Classes
class	Term
	Represent a term. More...

class	TaggedPolynomial
	Represent a tagged polynomial. More...

struct	NodeList
	Represent a node of the single chained list. More...

class	SingleList
	Represent a single chained list. More...

class	Polynomial
	Represent a polynomial. More...

class	MonomialArray
	Represent a array of monomials. More...

class	Monomial
	Represent a monomial. More...

class	Matrix
	Represent a matrix. More...

struct	Stat
	Structure used for statistics. More...

class	Ideal
	Represent an ideal. More...

class	ElementPrime
	Represent an element of a prime field, this class is a POD (Plain Old Data) because of the alignement required in class Matrix. More...

class	ElementGF2Extension
	Represent an element of an extension of GF2, this class is a POD (Plain Old Data) because of the alignement required in class Matrix. More...

class	ElementGF2
	Represent an element of the field GF(2), this class is a POD (Plain Old Data) because of the alignement required in class Matrix. More...

class	DynamicArray
	Represent a dynamic array whose the width is fixed, the memory is allocated by blocs. More...

class	CriticalPair
	Represent a critical pair. More...

struct	NodeAvlPolynomial
	Represent a node of the AVL of polynomial. More...

class	AvlPolynomial
	Represent an avl of triple (number of a polynomial, number of its leading monomial, number of terms). More...

struct	NodeAvlMonomial
	Represent a node of the AVL of monomials. More...

class	AvlMonomial
	Represent an avl of pair (number of a monomial, is leading monomial). More...

struct	NodeAvlCriticalPair
	Represent a node of the AVL of critical pairs. More...

class	AvlCriticalPair
	Represent an avl of critical pair. More...

Functions
template<typename Element >
std::ostream &	operator<< (std::ostream &stream, Term< Element > const &term)
	Overload the operator <<. More...

template<typename Element >
Term< Element >	operator* (Monomial const &mon, Term< Element > const &term)
	Overload the operator *. More...

template<typename Element >
Term< Element >	operator* (Term< Element > const &term, Monomial const &mon)
	Overload the operator *. More...

template<typename Element >
Term< Element >	operator* (Term< Element > const &term1, Term< Element > const &term2)
	Overload the operator *. More...

template<typename Element >
bool	operator> (Term< Element > const &term1, Term< Element > const &term2)
	Overload the operator >. More...

template<typename Element >
bool	operator< (Term< Element > const &term1, Term< Element > const &term2)
	Overload the operator <. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, TaggedPolynomial< Element > const &taggedPolynomial)
	Overload the operator <<. More...

template<typename Element >
bool	operator== (TaggedPolynomial< Element > const &taggedPolynomial1, TaggedPolynomial< Element > const &taggedPolynomial2)
	Overload the operator ==. More...

template<typename Element >
bool	operator> (TaggedPolynomial< Element > const &taggedPolynomial1, TaggedPolynomial< Element > const &taggedPolynomial2)
	Overload the operator >. More...

template<typename Element >
bool	operator>= (TaggedPolynomial< Element > const &taggedPolynomial1, TaggedPolynomial< Element > const &taggedPolynomial2)
	Overload the operator >=. More...

template<typename Element >
bool	operator< (TaggedPolynomial< Element > const &taggedPolynomial1, TaggedPolynomial< Element > const &taggedPolynomial2)
	Overload the operator <. More...

template<typename Element >
bool	operator<= (TaggedPolynomial< Element > const &taggedPolynomial1, TaggedPolynomial< Element > const &taggedPolynomial2)
	Overload the operator <=. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (Monomial const &monomial, TaggedPolynomial< Element > const &taggedPolynomial)
	Overload the operator *= to multiply this with a monomial. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (TaggedPolynomial< Element > const &taggedPolynomial, Monomial const &monomial)
	Overload the operator *= to multiply this with a monomial. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (Element element, TaggedPolynomial< Element > const &taggedPolynomial)
	Overload the operator *= to multiply this with an Element. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (TaggedPolynomial< Element > const &taggedPolynomial, Element element)
	Overload the operator *= to multiply this with an Element. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (Term< Element > const &term, TaggedPolynomial< Element > const &taggedPolynomial)
	Overload the operator *= to multiply this with a term. More...

template<typename Element >
TaggedPolynomial< Element >	operator* (TaggedPolynomial< Element > const &taggedPolynomial, Term< Element > const &term)
	Overload the operator *= to multiply this with a term. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, SingleList< Element > const &list)
	Overload the operator <<. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, Polynomial< Element > const &polynomial)
	Overload the operator <<. More...

template<typename Element >
Polynomial< Element >	operator* (Monomial const &monomial, Polynomial< Element > const &polynomial)
	Overload the operator *= to multiply this with a monomial. More...

template<typename Element >
Polynomial< Element >	operator* (Polynomial< Element > const &polynomial, Monomial const &monomial)
	Overload the operator *= to multiply this with a monomial. More...

template<typename Element >
Polynomial< Element >	operator* (Element element, Polynomial< Element > const &polynomial)
	Overload the operator *= to multiply this with an Element. More...

template<typename Element >
Polynomial< Element >	operator* (Polynomial< Element > const &polynomial, Element element)
	Overload the operator *= to multiply this with an Element. More...

template<typename Element >
Polynomial< Element >	operator* (Term< Element > const &term, Polynomial< Element > const &polynomial)
	Overload the operator *= to multiply this with a term. More...

template<typename Element >
Polynomial< Element >	operator* (Polynomial< Element > const &polynomial, Term< Element > const &term)
	Overload the operator *= to multiply this with a term. More...

std::ostream &	operator<< (std::ostream &stream, Monomial const &mon)
	Overload the operator <<. More...

bool	operator== (Monomial const &mon1, Monomial const &mon2)
	Overload the operator ==. More...

bool	operator> (Monomial const &mon1, Monomial const &mon2)
	Overload the operator >. More...

bool	operator>= (Monomial const &mon1, Monomial const &mon2)
	Overload the operator >=. More...

bool	operator< (Monomial const &mon1, Monomial const &mon2)
	Overload the operator <. More...

bool	operator<= (Monomial const &mon1, Monomial const &mon2)
	Overload the operator <=. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, Matrix< Element > const &matrix)
	Overload the operator <<. More...

template<typename baseType >
std::ostream &	operator<< (std::ostream &stream, ElementPrime< baseType > const &element)
	Overload the operator <<. More...

template<typename baseType >
ElementPrime< baseType >	operator* (ElementPrime< baseType > const &element1, ElementPrime< baseType > const &element2)
	Overload the operator *. More...

template<typename baseType >
ElementPrime< baseType >	operator- (ElementPrime< baseType > const &element)
	Overload the operator -. More...

template<typename baseType >
std::ostream &	operator<< (std::ostream &stream, ElementGF2Extension< baseType > const &element)
	Overload the operator <<. More...

template<typename baseType >
ElementGF2Extension< baseType >	operator* (ElementGF2Extension< baseType > const &element1, ElementGF2Extension< baseType > const &element2)
	Overload the operator *. More...

template<typename baseType >
ElementGF2Extension< baseType >	operator- (ElementGF2Extension< baseType > const &element)
	Overload the operator -. More...

std::ostream &	operator<< (std::ostream &stream, ElementGF2 const &element)
	Overload the operator <<. More...

ElementGF2	operator* (ElementGF2 const &element1, ElementGF2 const &element2)
	Overload the operator *. More...

ElementGF2	operator- (ElementGF2 const &element)
	Overload the operator -. More...

template<typename dataType >
std::ostream &	operator<< (std::ostream &stream, DynamicArray< dataType > const &dynamicArray)
	Overload the operator <<. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, CriticalPair< Element > const &criticalPair)
	Overload the operator <<. More...

template<typename Element >
bool	operator== (CriticalPair< Element > const &criticalPair1, CriticalPair< Element > const &criticalPair2)
	Overload the operator ==. More...

template<typename Element >
bool	operator> (CriticalPair< Element > const &criticalPair1, CriticalPair< Element > const &criticalPair2)
	Overload the operator >. More...

template<typename Element >
bool	operator>= (CriticalPair< Element > const &criticalPair1, CriticalPair< Element > const &criticalPair2)
	Overload the operator >=. More...

template<typename Element >
bool	operator< (CriticalPair< Element > const &criticalPair1, CriticalPair< Element > const &criticalPair2)
	Overload the operator <. More...

template<typename Element >
bool	operator<= (CriticalPair< Element > const &criticalPair1, CriticalPair< Element > const &criticalPair2)
	Overload the operator <=. More...

void	printNode (NodeAvlPolynomial *p, int indent=0)
	Print the AVL of root p. More...

template<typename dataType >
std::ostream &	operator<< (std::ostream &stream, AvlPolynomial const &AvlPolynomial)
	Overload the operator <<. More...

void	printNode (NodeAvlMonomial *p, int indent=0)
	Print the AVL of root p. More...

template<typename dataType >
std::ostream &	operator<< (std::ostream &stream, AvlMonomial const &avlMonomial)
	Overload the operator <<. More...

template<typename Element >
void	printNode (NodeAvlCriticalPair< Element > *p, int indent=0)
	Print the AVL of root p. More...

template<typename Element >
std::ostream &	operator<< (std::ostream &stream, AvlCriticalPair< Element > const &avlCriticalPair)
	Overload the operator <<. More...

Detailed Description

Group all the required tools used by the F4 algorithm.

Function Documentation

ElementGF2 F4::operator*	(	ElementGF2 const &	element1,
		ElementGF2 const &	element2
	)

Overload the operator *.

Returns: element1 * element2.

template<typename baseType >

ElementPrime<baseType> F4::operator*	(	ElementPrime< baseType > const &	element1,
		ElementPrime< baseType > const &	element2
	)

Overload the operator *.

Returns: element1 * element2.

template<typename Element >

Term<Element> F4::operator*	(	Monomial const &	mon,
		Term< Element > const &	term
	)

Overload the operator *.

Returns: mon * term.

template<typename Element >

Term<Element> F4::operator*	(	Term< Element > const &	term,
		Monomial const &	mon
	)

Overload the operator *.

Returns: term * mon.

template<typename Element >

Term<Element> F4::operator*	(	Term< Element > const &	term1,
		Term< Element > const &	term2
	)

Overload the operator *.

Returns: term1 * term2.

template<typename Element >

Polynomial<Element> F4::operator*	(	Monomial const &	monomial,
		Polynomial< Element > const &	polynomial
	)

Overload the operator *= to multiply this with a monomial.

Parameters

mon	Monomial.
polynomial	Polynomial.

Returns: Reference on this.

template<typename Element >

Polynomial<Element> F4::operator*	(	Polynomial< Element > const &	polynomial,
		Monomial const &	monomial
	)

Overload the operator *= to multiply this with a monomial.

Parameters

mon	Monomial.
polynomial	Polynomial.

Returns: Reference on this.

template<typename Element >

Polynomial<Element> F4::operator*	(	Element	element,
		Polynomial< Element > const &	polynomial
	)

Overload the operator *= to multiply this with an Element.

Parameters

element	Element.
polynomial	Polynomial.

Returns: Reference on this.

template<typename Element >

Polynomial<Element> F4::operator*	(	Polynomial< Element > const &	polynomial,
		Element	element
	)

Overload the operator *= to multiply this with an Element.

Parameters

element	Element.
polynomial	Polynomial.

Returns: Reference on this.

template<typename Element >

Polynomial<Element> F4::operator*	(	Term< Element > const &	term,
		Polynomial< Element > const &	polynomial
	)

Overload the operator *= to multiply this with a term.

Parameters

term	Term.
polynomial	Polynomial.

Returns: Reference on this.

template<typename Element >

Polynomial<Element> F4::operator*	(	Polynomial< Element > const &	polynomial,
		Term< Element > const &	term
	)

Overload the operator *= to multiply this with a term.

Parameters

term	Term.
polynomial	Polynomial.

Returns: Reference on this.

template<typename baseType >

ElementGF2Extension<baseType> F4::operator*	(	ElementGF2Extension< baseType > const &	element1,
		ElementGF2Extension< baseType > const &	element2
	)

Overload the operator *.

Returns: element1 * element2.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	Monomial const &	monomial,
		TaggedPolynomial< Element > const &	taggedPolynomial
	)

Overload the operator *= to multiply this with a monomial.

Parameters

mon	Monomial.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	TaggedPolynomial< Element > const &	taggedPolynomial,
		Monomial const &	monomial
	)

Overload the operator *= to multiply this with a monomial.

Parameters

mon	Monomial.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	Element	element,
		TaggedPolynomial< Element > const &	taggedPolynomial
	)

Overload the operator *= to multiply this with an Element.

Parameters

element	Element.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	TaggedPolynomial< Element > const &	taggedPolynomial,
		Element	element
	)

Overload the operator *= to multiply this with an Element.

Parameters

element	Element.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	Term< Element > const &	term,
		TaggedPolynomial< Element > const &	taggedPolynomial
	)

Overload the operator *= to multiply this with a term.

Parameters

term	Term.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

template<typename Element >

TaggedPolynomial<Element> F4::operator*	(	TaggedPolynomial< Element > const &	taggedPolynomial,
		Term< Element > const &	term
	)

Overload the operator *= to multiply this with a term.

Parameters

term	Term.
TaggedPolynomial	taggedPolynomial.

Returns: Reference on this.

ElementGF2 F4::operator- ( ElementGF2 const & element )

Overload the operator -.

Returns: -element.

template<typename baseType >

ElementPrime<baseType> F4::operator- ( ElementPrime< baseType > const & element )

Overload the operator -.

Returns: -element.

template<typename baseType >

ElementGF2Extension<baseType> F4::operator- ( ElementGF2Extension< baseType > const & element )

Overload the operator -.

Returns: -element.

template<typename Element >

bool F4::operator<	(	CriticalPair< Element > const &	criticalPair1,
		CriticalPair< Element > const &	criticalPair2
	)

Overload the operator <.

Returns: true if criticalPair1 < criticalPair2.; false otherwise.

template<typename Element >

bool F4::operator<	(	Term< Element > const &	term1,
		Term< Element > const &	term2
	)

Overload the operator <.

Parameters

term1	Term.
term2	Term.

Returns: true if term1<term2.; false otherwise.

template<typename Element >

bool F4::operator<	(	TaggedPolynomial< Element > const &	taggedPolynomial1,
		TaggedPolynomial< Element > const &	taggedPolynomial2
	)

Overload the operator <.

Returns: true if taggedPolynomial1 < taggedPolynomial2.; false otherwise.

bool F4::operator<	(	Monomial const &	mon1,
		Monomial const &	mon2
	)

Overload the operator <.

Parameters

mon1	Monomial.
mon2	Monomial.

Returns: true if mon1<mon2.; false otherwise.

std::ostream& F4::operator<<	(	std::ostream &	stream,
		ElementGF2 const &	element
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename dataType >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		DynamicArray< dataType > const &	dynamicArray
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename dataType >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		AvlMonomial const &	avlMonomial
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename dataType >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		AvlPolynomial const &	AvlPolynomial
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename baseType >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		ElementPrime< baseType > const &	element
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		CriticalPair< Element > const &	criticalPair
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		Term< Element > const &	term
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		AvlCriticalPair< Element > const &	avlCriticalPair
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		Polynomial< Element > const &	polynomial
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		TaggedPolynomial< Element > const &	taggedPolynomial
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		SingleList< Element > const &	list
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename baseType >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		ElementGF2Extension< baseType > const &	element
	)

Overload the operator <<.

Returns: ostream: Stream.

std::ostream& F4::operator<<	(	std::ostream &	stream,
		Monomial const &	mon
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

std::ostream& F4::operator<<	(	std::ostream &	stream,
		Matrix< Element > const &	matrix
	)

Overload the operator <<.

Returns: ostream: Stream.

template<typename Element >

bool F4::operator<=	(	CriticalPair< Element > const &	criticalPair1,
		CriticalPair< Element > const &	criticalPair2
	)

Overload the operator <=.

Returns: true if criticalPair1 <= criticalPair2.; false otherwise.

template<typename Element >

bool F4::operator<=	(	TaggedPolynomial< Element > const &	taggedPolynomial1,
		TaggedPolynomial< Element > const &	taggedPolynomial2
	)

Overload the operator <=.

Returns: true if taggedPolynomial1 <= taggedPolynomial2.; false otherwise.

bool F4::operator<=	(	Monomial const &	mon1,
		Monomial const &	mon2
	)

Overload the operator <=.

Parameters

mon1	Monomial.
mon2	Monomial.

Returns: true if mon1<=mon2.; false otherwise.

template<typename Element >

bool F4::operator==	(	CriticalPair< Element > const &	criticalPair1,
		CriticalPair< Element > const &	criticalPair2
	)

Overload the operator ==.

Returns: true if criticalPair1 == criticalPair2.; false otherwise.

template<typename Element >

bool F4::operator==	(	TaggedPolynomial< Element > const &	taggedPolynomial1,
		TaggedPolynomial< Element > const &	taggedPolynomial2
	)

Overload the operator ==.

Returns: true if taggedPolynomial1 == taggedPolynomial2.; false otherwise.

bool F4::operator==	(	Monomial const &	mon1,
		Monomial const &	mon2
	)

Overload the operator ==.

Parameters

mon1	Monomial.
mon2	Monomial.

Returns: true if mon1==mon2.; false otherwise.

template<typename Element >

bool F4::operator>	(	CriticalPair< Element > const &	criticalPair1,
		CriticalPair< Element > const &	criticalPair2
	)

Overload the operator >.

Returns: true if criticalPair1 > criticalPair2.; false otherwise.

template<typename Element >

bool F4::operator>	(	Term< Element > const &	term1,
		Term< Element > const &	term2
	)

Overload the operator >.

Parameters

term1	Term.
term2	Term.

Returns: true if term1>term2.; false otherwise.

template<typename Element >

bool F4::operator>	(	TaggedPolynomial< Element > const &	taggedPolynomial1,
		TaggedPolynomial< Element > const &	taggedPolynomial2
	)

Overload the operator >.

Returns: true if taggedPolynomial1 > taggedPolynomial2.; false otherwise.

bool F4::operator>	(	Monomial const &	mon1,
		Monomial const &	mon2
	)

Overload the operator >.

Parameters

mon1	Monomial.
mon2	Monomial.

Returns: true if mon1>mon2.; false otherwise.

template<typename Element >

bool F4::operator>=	(	CriticalPair< Element > const &	criticalPair1,
		CriticalPair< Element > const &	criticalPair2
	)

Overload the operator >=.

Returns: true if criticalPair1 >= criticalPair2.; false otherwise.

template<typename Element >

bool F4::operator>=	(	TaggedPolynomial< Element > const &	taggedPolynomial1,
		TaggedPolynomial< Element > const &	taggedPolynomial2
	)

Overload the operator >=.

Returns: true if taggedPolynomial1 >= taggedPolynomial2.; false otherwise.

bool F4::operator>=	(	Monomial const &	mon1,
		Monomial const &	mon2
	)

Overload the operator >=.

Parameters

mon1	Monomial.
mon2	Monomial.

Returns: true if mon1>=mon2.; false otherwise.

void F4::printNode	(	NodeAvlPolynomial *	p,
		int	indent = `0`
	)

Print the AVL of root p.

Parameters

p	Pointer on a node of the AVL.

void F4::printNode	(	NodeAvlMonomial *	p,
		int	indent = `0`
	)

Print the AVL of root p.

Parameters

p	Pointer on a node of the AVL.

template<typename Element >

void F4::printNode	(	NodeAvlCriticalPair< Element > *	p,
		int	indent = `0`
	)

Print the AVL of root p.

Parameters

p	Pointer on a node of the AVL.

Classes

Functions

Detailed Description

Function Documentation