A multivariate polynomial with coefficients in a small prime field using a dense representation. More...

#include <sdmpolynomial.h>

Simplified semantic inheritance diagram for SmallPrimeFieldDistributedDenseMultivariateModularPolynomial:

Full inheritance diagram for SmallPrimeFieldDistributedDenseMultivariateModularPolynomial:

Public Member Functions
	SmallPrimeFieldDistributedDenseMultivariateModularPolynomial ()
	Constructor using a default prime.

	SmallPrimeFieldDistributedDenseMultivariateModularPolynomial (sfixn m)
	Constructor with the field. More...

	SmallPrimeFieldDistributedDenseMultivariateModularPolynomial (int v, int *ds, sfixn m)
	Constructor with number of variables and terms. More...

	SmallPrimeFieldDistributedDenseMultivariateModularPolynomial (Symbol x, sfixn m)
	Construct with a variable name such that f(x) = x;. More...

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

	~SmallPrimeFieldDistributedDenseMultivariateModularPolynomial ()
	Deconstructor. More...

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

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator= (const sfixn &b)

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

void	zero ()
	Zero polynomial. More...

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

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

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

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

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

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

int	numberOfVariables () const
	Get the number of variables. More...

int	numberOfRingVariables () const
	Get the number of variables in this polynomial ring.

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

int	size () const
	Get the size of the polynomial. More...

Integer	degree () const
	Total degree.

Integer	degree (const Symbol &x) const
	Get a partial degree of variable x. More...

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

sfixn	trailingCoefficient () const

bool	isConstantTermZero () const

sfixn	coefficient (int v, const int *d) const
	Get a coefficient. More...

sfixn	coefficient (const std::vector< int > &v) const

void	setCoefficient (int v, const int *d, const sfixn &val)
	Set a coefficient. More...

void	setCoefficient (const std::vector< int > &v, const sfixn &val)

void	setCoefficient (int k, const sfixn &val)
	Set a coefficient. More...

std::vector< Symbol >	ringVariables () const
	Get variable names. More...

void	setRingVariables (const std::vector< Symbol > &xs)
	Set variable names. More...

std::vector< Symbol >	variables () const

void	differentiate (const Symbol &s, int k)
	Convert current object to its k-th derivative. More...

void	differentiate (const Symbol &s)
	Convert current object to its derivative. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	derivative (const Symbol &s, int k) const
	Return k-th derivative. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	derivative (const Symbol &s) const
	Compute derivative. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	evaluate (int, const Symbol syms, const sfixn xs) const
	Evaluate f(x) More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	evaluate (const std::vector< Symbol > &syms, const std::vector< sfixn > &xs) const
	Evaluate f(x) More...

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

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

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

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

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator+ (const sfixn &e) const
	Overload operator +. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator+= (const sfixn &e)
	Overload operator +=. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator- (const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &b) const
	Overload operator -. More...

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

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator- (const sfixn &e) const
	Overload operator -. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator-= (const sfixn &e)
	Overload operator -=. More...

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

void	negate ()
	Negate, f(-x) More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator* (const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &b) const
	Overload operator *. More...

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

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator* (const sfixn &e) const
	Overload operator *. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator*= (const sfixn &e)
	Overload operator *=. More...

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator^ (long long int e) const
	Overload operator ^ for exponentiation.

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator^= (long long int e)
	Overload operator ^ for exponentiation.

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator/ (const sfixn &e) const

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator/= (const sfixn &e)

sfixn	content () const

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	primitivePart () const

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

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

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator/ (const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &p) const
	Exact division.

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &	operator/= (const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &p)
	Exact division assignment.

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	gcd (const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &p) const
	Get GCD of *this and other.

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

Static Public Attributes
static mpz_class	characteristic

static RingProperties	properties

Friends
SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator+ (const sfixn &e, const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &f)

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator- (const sfixn &e, const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &r)

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	operator* (const sfixn &e, const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial &f)

Detailed Description

A multivariate polynomial with coefficients in a small prime field using a dense representation.

Constructor & Destructor Documentation

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [1/4]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::SmallPrimeFieldDistributedDenseMultivariateModularPolynomial ( sfixn m )

inline

Constructor with the field.

Parameters

m The prime

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [2/4]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	(	int	v,
		int *	ds,
		sfixn	m
	)

inline

Constructor with number of variables and terms.

Parameters

v	Number of variables
ds	Partial degrees
m	The prime

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [3/4]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::SmallPrimeFieldDistributedDenseMultivariateModularPolynomial	(	Symbol	x,
		sfixn	m
	)

inline

Construct with a variable name such that f(x) = x;.

Parameters

x	The variable name
m	The prime

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [4/4]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::SmallPrimeFieldDistributedDenseMultivariateModularPolynomial ( const SmallPrimeFieldDistributedDenseMultivariateModularPolynomial & b )

inline

Copy constructor.

Parameters

b	A multivariate modular polynomial

◆ ~SmallPrimeFieldDistributedDenseMultivariateModularPolynomial()

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::~SmallPrimeFieldDistributedDenseMultivariateModularPolynomial ( )

inline

Deconstructor.

Parameters

Member Function Documentation

◆ coefficient()

sfixn SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::coefficient	(	int	v,
		const int *	d
	)		const

inlinevirtual

Get a coefficient.

Parameters

v	Number of variables
d	The exponent of each variable

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ convertToExpressionTree()

ExpressionTree SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::convertToExpressionTree ( ) const

virtual

Convert *this to an expression tree.

Implements ExpressionTreeConvert.

◆ degree()

Integer SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::degree ( const Symbol & x ) const

inlinevirtual

Get a partial degree of variable x.

Parameters

x	The variable name

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ derivative() [1/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::derivative	(	const Symbol &	s,
		int	k
	)		const

inlinevirtual

Return k-th derivative.

Parameters

s	Symbol to differentiate with respect to
k	Order of the k-th derivative, k > 0

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ derivative() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::derivative ( const Symbol & s ) const

inlinevirtual

Compute derivative.

Parameters

s	Symbol to differentiate with respect to

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ differentiate() [1/2]

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::differentiate	(	const Symbol &	s,
		int	k
	)

inlinevirtual

Convert current object to its k-th derivative.

Parameters

s	Symbol to differentiate with respect to
k	Order of the derivative, k > 0

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ differentiate() [2/2]

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::differentiate ( const Symbol & s )

inlinevirtual

Convert current object to its derivative.

Parameters

s	Symbol to differentiate with respect to

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ evaluate() [1/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::evaluate	(	int	,
		const Symbol *	syms,
		const sfixn *	xs
	)		const

inlinevirtual

Evaluate f(x)

Parameters

syms	Array of Symbols to evaluate at corresponding xs
xs	Evaluation points

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ evaluate() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::evaluate	(	const std::vector< Symbol > &	syms,
		const std::vector< sfixn > &	xs
	)		const

inlinevirtual

Evaluate f(x)

Parameters

syms	Vector of Symbols to evaluate at corresponding xs
xs	Corresponding evaluation points

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ isConstant()

int SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isNegativeOne()

bool SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::isNegativeOne ( ) const

inline

Is polynomial -1.

Parameters

◆ isOne()

bool SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::isOne ( ) const

inlinevirtual

Is polynomial 1.

Parameters

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ isZero()

bool SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::isZero ( ) const

inlinevirtual

Is a zero polynomial.

Parameters

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ leadingCoefficient()

sfixn SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::leadingCoefficient ( ) const

inline

Get the leading coefficient.

Parameters

◆ negate()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::negate ( )

Negate, f(-x)

Parameters

◆ negativeOne()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::negativeOne ( )

inline

Set polynomial to -1.

Parameters

◆ numberOfTerms()

Integer SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::numberOfTerms ( ) const

inline

Get the number of non-zero terms.

Parameters

◆ numberOfVariables()

int SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::numberOfVariables ( ) const

inlinevirtual

Get the number of variables.

Parameters

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ one()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::one ( )

inlinevirtual

Set polynomial to 1.

Parameters

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator!=()

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

inlinevirtual

Overload operator !=.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator*() [1/2]

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

virtual

Overload operator *.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator*() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator* ( const sfixn & e ) const

inline

Overload operator *.

Parameters

e	A constant

◆ operator*=() [1/2]

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

inlinevirtual

Overload operator *=.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator*=() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial& SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator*= ( const sfixn & e )

Overload operator *=.

Parameters

e	A constant

◆ operator+() [1/2]

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

virtual

Overload operator +.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator+() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator+ ( const sfixn & e ) const

inline

Overload operator +.

Parameters

e	A constant

◆ operator+=() [1/2]

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

inlinevirtual

Overload operator +=.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator+=() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial& SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator+= ( const sfixn & e )

Overload operator +=.

Parameters

e	A constant

◆ operator-() [1/3]

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

virtual

Overload operator -.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator-() [2/3]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator- ( const sfixn & e ) const

inline

Overload operator -.

Parameters

e	A constant

◆ operator-() [3/3]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator- ( ) const

virtual

Overload operator -, negate.

Parameters

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator-=() [1/2]

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

inlinevirtual

Overload operator -=.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator-=() [2/2]

SmallPrimeFieldDistributedDenseMultivariateModularPolynomial& SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::operator-= ( const sfixn & e )

Overload operator -=.

Parameters

e	A constant

◆ operator=()

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

inlinevirtual

Overload operator =.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ operator==()

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

virtual

Overload operator ==.

Parameters

b	A multivariate modular polynomial

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ print()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::print ( std::ostream & ostream ) const

virtual

Print the Ring element.

Derived classes may override this to get custom printing that may be more expressive (and prettier) than expression tree printing.

Reimplemented from BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ ringVariables()

std::vector<Symbol> SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::ringVariables ( ) const

inlinevirtual

Get variable names.

Parameters

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ setCoefficient() [1/2]

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::setCoefficient	(	int	v,
		const int *	d,
		const sfixn &	val
	)

inlinevirtual

Set a coefficient.

Parameters

v	Number of variables
d	The exponent of each variable
val	Value of the coefficient

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ setCoefficient() [2/2]

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::setCoefficient	(	int	k,
		const sfixn &	val
	)

inline

Set a coefficient.

Parameters

k	The offset in the coefficient array
val	Value of the coefficient

◆ setRingVariables()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::setRingVariables ( const std::vector< Symbol > & xs )

inlinevirtual

Set variable names.

Parameters

xs	Variable names

Implements BPASMultivariatePolynomial< sfixn, SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

◆ size()

int SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::size ( ) const

inline

Get the size of the polynomial.

Parameters

◆ unitCanonical()

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

◆ zero()

void SmallPrimeFieldDistributedDenseMultivariateModularPolynomial::zero ( )

inlinevirtual

Zero polynomial.

Parameters

Implements BPASRing< SmallPrimeFieldDistributedDenseMultivariateModularPolynomial >.

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

include/ModularPolynomial/sdmpolynomial.h

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [1/4]

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [2/4]

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [3/4]

◆ SmallPrimeFieldDistributedDenseMultivariateModularPolynomial() [4/4]

◆ ~SmallPrimeFieldDistributedDenseMultivariateModularPolynomial()

Member Function Documentation

◆ coefficient()

◆ convertToExpressionTree()

◆ degree()

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ differentiate() [1/2]

◆ differentiate() [2/2]

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ isConstant()

◆ isNegativeOne()

◆ isOne()

◆ isZero()

◆ leadingCoefficient()

◆ negate()

◆ negativeOne()

◆ numberOfTerms()

◆ numberOfVariables()

◆ 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=()

◆ operator==()

◆ print()

◆ ringVariables()

◆ setCoefficient() [1/2]

◆ setCoefficient() [2/2]

◆ setRingVariables()

◆ size()

◆ unitCanonical()

◆ zero()