A multivariate polynomial with coefficients in an arbitrary finite field represented densely. More...

#include <dmpolynomial.h>

Simplified semantic inheritance diagram for DistributedDenseMultivariateModularPolynomial< Field >:

Full inheritance diagram for DistributedDenseMultivariateModularPolynomial< Field >:

Public Member Functions
	DistributedDenseMultivariateModularPolynomial ()
	Constructor using a default field.

	DistributedDenseMultivariateModularPolynomial (const Field &m)
	Constructor with the Field. More...

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

	DistributedDenseMultivariateModularPolynomial (const Symbol &x, const Field &m)
	Construct with a variable name such that f(x) = x;. More...

	DistributedDenseMultivariateModularPolynomial (const DistributedDenseMultivariateModularPolynomial< Field > &b)
	Copy constructor. More...

	~DistributedDenseMultivariateModularPolynomial ()
	Deconstructor. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator= (const DistributedDenseMultivariateModularPolynomial< Field > &b)
	Overload operator =. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator= (const Field &f)
	Overload operator =. More...

mpz_class	getCharacteristic () const override
	The characteristic of this ring class.

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...

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
	Get the total degree.

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

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

Field	trailingCoefficient () const

bool	isConstantTermZero () const

DistributedDenseMultivariateModularPolynomial< Field >	unitCanonical (DistributedDenseMultivariateModularPolynomial u=NULL, DistributedDenseMultivariateModularPolynomial v=NULL) const

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

Field	coefficient (const std::vector< int > &v) const
	Get the coefficient of this polynomial with respect to the monomial defined by exponent vector exps. More...

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

void	setCoefficient (const std::vector< int > &v, const Field &val)
	Set the coefficient of this polynomial for the monomial defined by exponent vector exps to r. More...

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

Field	content () const

DistributedDenseMultivariateModularPolynomial	primitivePart () const

bool	operator== (const DistributedDenseMultivariateModularPolynomial< Field > &b) const
	Overload operator ==. More...

bool	operator!= (const DistributedDenseMultivariateModularPolynomial< Field > &b) const
	Overload operator !=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator+ (const DistributedDenseMultivariateModularPolynomial< Field > &b) const
	Overload operator +. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator+= (const DistributedDenseMultivariateModularPolynomial< Field > &b)
	Overload operator +=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator+ (const Field &e) const
	Overload operator +. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator+= (const Field &e)
	Overload operator +=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator- (const DistributedDenseMultivariateModularPolynomial< Field > &b) const
	Overload operator -. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator-= (const DistributedDenseMultivariateModularPolynomial< Field > &b)
	Overload operator -=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator- () const
	Overload operator -, negate. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator- (const Field &e) const
	Overload operator -. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator-= (const Field &e)
	Overload operator -=. More...

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

DistributedDenseMultivariateModularPolynomial< Field >	operator* (const DistributedDenseMultivariateModularPolynomial< Field > &b) const
	Overload operator *. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator*= (const DistributedDenseMultivariateModularPolynomial< Field > &b)
	Overload operator *=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator* (const Field &e) const
	Overload operator *. More...

DistributedDenseMultivariateModularPolynomial< Field > &	operator*= (const Field &f)
	Overload operator *=. More...

DistributedDenseMultivariateModularPolynomial< Field >	operator^ (long long int e) const

DistributedDenseMultivariateModularPolynomial< Field > &	operator^= (long long int e)

DistributedDenseMultivariateModularPolynomial< Field >	operator/ (const DistributedDenseMultivariateModularPolynomial< Field > &p) const

DistributedDenseMultivariateModularPolynomial< Field > &	operator/= (const DistributedDenseMultivariateModularPolynomial< Field > &p)

DistributedDenseMultivariateModularPolynomial< Field >	operator/ (const Field &e) const

DistributedDenseMultivariateModularPolynomial< Field > &	operator/= (const Field &e)

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

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

std::vector< Symbol >	variables () const
	Get all the variables in this polynomial with positive degree. More...

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

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

void	differentiate (const Symbol &s, int k)
	Differentiate this polynomial k times, with respect to a particular variable, setting itself to its derivative. More...

void	differentiate (const Symbol &s)
	Differentiate this polynomial, with respect to a particular variable, setting itself to its derivative. More...

DistributedDenseMultivariateModularPolynomial< Field >	derivative (const Symbol &s, int k) const
	Differentiate this polynomial k times, with respect to a particular variable, setting itself to its derivative. More...

DistributedDenseMultivariateModularPolynomial< Field >	derivative (const Symbol &s) const
	Differentiate this polynomial, with respect to a particular variable, setting itself to its derivative. More...

DistributedDenseMultivariateModularPolynomial< Field >	evaluate (const std::vector< Symbol > &syms, const std::vector< Field > &vals) const
	Evaluate this polynomial by substituting the input ring elements elems for the variables vars, such that vars[i] = elems[i]. More...

DistributedDenseMultivariateModularPolynomial< Field >	evaluate (int n, const Symbol syms, const Field vals) const
	Evaluate this polynomial by substituting the input ring elements elems for the variables vars, such that vars[i] = elems[i]. More...

DistributedDenseMultivariateModularPolynomial< Field >	gcd (const DistributedDenseMultivariateModularPolynomial< Field > &p) const

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

Static Public Attributes
static mpz_class	characteristic

Friends
DistributedDenseMultivariateModularPolynomial< Field >	operator+ (const Field &e, const DistributedDenseMultivariateModularPolynomial< Field > &f)

DistributedDenseMultivariateModularPolynomial< Field >	operator- (const Field &e, const DistributedDenseMultivariateModularPolynomial< Field > &f)

DistributedDenseMultivariateModularPolynomial< Field >	operator* (const Field &e, const DistributedDenseMultivariateModularPolynomial< Field > &f)

Detailed Description

template<class Field>
class DistributedDenseMultivariateModularPolynomial< Field >

A multivariate polynomial with coefficients in an arbitrary finite field represented densely.

The class is templated by a Field which should be a BPASField.

Constructor & Destructor Documentation

◆ DistributedDenseMultivariateModularPolynomial() [1/4]

template<class Field>

DistributedDenseMultivariateModularPolynomial< Field >::DistributedDenseMultivariateModularPolynomial ( const Field & m )

inline

Constructor with the Field.

Parameters

m The prime

◆ DistributedDenseMultivariateModularPolynomial() [2/4]

template<class Field>

DistributedDenseMultivariateModularPolynomial< Field >::DistributedDenseMultivariateModularPolynomial	(	int	v,
		int *	ds,
		Field	m
	)

inline

Constructor with number of variables and terms.

Parameters

v	Number of variables
ds	Partial degrees
m	The prime

◆ DistributedDenseMultivariateModularPolynomial() [3/4]

template<class Field>

DistributedDenseMultivariateModularPolynomial< Field >::DistributedDenseMultivariateModularPolynomial	(	const Symbol &	x,
		const Field &	m
	)

inline

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

Parameters

x	The variable name
m	The prime

◆ DistributedDenseMultivariateModularPolynomial() [4/4]

template<class Field>

DistributedDenseMultivariateModularPolynomial< Field >::DistributedDenseMultivariateModularPolynomial ( const DistributedDenseMultivariateModularPolynomial< Field > & b )

inline

Copy constructor.

Parameters

b	A multivariate modular polynomial

◆ ~DistributedDenseMultivariateModularPolynomial()

template<class Field>

DistributedDenseMultivariateModularPolynomial< Field >::~DistributedDenseMultivariateModularPolynomial ( )

inline

Deconstructor.

Parameters

Member Function Documentation

◆ coefficient() [1/2]

template<class Field>

Field DistributedDenseMultivariateModularPolynomial< Field >::coefficient	(	int	v,
		const int *	d
	)		const

inlinevirtual

Get a coefficient.

Parameters

v	Number of variables
d	The exponent of each variable

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ coefficient() [2/2]

template<class Field>

Field DistributedDenseMultivariateModularPolynomial< Field >::coefficient ( const std::vector< int > & exps ) const

inlinevirtual

Get the coefficient of this polynomial with respect to the monomial defined by exponent vector exps.

The exponent vector should be defined over all variables in the polynomial ring.

Parameters

exps	the exponent vector

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ degree()

template<class Field>

Integer DistributedDenseMultivariateModularPolynomial< Field >::degree ( const Symbol & x ) const

inlinevirtual

Get a partial degree of variable x.

Parameters

x	The variable name

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ derivative() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::derivative	(	const Symbol &	,
		int
	)		const

inlinevirtual

Differentiate this polynomial k times, with respect to a particular variable, setting itself to its derivative.

Parameters

var	the variable to derive with respect to.
k	the number of times to differentiate.

Returns: the derivative.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ derivative() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::derivative ( const Symbol & ) const

inlinevirtual

Differentiate this polynomial, with respect to a particular variable, setting itself to its derivative.

Parameters

var	the variable to derive with respect to.

Returns: the derivative.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ differentiate() [1/2]

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::differentiate	(	const Symbol &	var,
		int	k
	)

inlinevirtual

Differentiate this polynomial k times, with respect to a particular variable, setting itself to its derivative.

Parameters

var	the variable to derive with respect to.
k	the number of times to differentiate.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ differentiate() [2/2]

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::differentiate ( const Symbol & var )

inlinevirtual

Differentiate this polynomial, with respect to a particular variable, setting itself to its derivative.

Parameters

var	the variable to derive with respect to.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ evaluate() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::evaluate	(	const std::vector< Symbol > &	vars,
		const std::vector< Field > &	elems
	)		const

inlinevirtual

Evaluate this polynomial by substituting the input ring elements elems for the variables vars, such that vars[i] = elems[i].

Parameters

vars	the variables to evaluate.
elems	the ring elements to substitute for the varibales.

Returns: the evaluation of this polynomial for the variables in vars.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ evaluate() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::evaluate	(	int	n,
		const Symbol *	vars,
		const Field *	elems
	)		const

inlinevirtual

Evaluate this polynomial by substituting the input ring elements elems for the variables vars, such that vars[i] = elems[i].

Parameters

n	the size of the vars and elems arrays.
vars	the variables to evaluate.
elems	the ring elements to substitute for the varibales.

Returns: the evaluation of this polynomial for the variables in vars.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ isConstant()

template<class Field>

int DistributedDenseMultivariateModularPolynomial< Field >::isConstant ( ) const

inline

Is a constant.

Parameters

◆ isNegativeOne()

template<class Field>

bool DistributedDenseMultivariateModularPolynomial< Field >::isNegativeOne ( ) const

inline

Is polynomial -1.

Parameters

◆ isOne()

template<class Field>

bool DistributedDenseMultivariateModularPolynomial< Field >::isOne ( ) const

inline

Is polynomial 1.

Parameters

◆ isZero()

template<class Field>

bool DistributedDenseMultivariateModularPolynomial< Field >::isZero ( ) const

inline

Is a zero polynomial.

Parameters

◆ leadingCoefficient()

template<class Field>

Field DistributedDenseMultivariateModularPolynomial< Field >::leadingCoefficient ( ) const

inline

Get the leading coefficient.

Parameters

◆ negate()

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::negate ( )

inline

Negate, f(-x)

Parameters

◆ negativeOne()

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::negativeOne ( )

inline

Set polynomial to -1.

Parameters

◆ numberOfTerms()

template<class Field>

Integer DistributedDenseMultivariateModularPolynomial< Field >::numberOfTerms ( ) const

inline

Get the number of non-zero terms.

Parameters

◆ numberOfVariables()

template<class Field>

int DistributedDenseMultivariateModularPolynomial< Field >::numberOfVariables ( ) const

inlinevirtual

Get the number of variables.

Parameters

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ one()

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::one ( )

inline

Set polynomial to 1.

Parameters

◆ operator!=()

template<class Field>

bool DistributedDenseMultivariateModularPolynomial< Field >::operator!= ( const DistributedDenseMultivariateModularPolynomial< Field > & b ) const

inline

Overload operator !=.

Parameters

b	A multivariate modular polynomial

◆ operator*() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator* ( const DistributedDenseMultivariateModularPolynomial< Field > & b ) const

inline

Overload operator *.

Parameters

b	A multivariate modular polynomial

◆ operator*() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator* ( const Field & e ) const

inline

Overload operator *.

Parameters

e	A constant

◆ operator*=() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator*= ( const DistributedDenseMultivariateModularPolynomial< Field > & b )

inline

Overload operator *=.

Parameters

b	A multivariate modular polynomial

◆ operator*=() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator*= ( const Field & f )

inline

Overload operator *=.

Parameters

e	A constant

◆ operator+() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator+ ( const DistributedDenseMultivariateModularPolynomial< Field > & b ) const

inline

Overload operator +.

Parameters

b	A multivariate modular polynomial

◆ operator+() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator+ ( const Field & e ) const

inline

Overload operator +.

Parameters

e	A constant

◆ operator+=() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator+= ( const DistributedDenseMultivariateModularPolynomial< Field > & b )

inline

Overload operator +=.

Parameters

b	A multivariate modular polynomial

◆ operator+=() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator+= ( const Field & e )

inline

Overload operator +=.

Parameters

e	A constant

◆ operator-() [1/3]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator- ( const DistributedDenseMultivariateModularPolynomial< Field > & b ) const

inline

Overload operator -.

Parameters

b	A multivariate modular polynomial

◆ operator-() [2/3]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator- ( ) const

inline

Overload operator -, negate.

Parameters

◆ operator-() [3/3]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field> DistributedDenseMultivariateModularPolynomial< Field >::operator- ( const Field & e ) const

inline

Overload operator -.

Parameters

e	A constant

◆ operator-=() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator-= ( const DistributedDenseMultivariateModularPolynomial< Field > & b )

inline

Overload operator -=.

Parameters

b	A multivariate modular polynomial

◆ operator-=() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator-= ( const Field & e )

inline

Overload operator -=.

Parameters

e	A constant

◆ operator=() [1/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator= ( const DistributedDenseMultivariateModularPolynomial< Field > & b )

inline

Overload operator =.

Parameters

b	A multivariate modular polynomial

◆ operator=() [2/2]

template<class Field>

DistributedDenseMultivariateModularPolynomial<Field>& DistributedDenseMultivariateModularPolynomial< Field >::operator= ( const Field & f )

inline

Overload operator =.

Assign this to a be a base Field element.

◆ operator==()

template<class Field>

bool DistributedDenseMultivariateModularPolynomial< Field >::operator== ( const DistributedDenseMultivariateModularPolynomial< Field > & b ) const

inline

Overload operator ==.

Parameters

b	A multivariate modular polynomial

◆ print()

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::print ( std::ostream & out ) const

inline

Overload stream operator <<.

Parameters

out	Stream object
b	The multivariate modular polynomial

◆ ringVariables()

template<class Field>

std::vector<Symbol> DistributedDenseMultivariateModularPolynomial< Field >::ringVariables ( ) const

inlinevirtual

Get variable names.

Parameters

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ setCoefficient() [1/3]

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::setCoefficient	(	int	v,
		const int *	d,
		const Field &	val
	)

inlinevirtual

Set a coefficient.

Parameters

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

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ setCoefficient() [2/3]

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::setCoefficient	(	const std::vector< int > &	v,
		const Field &	r
	)

inlinevirtual

Set the coefficient of this polynomial for the monomial defined by exponent vector exps to r.

The exponent vector should be defined over all variables in the polynomial ring.

Parameters

exps	the exponent vector
r	the ring element to set as coefficient.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ setCoefficient() [3/3]

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::setCoefficient	(	int	k,
		const Field &	val
	)

inline

Set a coefficient.

Parameters

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

◆ setRingVariables()

template<class Field>

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

inlinevirtual

Set variable names.

Parameters

xs	Variable names

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ size()

template<class Field>

int DistributedDenseMultivariateModularPolynomial< Field >::size ( ) const

inline

Get the size of the polynomial.

Parameters

◆ variables()

template<class Field>

std::vector<Symbol> DistributedDenseMultivariateModularPolynomial< Field >::variables ( ) const

inlinevirtual

Get all the variables in this polynomial with positive degree.

Returns: a vector of all the variables in this polynomial with positive degree.

Implements BPASMultivariatePolynomial< Field, DistributedDenseMultivariateModularPolynomial< Field > >.

◆ zero()

template<class Field>

void DistributedDenseMultivariateModularPolynomial< Field >::zero ( )

inline

Zero polynomial.

Parameters

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

include/RingPolynomial/dmpolynomial.h

Public Member Functions

Static Public Attributes

Friends

Detailed Description

template<class Field> class DistributedDenseMultivariateModularPolynomial< Field >

Constructor & Destructor Documentation

◆ DistributedDenseMultivariateModularPolynomial() [1/4]

◆ DistributedDenseMultivariateModularPolynomial() [2/4]

◆ DistributedDenseMultivariateModularPolynomial() [3/4]

◆ DistributedDenseMultivariateModularPolynomial() [4/4]

◆ ~DistributedDenseMultivariateModularPolynomial()

Member Function Documentation

◆ coefficient() [1/2]

◆ coefficient() [2/2]

◆ 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=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ print()

◆ ringVariables()

◆ setCoefficient() [1/3]

◆ setCoefficient() [2/3]

◆ setCoefficient() [3/3]

◆ setRingVariables()

◆ size()

◆ variables()

◆ zero()

template<class Field>
class DistributedDenseMultivariateModularPolynomial< Field >