A univariate polynomial with Integer coefficients using a dense representation. More...

#include <uzpolynomial.h>

Simplified semantic inheritance diagram for DenseUnivariateIntegerPolynomial:

Full inheritance diagram for DenseUnivariateIntegerPolynomial:

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

	DenseUnivariateIntegerPolynomial (int s)
	Construct a polynomial with degree. More...

	DenseUnivariateIntegerPolynomial (const Integer &e)
	Construct a polynomial with a coeffient. More...

	DenseUnivariateIntegerPolynomial (const RationalNumber &e)

	DenseUnivariateIntegerPolynomial (const DenseUnivariateIntegerPolynomial &b)
	Copy constructor. More...

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

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

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

Integer	trailingCoefficient () const

Integer	numberOfTerms () const

mpz_class *	coefficients (int k=0) const
	Get coefficients of the polynomial, given start offset. More...

Integer	coefficient (int k) const
	Get a coefficient of the polynomial. More...

void	setCoefficient (int k, const mpz_class value)
	Set a coefficient of the polynomial. More...

void	setCoefficient (int k, const Integer &value)
	Set the coefficient of the monomial with degree d to be the Ring element r. More...

void	setCoefficient (int k, const int value)

void	setCoefficient (Integer k, const Integer &value)
	Set a coefficient of the polynomial. More...

Symbol	variable () const
	Get variable's name. More...

void	setVariableName (const Symbol &x)
	Set variable's name. More...

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

DenseUnivariateIntegerPolynomial &	operator= (const Integer &i)

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

bool	operator== (const DenseUnivariateIntegerPolynomial &b) const
	Overload operator ==. More...

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

void	zero ()
	Zero polynomial. More...

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

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

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

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

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

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

Integer	content () const
	Content of the polynomial. More...

DenseUnivariateIntegerPolynomial	primitivePart () const

bool	isConstantTermZero () const
	Is the least signficant coefficient zero. More...

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

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

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

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

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

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

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

DenseUnivariateIntegerPolynomial &	operator+= (const DenseUnivariateIntegerPolynomial &b)
	Overload Operator +=. More...

void	add (const DenseUnivariateIntegerPolynomial &b)
	Add another polynomial to itself. More...

DenseUnivariateIntegerPolynomial	operator+ (const Integer &c) const
	Overload Operator +. More...

DenseUnivariateIntegerPolynomial	operator+ (const mpz_class &c) const

DenseUnivariateIntegerPolynomial	operator+ (int c) const

DenseUnivariateIntegerPolynomial &	operator+= (const Integer &c)
	Overload Operator +=. More...

DenseUnivariateIntegerPolynomial &	operator+= (const mpz_class &c)

DenseUnivariateIntegerPolynomial &	operator+= (int c)

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

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

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

void	negate ()
	Compute -f(x) More...

void	subtract (const DenseUnivariateIntegerPolynomial &b)
	Subtract another polynomial from itself. More...

DenseUnivariateIntegerPolynomial	operator- (const Integer &c) const
	Overload operator -. More...

DenseUnivariateIntegerPolynomial	operator- (const mpz_class &c) const

DenseUnivariateIntegerPolynomial	operator- (int c) const

DenseUnivariateIntegerPolynomial &	operator-= (const Integer &c)
	Overload operator -=. More...

DenseUnivariateIntegerPolynomial &	operator-= (const mpz_class &c)

DenseUnivariateIntegerPolynomial &	operator-= (int c)

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

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

DenseUnivariateIntegerPolynomial	operator* (const Integer &e) const
	Overload operator *. More...

DenseUnivariateIntegerPolynomial	operator* (const mpz_class &e) const

DenseUnivariateIntegerPolynomial	operator* (int e) const

DenseUnivariateIntegerPolynomial &	operator*= (const Integer &e)
	Overload operator *=. More...

DenseUnivariateIntegerPolynomial &	*operator=** (const mpz_class &e)

DenseUnivariateIntegerPolynomial &	operator*= (int e)
	Overload operator *=. More...

DenseUnivariateIntegerPolynomial	operator/ (const DenseUnivariateIntegerPolynomial &b) const
	Overload operator / ExactDivision. More...

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

DenseUnivariateIntegerPolynomial	operator/ (const Integer &e) const
	Overload operator /. More...

DenseUnivariateIntegerPolynomial	operator/ (const mpz_class &e) const

DenseUnivariateIntegerPolynomial	operator/ (int e) const

DenseUnivariateIntegerPolynomial &	operator/= (const Integer &e)
	Overload operator /=. More...

DenseUnivariateIntegerPolynomial &	operator/= (const mpz_class &e)

DenseUnivariateIntegerPolynomial &	operator/= (int e)

DenseUnivariateIntegerPolynomial	monicDivide (const DenseUnivariateIntegerPolynomial &b)
	Monic division Return quotient and itself become the remainder. More...

DenseUnivariateIntegerPolynomial	monicDivide (const DenseUnivariateIntegerPolynomial &b, DenseUnivariateIntegerPolynomial *rem) const
	Monic division Return quotient. More...

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

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

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

DenseUnivariateIntegerPolynomial	pseudoDivide (const DenseUnivariateIntegerPolynomial &b, DenseUnivariateIntegerPolynomial rem, Integer d) const
	Pseudo dividsion Return the quotient. More...

DenseUnivariateIntegerPolynomial	gcd (const DenseUnivariateIntegerPolynomial &q, int type) const
	GCD(p, q) More...

DenseUnivariateIntegerPolynomial	gcd (const DenseUnivariateIntegerPolynomial &q) const

void	differentiate (int k)
	Convert current object to its k-th derivative. More...

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

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

DenseUnivariateIntegerPolynomial	derivative () const
	Compute derivative. More...

void	integrate ()
	Convert current object to its integral with constant of integration 0. More...

DenseUnivariateIntegerPolynomial	integral ()
	Compute integral with constant of integration 0. More...

Integer	evaluate (const Integer &x) const
	/** Evaluate f(x) More...

Factors< DenseUnivariateIntegerPolynomial >	squareFree () const
	Square free. More...

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

ExpressionTree	convertToExpressionTree () const
	Convert this DUZP into an expression tree.

Static Public Attributes
static mpz_class	characteristic

Friends
DenseUnivariateIntegerPolynomial	operator+ (const mpz_class &c, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator+ (int c, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator- (const mpz_class &c, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator- (int c, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator* (const mpz_class &e, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator* (int e, const DenseUnivariateIntegerPolynomial &p)

DenseUnivariateIntegerPolynomial	operator/ (const mpz_class &e, const DenseUnivariateIntegerPolynomial &p)

Detailed Description

A univariate polynomial with Integer coefficients using a dense representation.

This representation stores all possible coefficients, up to a maximum degree, even if they are zero.

Constructor & Destructor Documentation

◆ DenseUnivariateIntegerPolynomial() [1/4]

DenseUnivariateIntegerPolynomial::DenseUnivariateIntegerPolynomial ( )

inline

Construct a polynomial.

Parameters

d

◆ DenseUnivariateIntegerPolynomial() [2/4]

DenseUnivariateIntegerPolynomial::DenseUnivariateIntegerPolynomial ( int s )

inline

Construct a polynomial with degree.

Parameters

d	Size of the polynomial

◆ DenseUnivariateIntegerPolynomial() [3/4]

DenseUnivariateIntegerPolynomial::DenseUnivariateIntegerPolynomial ( const Integer & e )

inline

Construct a polynomial with a coeffient.

Parameters

e	The coefficient

◆ DenseUnivariateIntegerPolynomial() [4/4]

DenseUnivariateIntegerPolynomial::DenseUnivariateIntegerPolynomial ( const DenseUnivariateIntegerPolynomial & b )

inline

Copy constructor.

Parameters

b	A densed univariate rationl polynomial

◆ ~DenseUnivariateIntegerPolynomial()

DenseUnivariateIntegerPolynomial::~DenseUnivariateIntegerPolynomial ( )

inline

Destroy the polynomial.

Parameters

Member Function Documentation

◆ add()

void DenseUnivariateIntegerPolynomial::add ( const DenseUnivariateIntegerPolynomial & b )

Add another polynomial to itself.

Parameters

b	A univariate integer polynomial

◆ coefficient()

Integer DenseUnivariateIntegerPolynomial::coefficient ( int k ) const

inlinevirtual

Get a coefficient of the polynomial.

Parameters

k Offset

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ coefficients()

mpz_class* DenseUnivariateIntegerPolynomial::coefficients ( int k = 0 ) const

inline

Get coefficients of the polynomial, given start offset.

Parameters

k Offset

◆ content()

Integer DenseUnivariateIntegerPolynomial::content ( ) const

inline

Content of the polynomial.

Parameters

◆ degree()

Integer DenseUnivariateIntegerPolynomial::degree ( ) const

inline

Get degree of the polynomial.

Parameters

◆ derivative() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::derivative ( int k ) const

inlinevirtual

Return k-th derivative.

Parameters

k	Order of the k-th derivative, k > 0

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ derivative() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::derivative ( ) const

inlinevirtual

Compute derivative.

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ differentiate() [1/2]

void DenseUnivariateIntegerPolynomial::differentiate ( int k )

virtual

Convert current object to its k-th derivative.

Parameters

k	Order of the derivative, k > 0

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ differentiate() [2/2]

void DenseUnivariateIntegerPolynomial::differentiate ( )

inlinevirtual

Convert current object to its derivative.

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ evaluate()

Integer DenseUnivariateIntegerPolynomial::evaluate ( const Integer & x ) const

virtual

/** Evaluate f(x)

Parameters

x	Evaluation point Evaluate f(x)
x	Evaluation point

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ gcd()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::gcd	(	const DenseUnivariateIntegerPolynomial &	q,
		int	type
	)		const

GCD(p, q)

Parameters

q	The other polynomial

◆ integral()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::integral ( )

inline

Compute integral with constant of integration 0.

◆ integrate()

void DenseUnivariateIntegerPolynomial::integrate ( )

Convert current object to its integral with constant of integration 0.

◆ isConstant()

int DenseUnivariateIntegerPolynomial::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isConstantTermZero()

bool DenseUnivariateIntegerPolynomial::isConstantTermZero ( ) const

inline

Is the least signficant coefficient zero.

Parameters

◆ isNegativeOne()

bool DenseUnivariateIntegerPolynomial::isNegativeOne ( ) const

inline

Is polynomial a constatn -1.

Parameters

◆ isOne()

bool DenseUnivariateIntegerPolynomial::isOne ( ) const

inline

Is polynomial a constatn 1.

Parameters

◆ isZero()

bool DenseUnivariateIntegerPolynomial::isZero ( ) const

inline

Is zero polynomial.

Parameters

◆ lazyPseudoDivide() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::lazyPseudoDivide	(	const DenseUnivariateIntegerPolynomial &	b,
		Integer *	c,
		Integer *	d = `NULL`
	)

virtual

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< Integer, DenseUnivariateIntegerPolynomial >.

◆ lazyPseudoDivide() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::lazyPseudoDivide	(	const DenseUnivariateIntegerPolynomial &	b,
		DenseUnivariateIntegerPolynomial *	rem,
		Integer *	c,
		Integer *	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< Integer, DenseUnivariateIntegerPolynomial >.

◆ leadingCoefficient()

Integer DenseUnivariateIntegerPolynomial::leadingCoefficient ( ) const

inline

Get the leading coefficient.

Parameters

◆ monicDivide() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::monicDivide ( const DenseUnivariateIntegerPolynomial & b )

virtual

Monic division Return quotient and itself become the remainder.

Parameters

b	The dividend polynomial

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ monicDivide() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::monicDivide	(	const DenseUnivariateIntegerPolynomial &	b,
		DenseUnivariateIntegerPolynomial *	rem
	)		const

inlinevirtual

Monic division Return quotient.

Parameters

b	The dividend polynomial
rem	The remainder polynomial

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ negate()

void DenseUnivariateIntegerPolynomial::negate ( )

inline

Compute -f(x)

Parameters

◆ negativeOne()

void DenseUnivariateIntegerPolynomial::negativeOne ( )

inline

Set polynomial to -1.

Parameters

◆ one()

void DenseUnivariateIntegerPolynomial::one ( )

inline

Set polynomial to 1.

Parameters

◆ operator!=()

bool DenseUnivariateIntegerPolynomial::operator!= ( const DenseUnivariateIntegerPolynomial & b ) const

inline

Overload operator !=.

Parameters

b	A univariate integer polynoial

◆ operator*() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator* ( const DenseUnivariateIntegerPolynomial & b ) const

Multiply to another polynomial.

Parameters

b	A univariate integer polynomial

◆ operator*() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator* ( const Integer & e ) const

inline

Overload operator *.

Parameters

e	An integer

◆ operator*=() [1/3]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator*= ( const DenseUnivariateIntegerPolynomial & b )

inline

Overload operator *=.

Parameters

b	A univariate integer polynomial

◆ operator*=() [2/3]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator*= ( const Integer & e )

inline

Overload operator *=.

Parameters

e	An integer

◆ operator*=() [3/3]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator*= ( int e )

inline

Overload operator *=.

Parameters

e	A constant

◆ operator+() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator+ ( const DenseUnivariateIntegerPolynomial & b ) const

Overload operator +.

Parameters

b	A univariate integer polynomial

◆ operator+() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator+ ( const Integer & c ) const

inline

Overload Operator +.

Parameters

c	An integer

◆ operator+=() [1/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator+= ( const DenseUnivariateIntegerPolynomial & b )

inline

Overload Operator +=.

Parameters

b	A univariate integer polynomial

◆ operator+=() [2/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator+= ( const Integer & c )

inline

Overload Operator +=.

Parameters

c	An integer

◆ operator-() [1/3]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator- ( const DenseUnivariateIntegerPolynomial & b ) const

Subtract another polynomial.

Parameters

b	A univariate integer polynomial

◆ operator-() [2/3]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator- ( ) const

Overload operator -, negate.

Parameters

◆ operator-() [3/3]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator- ( const Integer & c ) const

inline

Overload operator -.

Parameters

c	An integer

◆ operator-=() [1/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator-= ( const DenseUnivariateIntegerPolynomial & b )

inline

Overload operator -=.

Parameters

b	A univariate integer polynomial

◆ operator-=() [2/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator-= ( const Integer & c )

inline

Overload operator -=.

Parameters

c	An integer

◆ operator/() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator/ ( const DenseUnivariateIntegerPolynomial & b ) const

inline

Overload operator / ExactDivision.

Parameters

b	A univariate integer polynomial

◆ operator/() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator/ ( const Integer & e ) const

inline

Overload operator /.

Parameters

e	An integer

◆ operator/=() [1/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator/= ( const DenseUnivariateIntegerPolynomial & b )

Overload operator /= ExactDivision.

Parameters

b	A univariate integer polynomial

◆ operator/=() [2/2]

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator/= ( const Integer & e )

inline

Overload operator /=.

Parameters

e	An integer

◆ operator<<()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator<< ( int k ) const

virtual

Overload operator << replace by muplitying x^k.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ operator<<=()

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator<<= ( int k )

inlinevirtual

Overload operator << replace by muplitying x^k.

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ operator=()

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator= ( const DenseUnivariateIntegerPolynomial & b )

inline

Overload operator =.

Parameters

b	A univariate integer polynoial

◆ operator==()

bool DenseUnivariateIntegerPolynomial::operator== ( const DenseUnivariateIntegerPolynomial & b ) const

inline

Overload operator ==.

Parameters

b	A univariate integer polynoial

◆ operator>>()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator>> ( int k ) const

virtual

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

Parameters

k	The exponent of variable, k > 0

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ operator>>=()

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::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< Integer, DenseUnivariateIntegerPolynomial >.

◆ operator^()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::operator^ ( long long int e ) const

Overload operator ^ replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ operator^=()

DenseUnivariateIntegerPolynomial& DenseUnivariateIntegerPolynomial::operator^= ( long long int e )

inline

Overload operator ^= replace xor operation by exponentiation.

Parameters

e	The exponentiation, e > 0

◆ print()

void DenseUnivariateIntegerPolynomial::print ( std::ostream & out ) const

Overload stream operator <<.

Parameters

out	Stream object
b	A univariate Integer polynoial

◆ pseudoDivide() [1/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::pseudoDivide	(	const DenseUnivariateIntegerPolynomial &	b,
		Integer *	d = `NULL`
	)

virtual

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< Integer, DenseUnivariateIntegerPolynomial >.

◆ pseudoDivide() [2/2]

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::pseudoDivide	(	const DenseUnivariateIntegerPolynomial &	b,
		DenseUnivariateIntegerPolynomial *	rem,
		Integer *	d
	)		const

virtual

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< Integer, DenseUnivariateIntegerPolynomial >.

◆ setCoefficient() [1/3]

void DenseUnivariateIntegerPolynomial::setCoefficient	(	int	k,
		const mpz_class	value
	)

inline

Set a coefficient of the polynomial.

Parameters

k	Offset
val	Coefficient

◆ setCoefficient() [2/3]

void DenseUnivariateIntegerPolynomial::setCoefficient	(	int	d,
		const Integer &	r
	)

inlinevirtual

Set the coefficient of the monomial with degree d to be the Ring element r.

Parameters

d	the degree of the monomial.
r	the ring element

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ setCoefficient() [3/3]

void DenseUnivariateIntegerPolynomial::setCoefficient	(	Integer	k,
		const Integer &	value
	)

inline

Set a coefficient of the polynomial.

Parameters

k	Degree of the term of which you are setting the coefficient
val	Coefficient value

◆ setVariableName()

void DenseUnivariateIntegerPolynomial::setVariableName ( const Symbol & x )

inlinevirtual

Set variable's name.

Parameters

x	Varable's name

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ squareFree()

Factors<DenseUnivariateIntegerPolynomial> DenseUnivariateIntegerPolynomial::squareFree ( ) const

Square free.

Parameters

◆ subtract()

void DenseUnivariateIntegerPolynomial::subtract ( const DenseUnivariateIntegerPolynomial & b )

Subtract another polynomial from itself.

Parameters

b	A univariate integer polynomial

◆ unitCanonical()

DenseUnivariateIntegerPolynomial DenseUnivariateIntegerPolynomial::unitCanonical	(	DenseUnivariateIntegerPolynomial *	u = `NULL`,
		DenseUnivariateIntegerPolynomial *	v = `NULL`
	)		const

inline

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.

◆ variable()

Symbol DenseUnivariateIntegerPolynomial::variable ( ) const

inlinevirtual

Get variable's name.

Parameters

Implements BPASUnivariatePolynomial< Integer, DenseUnivariateIntegerPolynomial >.

◆ zero()

void DenseUnivariateIntegerPolynomial::zero ( )

inline

Zero polynomial.

Parameters

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

include/IntegerPolynomial/uzpolynomial.h

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ DenseUnivariateIntegerPolynomial() [1/4]

◆ DenseUnivariateIntegerPolynomial() [2/4]

◆ DenseUnivariateIntegerPolynomial() [3/4]

◆ DenseUnivariateIntegerPolynomial() [4/4]

◆ ~DenseUnivariateIntegerPolynomial()

Member Function Documentation

◆ add()

◆ coefficient()

◆ coefficients()

◆ content()

◆ degree()

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ differentiate() [1/2]

◆ differentiate() [2/2]

◆ evaluate()

◆ gcd()

◆ integral()

◆ integrate()

◆ isConstant()

◆ isConstantTermZero()

◆ isNegativeOne()

◆ isOne()

◆ isZero()

◆ lazyPseudoDivide() [1/2]

◆ lazyPseudoDivide() [2/2]

◆ leadingCoefficient()

◆ monicDivide() [1/2]

◆ monicDivide() [2/2]

◆ negate()

◆ negativeOne()

◆ one()

◆ operator!=()

◆ 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-() [1/3]

◆ 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=()

◆ operator==()

◆ operator>>()

◆ operator>>=()

◆ operator^()

◆ operator^=()

◆ print()

◆ pseudoDivide() [1/2]

◆ pseudoDivide() [2/2]

◆ setCoefficient() [1/3]

◆ setCoefficient() [2/3]

◆ setCoefficient() [3/3]

◆ setVariableName()

◆ squareFree()

◆ subtract()

◆ unitCanonical()

◆ variable()

◆ zero()