b.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< Fraction< Domain > >.

◆ squareFree()

template<class Domain>

Factors<Fraction<Domain> > Fraction< Domain >::squareFree ( ) const

inlinevirtual

Compute squarefree factorization of *this.

Returns: the square free factorization as a Factors object.

Implements BPASGCDDomain< Fraction< Domain > >.

◆ unitCanonical()

template<class Domain>

Fraction<Domain> Fraction< Domain >::unitCanonical	(	Fraction< Domain > *	u = `NULL`,
		Fraction< Domain > *	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< Fraction< Domain > >.

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

include/Ring/Fraction.hpp

Public Member Functions

Detailed Description

template<class Domain> class Fraction< Domain >

Constructor & Destructor Documentation

◆ Fraction() [1/3]

◆ Fraction() [2/3]

◆ Fraction() [3/3]

◆ ~Fraction()

Member Function Documentation

◆ convertToExpressionTree()

◆ denominator()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isOne()

◆ isZero()

◆ numerator()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator^()

◆ operator^=()

◆ print()

◆ quotient()

◆ remainder()

◆ squareFree()

◆ unitCanonical()

template<class Domain>
class Fraction< Domain >