smtrat::cad::projection Namespace Reference

Namespaces
	brown
	Contains the implementation of Browns projection operator as specified in [3] after Theorem 3.1.
	collins
	Contains the implementation of Collins projection operator as specified in [5] below Theorem 4.
	hong
	Contains the implementation of Hongs projection operator as specified in [15] in Section 2.2.
	lazard
	Contains the implementation of Lazards projection operator as specified in [Lauard1994].
	mccallum
	Contains the implementation of McCallums projection operator as specified in [23].
	mccallum_partial
	Contains the implementation of an optimized version McCallums projection operator.

Data Structures
struct	Reducta
	Construct the set of reducta of the given polynomial. More...

Functions
bool	canBeRemoved (const UPoly &p)
	Checks whether a polynomial can safely be ignored. More...
bool	canBeForwarded (std::size_t, const UPoly &p)
	Checks whether a polynomial can safely be forwarded to the next level. More...
template<typename Poly >
bool	doesNotVanish (const Poly &p)
	Tries to determine whether the given Poly vanishes for some assignment. More...
template<typename Poly >
Poly	normalize (const Poly &p)
	Normalizes the given Poly by removing constant and duplicate factors. More...
template<typename Poly >
Poly	resultant (carl::Variable variable, const Poly &p, const Poly &q)
	Computes the resultant of two polynomials. More...
template<typename Poly >
Poly	discriminant (carl::Variable variable, const Poly &p)
	Computes the discriminant of a polynomial. More...
template<typename Poly >
std::vector< Poly >	PSC (const Poly &p, const Poly &q)
	Computes the Principal Subresultant Coefficients of two polynomials. More...
template<typename Poly , typename Callback >
void	returnPoly (const Poly &p, Callback &&cb)

Function Documentation

canBeForwarded()

bool smtrat::cad::projection::canBeForwarded ( std::size_t  , const UPoly &  p  )

inline

Checks whether a polynomial can safely be forwarded to the next level.

Definition at line 12 of file Projection_utils.h.

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canBeRemoved()

bool smtrat::cad::projection::canBeRemoved ( const UPoly &  p )

inline

Checks whether a polynomial can safely be ignored.

Definition at line 8 of file Projection_utils.h.

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discriminant()

template<typename Poly >

Poly smtrat::cad::projection::discriminant	(	carl::Variable	variable,
		const Poly &	p
	)

Computes the discriminant of a polynomial.

The polynomial is assumed to be univariate and thus knows is main variable. The given variable instead indicates the main variable of the resulting polynomial.

Parameters

variable	Main variable of the resulting polynomial.
p	Input polynomial.

Returns

Discriminant of p in main variable variable.

Definition at line 63 of file utils.h.

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doesNotVanish()

template<typename Poly >

bool smtrat::cad::projection::doesNotVanish

(

const Poly &

p

)

Tries to determine whether the given Poly vanishes for some assignment.

Returns true if the Poly is guaranteed not to vanish. Returns false otherwise.

Definition at line 19 of file utils.h.

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normalize()

template<typename Poly >

Poly smtrat::cad::projection::normalize

(

const Poly &

p

)

Normalizes the given Poly by removing constant and duplicate factors.

Definition at line 32 of file utils.h.

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PSC()

template<typename Poly >

std::vector<Poly> smtrat::cad::projection::PSC	(	const Poly &	p,
		const Poly &	q
	)

Computes the Principal Subresultant Coefficients of two polynomials.

Definition at line 90 of file utils.h.

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resultant()

template<typename Poly >

Poly smtrat::cad::projection::resultant	(	carl::Variable	variable,
		const Poly &	p,
		const Poly &	q
	)

Computes the resultant of two polynomials.

The polynomials are assumed to be univariate polynomials and thus know their respective main variables. The given variable instead indicates the main variable of the resulting polynomial.

Parameters

variable	Main variable of the resulting polynomial.
p	First input polynomial.
q	Second input polynomial.

Returns

Resultant of p and q in main variable variable.

Definition at line 48 of file utils.h.

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returnPoly()

template<typename Poly , typename Callback >

void smtrat::cad::projection::returnPoly	(	const Poly &	p,
		Callback &&	cb
	)

Definition at line 95 of file utils.h.

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