A field of fractions templated by an arbitrary BPASGCDDomain making use of factor refinement. More...

#include <SmartFraction.hpp>

Simplified semantic inheritance diagram for SmartFraction< Domain >:

Full inheritance diagram for SmartFraction< Domain >:

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

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

	SmartFraction (std::vector< Factor< Domain >> a, std::vector< Factor< Domain >> b)
	constructor with two parameter More...

	SmartFraction (Domain a, Domain b)

void	setNumerator (const std::vector< std::pair< Domain, int >> &b)

void	setDenominator (const std::vector< std::pair< Domain, int >> &b)

void	set (const std::vector< std::pair< Domain, int >> &a, const std::vector< std::pair< Domain, int >> &b)

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

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

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

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

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

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

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

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

void	normalize ()

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

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

void	zero ()
	Make *this ring element zero.

void	one ()
	Make *this ring element one.

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

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

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

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

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

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

SmartFraction< Domain >	operator- () const
	Negation.

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

SmartFraction< Domain >	operator^ (long long int e) const
	Exponentiation.

SmartFraction< Domain > &	operator^= (long long int e)
	Exponentiation assignment.

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

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

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

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

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

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

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

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

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

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

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

Detailed Description

template<class Domain>
class SmartFraction< Domain >

A field of fractions templated by an arbitrary BPASGCDDomain making use of factor refinement.

Constructor & Destructor Documentation

◆ SmartFraction() [1/3]

template<class Domain>

SmartFraction< Domain >::SmartFraction ( )

inline

Construct the zero fraction function.

Parameters

◆ SmartFraction() [2/3]

template<class Domain>

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

inline

Copy constructor.

Parameters

b	A rational function

◆ SmartFraction() [3/3]

template<class Domain>

SmartFraction< Domain >::SmartFraction	(	std::vector< Factor< Domain >>	a,
		std::vector< Factor< Domain >>	b
	)

inline

constructor with two parameter

Parameters

a	the numerator
b	the denominator

Member Function Documentation

◆ convertToExpressionTree()

template<class Domain>

ExpressionTree SmartFraction< Domain >::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ denominator()

template<class Domain>

Domain SmartFraction< Domain >::denominator ( ) const

virtual

Get the fraction's denominator.

Returns: the denominator

Implements BPASFieldOfFractions< Domain, SmartFraction< Domain > >.

◆ euclideanDivision()

template<class Domain>

SmartFraction<Domain> SmartFraction< Domain >::euclideanDivision	(	const SmartFraction< Domain > &	b,
		SmartFraction< Domain > *	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.

Parameters

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

Returns: the remainder.

Implements BPASEuclideanDomain< SmartFraction< Domain > >.

◆ extendedEuclidean()

template<class Domain>

SmartFraction<Domain> SmartFraction< Domain >::extendedEuclidean	(	const SmartFraction< Domain > &	b,
		SmartFraction< Domain > *	s = `NULL`,
		SmartFraction< 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< SmartFraction< Domain > >.

◆ gcd()

template<class Domain>

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

virtual

Get GCD of *this and other.

Parameters

other the other element to get a gcd with.

Returns: the gcd.

Implements BPASGCDDomain< SmartFraction< Domain > >.

◆ inverse()

template<class Domain>

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

virtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< SmartFraction< Domain > >.

◆ isOne()

template<class Domain>

bool SmartFraction< Domain >::isOne ( ) const

virtual

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

returns true iff *this is one.

Implements BPASRing< SmartFraction< Domain > >.

◆ isZero()

template<class Domain>

bool SmartFraction< Domain >::isZero ( ) const

virtual

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

returns true iff *this is zero.

Implements BPASRing< SmartFraction< Domain > >.

◆ numerator()

template<class Domain>

Domain SmartFraction< Domain >::numerator ( ) const

virtual

Get the fraction's numerator.

Returns: the numerator.

Implements BPASFieldOfFractions< Domain, SmartFraction< Domain > >.

◆ operator!=()

template<class Domain>

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

virtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< SmartFraction< Domain > >.

◆ operator%()

template<class Domain>

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

virtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< SmartFraction< Domain > >.

◆ operator%=()

template<class Domain>

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

virtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< SmartFraction< Domain > >.

◆ operator/()

template<class Domain>

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

virtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< SmartFraction< Domain > >.

◆ operator/=()

template<class Domain>

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

virtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< SmartFraction< Domain > >.

◆ operator==()

template<class Domain>

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

virtual

Equality test,.

returns true iff equal

Implements BPASRing< SmartFraction< Domain > >.

◆ print()

template<class Domain>

void SmartFraction< 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< SmartFraction< Domain > >.

◆ quotient()

template<class Domain>

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

virtual

Get the quotient of *this and b.

Parameters

b	the divisor

Returns: the quotient

Implements BPASEuclideanDomain< SmartFraction< Domain > >.

◆ remainder()

template<class Domain>

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

virtual

Get the remainder of *this and b.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< SmartFraction< Domain > >.

◆ squareFree()

template<class Domain>

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

inlinevirtual

Compute squarefree factorization of *this.

Returns: the square free factorization as a Factors object.

Implements BPASGCDDomain< SmartFraction< Domain > >.

◆ unitCanonical()

template<class Domain>

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

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

include/Ring/SmartFraction.hpp

Public Member Functions

Detailed Description

template<class Domain> class SmartFraction< Domain >

Constructor & Destructor Documentation

◆ SmartFraction() [1/3]

◆ SmartFraction() [2/3]

◆ SmartFraction() [3/3]

Member Function Documentation

◆ convertToExpressionTree()

◆ denominator()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isOne()

◆ isZero()

◆ numerator()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ print()

◆ quotient()

◆ remainder()

◆ squareFree()

◆ unitCanonical()

template<class Domain>
class SmartFraction< Domain >