A univariate rational function templated by a unvariate polynomial over a field. More...

#include <urationalfunction.h>

Simplified semantic inheritance diagram for UnivariateRationalFunction< UnivariatePolynomialOverField, Field >:

Full inheritance diagram for UnivariateRationalFunction< UnivariatePolynomialOverField, Field >:

Public Member Functions
	UnivariateRationalFunction ()
	Construct the zero univariate rational function. More...

	UnivariateRationalFunction (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Copy constructor. More...

	UnivariateRationalFunction (UnivariatePolynomialOverField a, UnivariatePolynomialOverField b)

	~UnivariateRationalFunction ()
	Destroy the rational function. More...

void	setVariableName (Symbol name)

Symbol	variable ()

bool	isProfiling ()

void	setProfiling (bool a)

bool	isAnalyzingError ()

void	setAnalyzingError (bool a)

bool	isPFDLogPart ()

void	setPFDLogPart (bool a)

bool	isFloatingPointPrinting ()

void	setFloatingPointPrinting (bool a)

bool	isMapleOutput ()

void	setMapleOutput ()

bool	isMatlabOutput ()

void	setMatlabOutput ()

void	setNumerator (const UnivariatePolynomialOverField &b)

void	setDenominator (const UnivariatePolynomialOverField &b)

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

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

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

Field	evaluate (const Field &c)

bool	operator!= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Inequality test,. More...

bool	operator== (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Equality test,. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator+ (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Addition.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator+= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Addition assignment.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator- (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Subtraction.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator-= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Subtraction assignment.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator- () const
	Negation.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator^ (long long int e) const
	Overload operator ^ replace xor operation by exponentiation. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator^= (long long int e)
	Overload operator ^= replace xor operation by exponentiation. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	inverse () const
	Get the inverse of *this. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator* (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Multiplication.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator*= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Multiplication assignment.

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator/ (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Exact division. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator/= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Exact division assignment. More...

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

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

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

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Overload operator =. More...

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

void	print (std::ostream &ostream) const
	Overload stream operator <<. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	gcd (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	BPASGCDDomain, BPASEuclideanDomain, BPASField virtual methods. More...

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

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

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

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	quotient (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Get the quotient of *this and b. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	remainder (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Get the remainder of *this and b. More...

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

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >	operator% (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b) const
	Get the remainder of *this and b;. More...

UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	operator%= (const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &b)
	Assign this to be the remainder of this and b. More...

void	hermiteReduce (std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, UnivariateRationalFunction< UnivariatePolynomialOverField, Field > h)

void	integrateRationalFunctionLogPart (std::vector< SparseUnivariatePolynomial< UnivariatePolynomialOverField > > S, std::vector< UnivariatePolynomialOverField > U)

void	differentiate ()

void	integrate (UnivariatePolynomialOverField P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, std::vector< UnivariatePolynomialOverField > U, std::vector< SparseUnivariatePolynomial< UnivariatePolynomialOverField > > S)

void	realSymbolicNumericIntegrate (UnivariatePolynomialOverField P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, std::vector< Field > lg, std::vector< UnivariatePolynomialOverField > Lg, std::vector< Field > atn, std::vector< UnivariatePolynomialOverField > Atn, int prec)

void	realSymbolicNumericIntegrate (UnivariatePolynomialOverField P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, std::vector< Field > lg, std::vector< UnivariatePolynomialOverField > Lg, std::vector< Field > atn, std::vector< UnivariatePolynomialOverField > Atn1, std::vector< UnivariatePolynomialOverField > *Atn2, int prec)

void	realSymbolicNumericIntegratePFD (UnivariatePolynomialOverField P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, std::vector< Field > lg, std::vector< UnivariatePolynomialOverField > Lg, std::vector< Field > atn, std::vector< UnivariatePolynomialOverField > Atn, int prec)

void	realSymbolicNumericIntegrateSimplePFD (UnivariatePolynomialOverField P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > g, std::vector< Field > lg, std::vector< UnivariatePolynomialOverField > Lg, std::vector< Field > atn, std::vector< UnivariatePolynomialOverField > Atn, int prec)

void	printIntegral (UnivariatePolynomialOverField &P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > &g, std::vector< UnivariatePolynomialOverField > &U, std::vector< SparseUnivariatePolynomial< UnivariatePolynomialOverField > > &S)

void	printIntegral (UnivariatePolynomialOverField &P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > &g, std::vector< Field > &lg, std::vector< UnivariatePolynomialOverField > &Lg, std::vector< Field > &atn, std::vector< UnivariatePolynomialOverField > &Atn)

void	printIntegral (UnivariatePolynomialOverField &P, std::vector< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > > &g, std::vector< Field > &lg, std::vector< UnivariatePolynomialOverField > &Lg, std::vector< Field > &atn, std::vector< UnivariatePolynomialOverField > &Atn1, std::vector< UnivariatePolynomialOverField > &Atn2)

void	realSymbolicNumericIntegrate (int prec)

void	integrate ()

Public Attributes
mpz_class	characteristic

Static Public Attributes
static bool	isPrimeField

static bool	isSmallPrimeField

static bool	isComplexField

Detailed Description

template<class UnivariatePolynomialOverField, class Field>
class UnivariateRationalFunction< UnivariatePolynomialOverField, Field >

A univariate rational function templated by a unvariate polynomial over a field.

The univariate polynomial and the coefficient BPASField must be passed separately and explicitly.

Constructor & Destructor Documentation

◆ UnivariateRationalFunction() [1/3]

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::UnivariateRationalFunction ( )

inline

Construct the zero univariate rational function.

Parameters

◆ UnivariateRationalFunction() [2/3]

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::UnivariateRationalFunction ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b )

inline

Copy constructor.

Parameters

b	A rational function

◆ UnivariateRationalFunction() [3/3]

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::UnivariateRationalFunction	(	UnivariatePolynomialOverField	a,
		UnivariatePolynomialOverField	b
	)

inline

Parameters

a	the numerator
b	the denominator

◆ ~UnivariateRationalFunction()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::~UnivariateRationalFunction ( )

inline

Destroy the rational function.

Parameters

Member Function Documentation

◆ convertToExpressionTree()

template<class UnivariatePolynomialOverField, class Field>

ExpressionTree UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::convertToExpressionTree ( ) const

inlinevirtual

Convert this to an expression tree.

returns an expression tree describing *this.

Implements ExpressionTreeConvert.

◆ denominator()

template<class UnivariatePolynomialOverField, class Field>

UnivariatePolynomialOverField UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::denominator ( ) const

inlinevirtual

Get the fraction's denominator.

Returns: the denominator

Implements BPASFieldOfFractions< UnivariatePolynomialOverField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ euclideanDivision()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::euclideanDivision	(	const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	b,
		UnivariateRationalFunction< UnivariatePolynomialOverField, Field > *	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< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ extendedEuclidean()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::extendedEuclidean	(	const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > &	b,
		UnivariateRationalFunction< UnivariatePolynomialOverField, Field > *	s = `NULL`,
		UnivariateRationalFunction< UnivariatePolynomialOverField, Field > *	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< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ gcd()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::gcd ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b ) const

inlinevirtual

BPASGCDDomain, BPASEuclideanDomain, BPASField virtual methods.

Get this GCD of *this and b.

Implements BPASGCDDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ inverse()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::inverse ( ) const

inlinevirtual

Get the inverse of *this.

Returns: the inverse

Implements BPASField< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ isOne()

template<class UnivariatePolynomialOverField, class Field>

bool UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::isOne ( ) const

inlinevirtual

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

returns true iff *this is one.

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ isZero()

template<class UnivariatePolynomialOverField, class Field>

bool UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::isZero ( ) const

inlinevirtual

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

returns true iff *this is zero.

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ numerator()

template<class UnivariatePolynomialOverField, class Field>

UnivariatePolynomialOverField UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::numerator ( ) const

inlinevirtual

Get the fraction's numerator.

Returns: the numerator.

Implements BPASFieldOfFractions< UnivariatePolynomialOverField, UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator!=()

template<class UnivariatePolynomialOverField, class Field>

bool UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator!= ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & ) const

inlinevirtual

Inequality test,.

returns true iff not equal.

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator%()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator% ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b ) const

inlinevirtual

Get the remainder of *this and b;.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator%=()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field>& UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator%= ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b )

inlinevirtual

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

Parameters

b	the divisor

Returns: this after assignment.

Implements BPASEuclideanDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator/()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator/ ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & d ) const

inlinevirtual

Exact division.

Parameters

d	the divisor.

Returns: the equotient.

Implements BPASIntegralDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator/=()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field>& UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator/= ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & d )

inlinevirtual

Exact division assignment.

Parameters

d	the divisor.

Returns: a reference to this after assignment.

Implements BPASIntegralDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator=()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field>& UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator= ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b )

inlinevirtual

Overload operator =.

Parameters

b	A rational function

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator==()

template<class UnivariatePolynomialOverField, class Field>

bool UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator== ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & ) const

inlinevirtual

Equality test,.

returns true iff equal

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator^()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator^ ( long long int e ) const

inlinevirtual

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ operator^=()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field>& UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::operator^= ( long long int e )

inlinevirtual

Overload operator ^= replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

Implements BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ print()

template<class UnivariatePolynomialOverField, class Field>

void UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::print ( std::ostream & ostream ) const

inlinevirtual

Overload stream operator <<.

Parameters

out	Stream object
b	The rational function

Reimplemented from BPASRing< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ quotient()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::quotient ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b ) const

inlinevirtual

Get the quotient of *this and b.

Parameters

b	the divisor

Returns: the quotient

Implements BPASEuclideanDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ remainder()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField, Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::remainder ( const UnivariateRationalFunction< UnivariatePolynomialOverField, Field > & b ) const

inlinevirtual

Get the remainder of *this and b.

Parameters

b	the divisor

Returns: the remainder

Implements BPASEuclideanDomain< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

◆ unitCanonical()

template<class UnivariatePolynomialOverField, class Field>

UnivariateRationalFunction<UnivariatePolynomialOverField,Field> UnivariateRationalFunction< UnivariatePolynomialOverField, Field >::unitCanonical	(	UnivariateRationalFunction< UnivariatePolynomialOverField, Field > *	u = `NULL`,
		UnivariateRationalFunction< UnivariatePolynomialOverField, Field > *	v = `NULL`
	)		const

inlinevirtual

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< UnivariateRationalFunction< UnivariatePolynomialOverField, Field > >.

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

include/RationalFunction/urationalfunction.h

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

template<class UnivariatePolynomialOverField, class Field> class UnivariateRationalFunction< UnivariatePolynomialOverField, Field >

Constructor & Destructor Documentation

◆ UnivariateRationalFunction() [1/3]

◆ UnivariateRationalFunction() [2/3]

◆ UnivariateRationalFunction() [3/3]

◆ ~UnivariateRationalFunction()

Member Function Documentation

◆ convertToExpressionTree()

◆ denominator()

◆ euclideanDivision()

◆ extendedEuclidean()

◆ gcd()

◆ inverse()

◆ isOne()

◆ isZero()

◆ numerator()

◆ operator!=()

◆ operator%()

◆ operator%=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()

◆ operator^()

◆ operator^=()

◆ print()

◆ quotient()

◆ remainder()

◆ unitCanonical()

template<class UnivariatePolynomialOverField, class Field>
class UnivariateRationalFunction< UnivariatePolynomialOverField, Field >