DistributedDenseMultivariateModularPolynomial< Field > Class Template Reference

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...
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
void	setCoefficient (int v, const int *d, const Field &val)
	Set a coefficient. More...
void	setCoefficient (const std::vector< int > &v, const Field &val)
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
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)
void	differentiate (const Symbol &s)
DistributedDenseMultivariateModularPolynomial< Field >	derivative (const Symbol &s, int k) const
DistributedDenseMultivariateModularPolynomial< Field >	derivative (const Symbol &s) const
DistributedDenseMultivariateModularPolynomial< Field >	evaluate (const std::vector< Symbol > &syms, const std::vector< Field > &vals) const
DistributedDenseMultivariateModularPolynomial< Field >	evaluate (int n, const Symbol *syms, const Field *vals) const
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()

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 > >.

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 > >.

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() [1/2]

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() [2/2]

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

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