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

#include <upolynomial.h>

Simplified semantic inheritance diagram for SparseUnivariateTempPoly< Ring, Derived >:

Full inheritance diagram for SparseUnivariateTempPoly< Ring, Derived >:

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

	SparseUnivariateTempPoly (const SparseUnivariateTempPoly< Ring, Derived > &b)
	Copy constructor. More...

	SparseUnivariateTempPoly (int a)

	SparseUnivariateTempPoly (const Integer &c)

	SparseUnivariateTempPoly (const RationalNumber &c)

	SparseUnivariateTempPoly (const ComplexRationalNumber &c)

	SparseUnivariateTempPoly (const DenseUnivariateIntegerPolynomial &b)

	SparseUnivariateTempPoly (const DenseUnivariateRationalPolynomial &b)

	SparseUnivariateTempPoly (Symbol sym)

	~SparseUnivariateTempPoly ()
	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...

Derived	unitCanonical (Derived u=NULL, Derived v=NULL) const

Derived &	operator= (const Derived &b)
	Overload operator =. More...

Derived &	operator= (const Ring &r)
	Overload operator =. More...

bool	operator!= (const Derived &b) const
	Overload operator !=. More...

bool	operator== (const Derived &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...

Derived	primitivePart () const

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

Derived &	operator^= (long long int e)
	Overload operator ^= replace xor operation by exponentiation. More...

Derived	operator<< (int k) const
	Overload operator << replace by muplitying x^k. More...

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

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

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

Derived	operator+ (const Derived &b) const
	Overload operator +. More...

Derived &	operator+= (const Derived &b)
	Overload operator+=. More...

Derived	operator+ (const Ring &e) const
	Overload operator +. More...

Derived &	operator+= (const Ring &e)
	Overload operator +=. More...

Derived	operator- () const
	Overload operator -, negate. More...

Derived	operator- (const Derived &b) const
	Subtract another polynomial. More...

Derived &	operator-= (const Derived &b)
	Overload operator -=. More...

Derived	operator- (const Ring &e) const
	Overload operator -. More...

Derived &	operator-= (const Ring &e)
	Overload operator -=. More...

Derived	operator* (const Derived &b) const
	Multiply another polynomial. More...

Derived &	operator*= (const Derived &b)
	Overload operator *=. More...

Derived	operator* (const Ring &c) const
	Overload operator *. More...

Derived	operator* (const sfixn &e) const

Derived &	operator*= (const Ring &c)
	Overload operator *=. More...

Derived &	*operator=** (const sfixn &e)

Derived	operator/ (const Derived &b) const
	Overload operator / EdeDivision. More...

Derived &	operator/= (const Derived &b)
	Overload operator /= ExactDivision. More...

Derived	operator/ (const Ring &e) const
	Overload operator /. More...

Derived &	operator/= (const Ring &e)
	Overload operator /=. More...

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

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

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

Derived	lazyPseudoDivide (const Derived &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...

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

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

Derived	pseudoDivide (const Derived &b, Derived 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...

Derived	derivative (int k) const
	Return k-th derivative. More...

Derived	derivative () const
	Compute derivative. More...

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

Derived	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< Derived > &chain) const

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

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

Derived	resultant (const Derived &q)
	Resultant. More...

Derived	gcd (const Derived &q) const
	GCD(p, q) More...

Factors< Derived >	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
Derived	operator+ (const Ring &c, const Derived &p)

Derived	operator- (const Ring &c, const Derived &p)

Derived	operator* (const Ring &e, const Derived &p)

Derived	operator* (const sfixn &e, const Derived &p)

Derived	operator/ (const Ring &e, const Derived &p)

Detailed Description

template<class Ring, class Derived>
class SparseUnivariateTempPoly< Ring, Derived >

A univariate polynomial over an arbitrary BPASRing represented sparsely.

This is the base for all possible template instantiations. Users should use SparseUnivariatePolynomial directly and not thing class.

See also: SparseUnivariatePolynomial SparseUnivariateTempFieldPoly

Constructor & Destructor Documentation

◆ SparseUnivariateTempPoly() [1/2]

template<class Ring, class Derived>

SparseUnivariateTempPoly< Ring, Derived >::SparseUnivariateTempPoly ( )

inline

Construct a polynomial.

Parameters

◆ SparseUnivariateTempPoly() [2/2]

template<class Ring, class Derived>

SparseUnivariateTempPoly< Ring, Derived >::SparseUnivariateTempPoly ( const SparseUnivariateTempPoly< Ring, Derived > & b )

inline

Copy constructor.

Parameters

b	A sparse univariate polynomial

◆ ~SparseUnivariateTempPoly()

template<class Ring, class Derived>

SparseUnivariateTempPoly< Ring, Derived >::~SparseUnivariateTempPoly ( )

inline

Destroy the polynomial.

Parameters

Member Function Documentation

◆ coefficient()

template<class Ring, class Derived>

Ring SparseUnivariateTempPoly< Ring, Derived >::coefficient ( int k ) const

inlinevirtual

Get a coefficient.

Parameters

k	The exponent

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ content()

template<class Ring, class Derived>

Ring SparseUnivariateTempPoly< Ring, Derived >::content ( ) const

inlineoverride

Content of the polynomial.

Parameters

◆ convertToConstant()

template<class Ring, class Derived>

Ring SparseUnivariateTempPoly< Ring, Derived >::convertToConstant ( )

inline

Convert to a constant.

Parameters

◆ degree()

template<class Ring, class Derived>

Integer SparseUnivariateTempPoly< Ring, Derived >::degree ( ) const

inline

Get the degree of the polynomial.

Parameters

◆ derivative() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::derivative ( int k ) const

inlinevirtual

Return k-th derivative.

Parameters

k	k-th derivative, k > 0

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ derivative() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::derivative ( ) const

inlinevirtual

Compute derivative.

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ differentiate() [1/2]

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::differentiate ( int k )

inlinevirtual

Compute k-th derivative.

Parameters

k	k-th derivative

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ differentiate() [2/2]

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::differentiate ( )

inlinevirtual

Convert current object to its derivative.

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ evaluate() [1/2]

template<class Ring, class Derived>

Ring SparseUnivariateTempPoly< Ring, Derived >::evaluate ( const Ring & x ) const

inlinevirtual

Evaluate f(x)

Parameters

x	Evaluation point

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ evaluate() [2/2]

template<class Ring, class Derived>

template<class LargerRing >

LargerRing SparseUnivariateTempPoly< Ring, Derived >::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, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::gcd ( const Derived & q ) const

inline

GCD(p, q)

Parameters

q	The other polynomial

◆ integral()

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::integral ( ) const

inline

Compute integral with constant of integration 0.

◆ integrate()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::integrate ( )

inline

Compute integral with constant of integration set to 0.

Parameters

◆ isConstant()

template<class Ring, class Derived>

int SparseUnivariateTempPoly< Ring, Derived >::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isConstantTermZero()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::isConstantTermZero ( ) const

inline

Is trailing coefficient zero.

Parameters

◆ isNegativeOne()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::isNegativeOne ( ) const

inline

Is polynomial a constant -1.

Parameters

◆ isOne()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::isOne ( ) const

inline

Is polynomial a constant 1.

Parameters

◆ isZero()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::isZero ( ) const

inline

Is zero polynomial.

Parameters

◆ lazyPseudoDivide() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::lazyPseudoDivide	(	const Derived &	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, Derived >.

◆ lazyPseudoDivide() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::lazyPseudoDivide	(	const Derived &	b,
		Derived *	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, Derived >.

◆ leadingCoefficient()

template<class Ring, class Derived>

Ring SparseUnivariateTempPoly< Ring, Derived >::leadingCoefficient ( ) const

inline

Get the leading coefficient.

Parameters

◆ monicDivide() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::monicDivide ( const Derived & 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, Derived >.

◆ monicDivide() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::monicDivide	(	const Derived &	b,
		Derived *	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, Derived >.

◆ monomialBasisSubresultantChain()

template<class Ring, class Derived>

std::vector<Derived > SparseUnivariateTempPoly< Ring, Derived >::monomialBasisSubresultantChain ( const Derived & q )

inline

monomialBasisSubResultantChain

Parameters

q	The other sparse univariate polynomial

◆ negate()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::negate ( )

inline

Negate the polynomial.

Parameters

◆ negativeOne()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::negativeOne ( )

inline

Set polynomial to -1.

Parameters

◆ numberOfTerms()

template<class Ring, class Derived>

Integer SparseUnivariateTempPoly< Ring, Derived >::numberOfTerms ( ) const

inline

Get the number of terms.

Parameters

◆ one()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::one ( )

inline

Set polynomial to 1.

Parameters

◆ operator!=()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::operator!= ( const Derived & b ) const

inline

Overload operator !=.

Parameters

b	A sparse univariate polynomial

◆ operator*() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator* ( const Derived & b ) const

inline

Multiply another polynomial.

Parameters

b	A univariate polynomial

◆ operator*() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator* ( const Ring & c ) const

inline

Overload operator *.

Parameters

c	A coefficient

◆ operator*=() [1/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator*= ( const Derived & b )

inline

Overload operator *=.

Parameters

b	A univariate polynomial

◆ operator*=() [2/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator*= ( const Ring & c )

inline

Overload operator *=.

Parameters

c	A coefficient

◆ operator+() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator+ ( const Derived & b ) const

inline

Overload operator +.

Parameters

b	A univariate polynomial

◆ operator+() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator+ ( const Ring & e ) const

inline

Overload operator +.

Parameters

e	A coefficient constant

◆ operator+=() [1/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator+= ( const Derived & b )

inline

Overload operator+=.

Parameters

b	A univariate polynomial

◆ operator+=() [2/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator+= ( const Ring & e )

inline

Overload operator +=.

Parameters

e	A coefficient constant

◆ operator-() [1/3]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator- ( ) const

inline

Overload operator -, negate.

Parameters

◆ operator-() [2/3]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator- ( const Derived & b ) const

inline

Subtract another polynomial.

Parameters

b	A univariate polynomial

◆ operator-() [3/3]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator- ( const Ring & e ) const

inline

Overload operator -.

Parameters

e	A coefficient constant

◆ operator-=() [1/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator-= ( const Derived & b )

inline

Overload operator -=.

Parameters

b	A univariate polynomial

◆ operator-=() [2/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator-= ( const Ring & e )

inline

Overload operator -=.

Parameters

e	A coefficient constant

◆ operator/() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator/ ( const Derived & b ) const

inline

Overload operator / EdeDivision.

Parameters

b	A univariate polynomial

◆ operator/() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator/ ( const Ring & e ) const

inline

Overload operator /.

Parameters

e	A coefficient constant

◆ operator/=() [1/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator/= ( const Derived & b )

inline

Overload operator /= ExactDivision.

Parameters

b	A univariate polynomial

◆ operator/=() [2/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator/= ( const Ring & e )

inline

Overload operator /=.

Parameters

e	A coefficient constant

◆ operator<<()

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator<< ( int k ) const

inlinevirtual

Overload operator << replace by muplitying x^k.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ operator<<=()

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator<<= ( int k )

inlinevirtual

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

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ operator=() [1/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator= ( const Derived & b )

inline

Overload operator =.

Parameters

b	A sparse univariate polynomial

◆ operator=() [2/2]

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator= ( const Ring & r )

inline

Overload operator =.

Parameters

r	A base ring element

◆ operator==()

template<class Ring, class Derived>

bool SparseUnivariateTempPoly< Ring, Derived >::operator== ( const Derived & b ) const

inline

Overload operator ==.

Parameters

b	A sparse univariate polynomial

◆ operator>>()

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::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, Derived >.

◆ operator>>=()

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::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, Derived >.

◆ operator^()

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::operator^ ( long long int e ) const

inline

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ operator^=()

template<class Ring, class Derived>

Derived& SparseUnivariateTempPoly< Ring, Derived >::operator^= ( long long int e )

inline

Overload operator ^= replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ print()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::print ( std::ostream & out ) const

inline

Overload stream operator <<.

Parameters

out	Stream object
b	The univariate polynomial

◆ pseudoDivide() [1/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::pseudoDivide	(	const Derived &	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, Derived >.

◆ pseudoDivide() [2/2]

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::pseudoDivide	(	const Derived &	b,
		Derived *	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, Derived >.

◆ resultant()

template<class Ring, class Derived>

Derived SparseUnivariateTempPoly< Ring, Derived >::resultant ( const Derived & q )

inline

Resultant.

Parameters

q	The other sparse univariate polynomial

◆ setCoefficient()

template<class Ring, class Derived>

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

inlinevirtual

Set a coeffcient with its exponent.

Parameters

e	The exponent
c	The coefficient

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ setVariableName()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::setVariableName ( const Symbol & c )

inlinevirtual

Set the variable name.

Parameters

c	Variable's name

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ squareFree()

template<class Ring, class Derived>

Factors<Derived> SparseUnivariateTempPoly< Ring, Derived >::squareFree ( ) const

inline

Square free.

Parameters

◆ subresultantChain()

template<class Ring, class Derived>

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

inline

Subresultant Chain Return the list of subresultants.

Parameters

q	The other sparse univariate polynomial

◆ variable()

template<class Ring, class Derived>

Symbol SparseUnivariateTempPoly< Ring, Derived >::variable ( ) const

inlinevirtual

Get the variable name.

Parameters

Implements BPASUnivariatePolynomial< Ring, Derived >.

◆ zero()

template<class Ring, class Derived>

void SparseUnivariateTempPoly< Ring, Derived >::zero ( )

inline

Zero polynomial.

Parameters

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

include/RingPolynomial/upolynomial.h

Public Member Functions

Public Attributes

Friends

Detailed Description

template<class Ring, class Derived> class SparseUnivariateTempPoly< Ring, Derived >

Constructor & Destructor Documentation

◆ SparseUnivariateTempPoly() [1/2]

◆ SparseUnivariateTempPoly() [2/2]

◆ ~SparseUnivariateTempPoly()

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 Derived>
class SparseUnivariateTempPoly< Ring, Derived >