EUCLIDIAN Namespace Reference

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Detailed Description

Module for Euclidean ring.

Functions
template<class R>
void	div_rem (R &q, R &a, const R &b)
template<class R>
void	pseudo_div_rem (R &q, R &a, const R &b)
template<class Poly>
void	prem (const Poly &f, const Poly &g, Poly &q, Poly &r)
template<class Poly>
Poly	prem (const Poly &f, const Poly &g, Poly &q)
template<class Poly>
Poly	prem (const Poly &f, const Poly &g)
template<class Poly>
Poly	pquo (const Poly &f, const Poly &g)
template<class R>
void	div_pseudorem0 (R &q, R &a, const R &b)

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Function Documentation

template<class R>

void EUCLIDIAN::div_rem	(	R &	q,
		R &	a,
		const R &	b
	)

Quotient and remainder of a by b. The polynomial a is modified. At the end of the computation, it is equal to the remainder in the euclidean division. The type R should provide a degree function and a direct access operator.

Definition at line 25 of file EUCLIDIAN.h.

References degree().

template<class Poly>

Poly EUCLIDIAN::pquo	(	const Poly &	f,
		const Poly &	g
	)

Pseudo quotient and remainder of f by g. Returns the pseudo quotient.

Definition at line 120 of file EUCLIDIAN.h.

References degree().

template<class Poly>

Poly EUCLIDIAN::prem	(	const Poly &	f,
		const Poly &	g
	)

Pseudo quotient and remainder of f by g. Returns the pseudo remainder.

Definition at line 104 of file EUCLIDIAN.h.

References degree().

template<class Poly>

Poly EUCLIDIAN::prem	(	const Poly &	f,
		const Poly &	g,
		Poly &	q
	)

Pseudo quotient and remainder of f by g. Returns the pseudo remainder, while q holds the pseudo quotient.

Definition at line 87 of file EUCLIDIAN.h.

References degree().

template<class Poly>

void EUCLIDIAN::prem	(	const Poly &	f,
		const Poly &	g,
		Poly &	q,
		Poly &	r
	)

Pseudo quotient and remainder of f by g. At the end of the computation, q is equal to pseudo quotient and r is equal to the remainder in the euclidean division.

Definition at line 70 of file EUCLIDIAN.h.

References degree().

Referenced by sturmseq::init().

template<class R>

void EUCLIDIAN::pseudo_div_rem	(	R &	q,
		R &	a,
		const R &	b
	)

Pseudo quotient and remainder of a by b. The polynomial a is modified. At the end of the computation, it is equal to the remainder in the euclidean division. The type R should provide a degree function and a direct access operator.

Definition at line 48 of file EUCLIDIAN.h.

References degree().