A univariate polynomial over an arbitrary BPASRing represented sparsely. More...

#include <upolynomial.h>

Simplified semantic inheritance diagram for SparseUnivariatePolynomial< Ring >:

Full inheritance diagram for SparseUnivariatePolynomial< Ring >:

Public Member Functions
	SparseUnivariatePolynomial ()
	Construct a polynomial. More...

	SparseUnivariatePolynomial (const SparseUnivariatePolynomial< Ring > &b)
	Copy constructor. More...

	SparseUnivariatePolynomial (int a)

	SparseUnivariatePolynomial (const Integer &c)

	SparseUnivariatePolynomial (const RationalNumber &c)

	SparseUnivariatePolynomial (const ComplexRationalNumber &c)

	SparseUnivariatePolynomial (const DenseUnivariateIntegerPolynomial &b)

	SparseUnivariatePolynomial (const DenseUnivariateRationalPolynomial &b)

	SparseUnivariatePolynomial (Symbol sym)

	~SparseUnivariatePolynomial ()
	Destroy the polynomial. More...

Integer	numberOfTerms () const
	Get the number of terms. More...

Integer	degree () const
	Get the degree of the polynomial. More...

Ring	leadingCoefficient () const
	Get the leading coefficient. More...

Ring	trailingCoefficient () const

Ring	coefficient (int k) const
	Get a coefficient. More...

void	setCoefficient (int e, const Ring &c)
	Set a coeffcient with its exponent. More...

Symbol	variable () const
	Get the variable name. More...

void	setVariableName (const Symbol &c)
	Set the variable name. More...

SparseUnivariatePolynomial< Ring >	unitCanonical (SparseUnivariatePolynomial< Ring > u=NULL, SparseUnivariatePolynomial< Ring > v=NULL) const

SparseUnivariatePolynomial< Ring > &	operator= (const SparseUnivariatePolynomial< Ring > &b)
	Overload operator =. More...

SparseUnivariatePolynomial< Ring > &	operator= (const Ring &r)
	Overload operator =. More...

bool	operator!= (const SparseUnivariatePolynomial< Ring > &b) const
	Overload operator !=. More...

bool	operator== (const SparseUnivariatePolynomial< Ring > &b) const
	Overload operator ==. More...

bool	operator== (const DenseUnivariateRationalPolynomial &b) const

bool	operator== (const DenseUnivariateIntegerPolynomial &b) const

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

void	zero ()
	Zero polynomial. More...

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

void	one ()
	Set polynomial to 1. More...

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

void	negativeOne ()
	Set polynomial to -1. More...

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

Ring	convertToConstant ()
	Convert to a constant. More...

Ring	content () const override
	Content of the polynomial. More...

SparseUnivariatePolynomial< Ring >	primitivePart () const

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

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

SparseUnivariatePolynomial< Ring >	operator<< (int k) const
	Overload operator << replace by muplitying x^k. More...

SparseUnivariatePolynomial< Ring > &	operator<<= (int k)
	Overload operator <<= replace by muplitying x^k. More...

SparseUnivariatePolynomial< Ring >	operator>> (int k) const
	Overload operator >> replace by dividing x^k, and return the quotient. More...

SparseUnivariatePolynomial< Ring > &	operator>>= (int k)
	Overload operator >>= replace by dividing x^k, and return the quotient. More...

SparseUnivariatePolynomial< Ring >	operator+ (const SparseUnivariatePolynomial< Ring > &b) const
	Overload operator +. More...

SparseUnivariatePolynomial< Ring > &	operator+= (const SparseUnivariatePolynomial< Ring > &b)
	Overload operator+=. More...

SparseUnivariatePolynomial< Ring >	operator+ (const Ring &e) const
	Overload operator +. More...

SparseUnivariatePolynomial< Ring > &	operator+= (const Ring &e)
	Overload operator +=. More...

SparseUnivariatePolynomial< Ring >	operator- () const
	Overload operator -, negate. More...

SparseUnivariatePolynomial< Ring >	operator- (const SparseUnivariatePolynomial< Ring > &b) const
	Subtract another polynomial. More...

SparseUnivariatePolynomial< Ring > &	operator-= (const SparseUnivariatePolynomial< Ring > &b)
	Overload operator -=. More...

SparseUnivariatePolynomial< Ring >	operator- (const Ring &e) const
	Overload operator -. More...

SparseUnivariatePolynomial< Ring > &	operator-= (const Ring &e)
	Overload operator -=. More...

SparseUnivariatePolynomial< Ring >	operator* (const SparseUnivariatePolynomial< Ring > &b) const
	Multiply another polynomial. More...

SparseUnivariatePolynomial< Ring > &	operator*= (const SparseUnivariatePolynomial< Ring > &b)
	Overload operator *=. More...

SparseUnivariatePolynomial< Ring >	operator* (const Ring &c) const
	Overload operator *. More...

SparseUnivariatePolynomial< Ring >	operator* (const sfixn &e) const

SparseUnivariatePolynomial< Ring > &	operator*= (const Ring &c)
	Overload operator *=. More...

SparseUnivariatePolynomial< Ring > &	*operator=** (const sfixn &e)

SparseUnivariatePolynomial< Ring >	operator/ (const SparseUnivariatePolynomial< Ring > &b) const
	Overload operator / EdeDivision. More...

SparseUnivariatePolynomial< Ring > &	operator/= (const SparseUnivariatePolynomial< Ring > &b)
	Overload operator /= ExactDivision. More...

SparseUnivariatePolynomial< Ring >	operator/ (const Ring &e) const
	Overload operator /. More...

SparseUnivariatePolynomial< Ring > &	operator/= (const Ring &e)
	Overload operator /=. More...

void	negate ()
	Negate the polynomial. More...

SparseUnivariatePolynomial< Ring >	monicDivide (const SparseUnivariatePolynomial< Ring > &b)
	Monic division Assuming the leading coefficient of dividend is 1 Return quotient and itself becomes remainder. More...

SparseUnivariatePolynomial< Ring >	monicDivide (const SparseUnivariatePolynomial< Ring > &b, SparseUnivariatePolynomial< Ring > *rem) const
	Monic division Assuming the leading coefficient of dividend is 1 Return quotient. More...

SparseUnivariatePolynomial< Ring >	lazyPseudoDivide (const SparseUnivariatePolynomial< Ring > &b, Ring c, Ring d=NULL)
	Lazy pseudo dividsion Return the quotient and itself becomes remainder e is the exact number of division steps. More...

SparseUnivariatePolynomial< Ring >	lazyPseudoDivide (const SparseUnivariatePolynomial< Ring > &b, SparseUnivariatePolynomial< Ring > rem, Ring c, Ring *d) const
	Lazy pseudo dividsion Return the quotient e is the exact number of division steps. More...

SparseUnivariatePolynomial< Ring >	pseudoDivide (const SparseUnivariatePolynomial< Ring > &b, Ring *d=NULL)
	Pseudo dividsion Return the quotient and itself becomes remainder. More...

SparseUnivariatePolynomial< Ring >	pseudoDivide (const SparseUnivariatePolynomial< Ring > &b, SparseUnivariatePolynomial< Ring > rem, Ring d) const
	Pseudo dividsion Return the quotient. More...

void	differentiate (int k)
	Compute k-th derivative. More...

void	differentiate ()
	Convert current object to its derivative. More...

SparseUnivariatePolynomial< Ring >	derivative (int k) const
	Return k-th derivative. More...

SparseUnivariatePolynomial< Ring >	derivative () const
	Compute derivative. More...

void	integrate ()
	Compute integral with constant of integration set to 0. More...

SparseUnivariatePolynomial< Ring >	integral () const
	Compute integral with constant of integration 0. More...

bool	isConstantTermZero () const
	Is trailing coefficient zero. More...

Ring	evaluate (const Ring &x) const
	Evaluate f(x) More...

template<class LargerRing >
LargerRing	evaluate (const LargerRing &x) const
	Evaluate f(x) More...

void	fillChain (std::vector< SparseUnivariatePolynomial< Ring >> &chain) const

std::vector< SparseUnivariatePolynomial< Ring > >	subresultantChain (const SparseUnivariatePolynomial< Ring > &q, int filled=0) const
	Subresultant Chain Return the list of subresultants. More...

std::vector< SparseUnivariatePolynomial< Ring > >	monomialBasisSubresultantChain (const SparseUnivariatePolynomial< Ring > &q)
	monomialBasisSubResultantChain More...

SparseUnivariatePolynomial< Ring >	resultant (const SparseUnivariatePolynomial< Ring > &q)
	Resultant. More...

SparseUnivariatePolynomial< Ring >	gcd (const SparseUnivariatePolynomial< Ring > &q) const
	GCD(p, q) More...

Factors< SparseUnivariatePolynomial< Ring > >	squareFree () const
	Square free. More...

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

ExpressionTree	convertToExpressionTree () const

DenseUnivariateRationalPolynomial	convertToDUQP ()

DenseUnivariateIntegerPolynomial	convertToDUZP ()

Public Attributes
mpz_class	characteristic

Friends
SparseUnivariatePolynomial< Ring >	operator+ (const Ring &c, const SparseUnivariatePolynomial< Ring > &p)

SparseUnivariatePolynomial< Ring >	operator- (const Ring &c, const SparseUnivariatePolynomial< Ring > &p)

SparseUnivariatePolynomial< Ring >	operator* (const Ring &e, const SparseUnivariatePolynomial< Ring > &p)

SparseUnivariatePolynomial< Ring >	operator* (const sfixn &e, const SparseUnivariatePolynomial< Ring > &p)

SparseUnivariatePolynomial< Ring >	operator/ (const Ring &e, const SparseUnivariatePolynomial< Ring > &p)

Detailed Description

template<class Ring>
class SparseUnivariatePolynomial< Ring >

A univariate polynomial over an arbitrary BPASRing represented sparsely.

This class is used as part of the automatic template deduction of SparseUnivariatePolynomial, whether the template is a BPASRing or a BPASGCDDomain. A univariate polynomial over an arbitrary BPASRing represented sparsely.

Inheritance of proper base class, and exporting of proper functions, is automatic when the Ring template parameter is specified at compile time by means of std::conditional.

Constructor & Destructor Documentation

◆ SparseUnivariatePolynomial() [1/2]

template<class Ring>

SparseUnivariatePolynomial< Ring >::SparseUnivariatePolynomial ( )

inline

Construct a polynomial.

Parameters

◆ SparseUnivariatePolynomial() [2/2]

template<class Ring>

SparseUnivariatePolynomial< Ring >::SparseUnivariatePolynomial ( const SparseUnivariatePolynomial< Ring > & b )

inline

Copy constructor.

Parameters

b	A sparse univariate polynomial

◆ ~SparseUnivariatePolynomial()

template<class Ring>

SparseUnivariatePolynomial< Ring >::~SparseUnivariatePolynomial ( )

inline

Destroy the polynomial.

Parameters

Member Function Documentation

◆ coefficient()

template<class Ring>

Ring SparseUnivariatePolynomial< Ring >::coefficient ( int k ) const

inlinevirtual

Get a coefficient.

Parameters

k	The exponent

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ content()

template<class Ring>

Ring SparseUnivariatePolynomial< Ring >::content ( ) const

inlineoverride

Content of the polynomial.

Parameters

◆ convertToConstant()

template<class Ring>

Ring SparseUnivariatePolynomial< Ring >::convertToConstant ( )

inline

Convert to a constant.

Parameters

◆ degree()

template<class Ring>

Integer SparseUnivariatePolynomial< Ring >::degree ( ) const

inline

Get the degree of the polynomial.

Parameters

◆ derivative() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::derivative ( int k ) const

inlinevirtual

Return k-th derivative.

Parameters

k	k-th derivative, k > 0

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ derivative() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::derivative ( ) const

inlinevirtual

Compute derivative.

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ differentiate() [1/2]

template<class Ring>

void SparseUnivariatePolynomial< Ring >::differentiate ( int k )

inlinevirtual

Compute k-th derivative.

Parameters

k	k-th derivative

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ differentiate() [2/2]

template<class Ring>

void SparseUnivariatePolynomial< Ring >::differentiate ( )

inlinevirtual

Convert current object to its derivative.

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ evaluate() [1/2]

template<class Ring>

Ring SparseUnivariatePolynomial< Ring >::evaluate ( const Ring & x ) const

inlinevirtual

Evaluate f(x)

Parameters

x	Evaluation point

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ evaluate() [2/2]

template<class Ring>

template<class LargerRing >

LargerRing SparseUnivariatePolynomial< Ring >::evaluate ( const LargerRing & x ) const

inline

Evaluate f(x)

Parameters

x	Evaluation point in larger ring, i.e. a ring in which the Ring of SUP<Ring> can be embedded

◆ gcd()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::gcd ( const SparseUnivariatePolynomial< Ring > & q ) const

inline

GCD(p, q)

Parameters

q	The other polynomial

◆ integral()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::integral ( ) const

inline

Compute integral with constant of integration 0.

◆ integrate()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::integrate ( )

inline

Compute integral with constant of integration set to 0.

Parameters

◆ isConstant()

template<class Ring>

int SparseUnivariatePolynomial< Ring >::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isConstantTermZero()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::isConstantTermZero ( ) const

inline

Is trailing coefficient zero.

Parameters

◆ isNegativeOne()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::isNegativeOne ( ) const

inline

Is polynomial a constant -1.

Parameters

◆ isOne()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::isOne ( ) const

inline

Is polynomial a constant 1.

Parameters

◆ isZero()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::isZero ( ) const

inline

Is zero polynomial.

Parameters

◆ lazyPseudoDivide() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::lazyPseudoDivide	(	const SparseUnivariatePolynomial< Ring > &	b,
		Ring *	c,
		Ring *	d = `NULL`
	)

inlinevirtual

Lazy pseudo dividsion Return the quotient and itself becomes remainder e is the exact number of division steps.

Parameters

b	The dividend polynomial
c	The leading coefficient of b to the power e
d	That to the power deg(a) - deg(b) + 1 - e

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ lazyPseudoDivide() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::lazyPseudoDivide	(	const SparseUnivariatePolynomial< Ring > &	b,
		SparseUnivariatePolynomial< Ring > *	rem,
		Ring *	c,
		Ring *	d
	)		const

inlinevirtual

Lazy pseudo dividsion Return the quotient e is the exact number of division steps.

Parameters

b	The divident polynomial
rem	The remainder polynomial
c	The leading coefficient of b to the power e
d	That to the power deg(a) - deg(b) + 1 - e

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ leadingCoefficient()

template<class Ring>

Ring SparseUnivariatePolynomial< Ring >::leadingCoefficient ( ) const

inline

Get the leading coefficient.

Parameters

◆ monicDivide() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::monicDivide ( const SparseUnivariatePolynomial< Ring > & b )

inlinevirtual

Monic division Assuming the leading coefficient of dividend is 1 Return quotient and itself becomes remainder.

Parameters

b	The dividend polynomial

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ monicDivide() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::monicDivide	(	const SparseUnivariatePolynomial< Ring > &	b,
		SparseUnivariatePolynomial< Ring > *	rem
	)		const

inlinevirtual

Monic division Assuming the leading coefficient of dividend is 1 Return quotient.

Parameters

b	The dividend polynomial
rem	The remainder polynomial

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ monomialBasisSubresultantChain()

template<class Ring>

std::vector<SparseUnivariatePolynomial<Ring> > SparseUnivariatePolynomial< Ring >::monomialBasisSubresultantChain ( const SparseUnivariatePolynomial< Ring > & q )

inline

monomialBasisSubResultantChain

Parameters

q	The other sparse univariate polynomial

◆ negate()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::negate ( )

inline

Negate the polynomial.

Parameters

◆ negativeOne()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::negativeOne ( )

inline

Set polynomial to -1.

Parameters

◆ numberOfTerms()

template<class Ring>

Integer SparseUnivariatePolynomial< Ring >::numberOfTerms ( ) const

inline

Get the number of terms.

Parameters

◆ one()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::one ( )

inline

Set polynomial to 1.

Parameters

◆ operator!=()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::operator!= ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Overload operator !=.

Parameters

b	A sparse univariate polynomial

◆ operator*() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator* ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Multiply another polynomial.

Parameters

b	A univariate polynomial

◆ operator*() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator* ( const Ring & c ) const

inline

Overload operator *.

Parameters

c	A coefficient

◆ operator*=() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator*= ( const SparseUnivariatePolynomial< Ring > & b )

inline

Overload operator *=.

Parameters

b	A univariate polynomial

◆ operator*=() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator*= ( const Ring & c )

inline

Overload operator *=.

Parameters

c	A coefficient

◆ operator+() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator+ ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Overload operator +.

Parameters

b	A univariate polynomial

◆ operator+() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator+ ( const Ring & e ) const

inline

Overload operator +.

Parameters

e	A coefficient constant

◆ operator+=() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator+= ( const SparseUnivariatePolynomial< Ring > & b )

inline

Overload operator+=.

Parameters

b	A univariate polynomial

◆ operator+=() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator+= ( const Ring & e )

inline

Overload operator +=.

Parameters

e	A coefficient constant

◆ operator-() [1/3]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator- ( ) const

inline

Overload operator -, negate.

Parameters

◆ operator-() [2/3]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator- ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Subtract another polynomial.

Parameters

b	A univariate polynomial

◆ operator-() [3/3]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator- ( const Ring & e ) const

inline

Overload operator -.

Parameters

e	A coefficient constant

◆ operator-=() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator-= ( const SparseUnivariatePolynomial< Ring > & b )

inline

Overload operator -=.

Parameters

b	A univariate polynomial

◆ operator-=() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator-= ( const Ring & e )

inline

Overload operator -=.

Parameters

e	A coefficient constant

◆ operator/() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator/ ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Overload operator / EdeDivision.

Parameters

b	A univariate polynomial

◆ operator/() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator/ ( const Ring & e ) const

inline

Overload operator /.

Parameters

e	A coefficient constant

◆ operator/=() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator/= ( const SparseUnivariatePolynomial< Ring > & b )

inline

Overload operator /= ExactDivision.

Parameters

b	A univariate polynomial

◆ operator/=() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator/= ( const Ring & e )

inline

Overload operator /=.

Parameters

e	A coefficient constant

◆ operator<<()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator<< ( int k ) const

inlinevirtual

Overload operator << replace by muplitying x^k.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ operator<<=()

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator<<= ( int k )

inlinevirtual

Overload operator <<= replace by muplitying x^k.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ operator=() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator= ( const SparseUnivariatePolynomial< Ring > & b )

inline

Overload operator =.

Parameters

b	A sparse univariate polynomial

◆ operator=() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator= ( const Ring & r )

inline

Overload operator =.

Parameters

r	A base ring element

◆ operator==()

template<class Ring>

bool SparseUnivariatePolynomial< Ring >::operator== ( const SparseUnivariatePolynomial< Ring > & b ) const

inline

Overload operator ==.

Parameters

b	A sparse univariate polynomial

◆ operator>>()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator>> ( int k ) const

inlinevirtual

Overload operator >> replace by dividing x^k, and return the quotient.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ operator>>=()

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator>>= ( int k )

inlinevirtual

Overload operator >>= replace by dividing x^k, and return the quotient.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ operator^()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::operator^ ( long long int e ) const

inline

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ operator^=()

template<class Ring>

SparseUnivariatePolynomial<Ring>& SparseUnivariatePolynomial< Ring >::operator^= ( long long int e )

inline

Overload operator ^= replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ print()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::print ( std::ostream & out ) const

inline

Overload stream operator <<.

Parameters

out	Stream object
b	The univariate polynomial

◆ pseudoDivide() [1/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::pseudoDivide	(	const SparseUnivariatePolynomial< Ring > &	b,
		Ring *	d = `NULL`
	)

inlinevirtual

Pseudo dividsion Return the quotient and itself becomes remainder.

Parameters

b	The divident polynomial
d	The leading coefficient of b to the power deg(a) - deg(b) + 1

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ pseudoDivide() [2/2]

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::pseudoDivide	(	const SparseUnivariatePolynomial< Ring > &	b,
		SparseUnivariatePolynomial< Ring > *	rem,
		Ring *	d
	)		const

inlinevirtual

Pseudo dividsion Return the quotient.

Parameters

b	The divident polynomial
rem	The remainder polynomial
d	The leading coefficient of b to the power deg(a) - deg(b) + 1

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ resultant()

template<class Ring>

SparseUnivariatePolynomial<Ring> SparseUnivariatePolynomial< Ring >::resultant ( const SparseUnivariatePolynomial< Ring > & q )

inline

Resultant.

Parameters

q	The other sparse univariate polynomial

◆ setCoefficient()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::setCoefficient	(	int	e,
		const Ring &	c
	)

inlinevirtual

Set a coeffcient with its exponent.

Parameters

e	The exponent
c	The coefficient

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ setVariableName()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::setVariableName ( const Symbol & c )

inlinevirtual

Set the variable name.

Parameters

c	Variable's name

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ squareFree()

template<class Ring>

Factors<SparseUnivariatePolynomial<Ring> > SparseUnivariatePolynomial< Ring >::squareFree ( ) const

inline

Square free.

Parameters

◆ subresultantChain()

template<class Ring>

std::vector< SparseUnivariatePolynomial<Ring> > SparseUnivariatePolynomial< Ring >::subresultantChain	(	const SparseUnivariatePolynomial< Ring > &	q,
		int	filled = `0`
	)		const

inline

Subresultant Chain Return the list of subresultants.

Parameters

q	The other sparse univariate polynomial

◆ variable()

template<class Ring>

Symbol SparseUnivariatePolynomial< Ring >::variable ( ) const

inlinevirtual

Get the variable name.

Parameters

Implements BPASUnivariatePolynomial< Ring, SparseUnivariatePolynomial< Ring > >.

◆ zero()

template<class Ring>

void SparseUnivariatePolynomial< Ring >::zero ( )

inline

Zero polynomial.

Parameters

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

include/FiniteFields/BigPrimeField.hpp
include/RingPolynomial/upolynomial.h

Public Member Functions

Public Attributes

Friends

Detailed Description

template<class Ring> class SparseUnivariatePolynomial< Ring >

Constructor & Destructor Documentation

◆ SparseUnivariatePolynomial() [1/2]

◆ SparseUnivariatePolynomial() [2/2]

◆ ~SparseUnivariatePolynomial()

Member Function Documentation

◆ coefficient()

◆ content()

◆ convertToConstant()

◆ degree()

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ differentiate() [1/2]

◆ differentiate() [2/2]

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ gcd()

◆ integral()

◆ integrate()

◆ isConstant()

◆ isConstantTermZero()

◆ isNegativeOne()

◆ isOne()

◆ isZero()

◆ lazyPseudoDivide() [1/2]

◆ lazyPseudoDivide() [2/2]

◆ leadingCoefficient()

◆ monicDivide() [1/2]

◆ monicDivide() [2/2]

◆ monomialBasisSubresultantChain()

◆ negate()

◆ negativeOne()

◆ numberOfTerms()

◆ one()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator<<()

◆ operator<<=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>>()

◆ operator>>=()

◆ operator^()

◆ operator^=()

◆ print()

◆ pseudoDivide() [1/2]

◆ pseudoDivide() [2/2]

◆ resultant()

◆ setCoefficient()

◆ setVariableName()

◆ squareFree()

◆ subresultantChain()

◆ variable()

◆ zero()

template<class Ring>
class SparseUnivariatePolynomial< Ring >