A class for a multivariate polynomial providing a degree-based representation. More...

#include <MultivariatePolynomialMR.h>

Collaboration diagram for GiNaCRA::MultivariatePolynomialMR:

Public Member Functions
	MultivariatePolynomialMR ()
	MultivariatePolynomialMR (const MonomMRCompare &comp)
	MultivariatePolynomialMR (const MultivariateTermMR &t1, const MonomMRCompare &comp)
	MultivariatePolynomialMR (const MultivariateTermMR &t1, const MultivariateTermMR &t2, const MonomMRCompare &comp)
	MultivariatePolynomialMR (sMT_It begin, sMT_It last, const MonomMRCompare &comp)
	MultivariatePolynomialMR (const GiNaC::ex &expr, const MonomMRCompare &cmp)
	Constructs a multivariate polynomial with standard variables using graded degree lexicographic monomial ordering.
	MultivariatePolynomialMR (const sMT_It begin1, const sMT_It last1, const sMT_It begin2, const sMT_It last2, const MonomMRCompare &comp)
	Creates an object with the sum of the given terms.
MonomOrderingFc	getMonomOrderFunction () const
MonomMRCompare	getMonomOrder () const
bool	isZero () const
	Checks whether there are any terms.
bool	isConstant () const
MultivariateMonomialMR	lmon () const
MultivariateTermMR	lterm () const
GiNaC::ex	lcoeff () const
unsigned	nrOfTerms () const
const MultivariatePolynomialMR	truncLT () const
GiNaC::ex	toEx () const
	GiNaC expression representing the same multivariate polynomial.
MultivariatePolynomialMR	CalculateRemainder (std::list< MultivariatePolynomialMR >::const_iterator ideallistBegin, std::list< MultivariatePolynomialMR >::const_iterator ideallistEnd) const
	Calculates the remainder with respect to the ideal.
MultivariatePolynomialMR	normalized ()

MultivariatePolynomialMR	multiply (const MultivariateTermMR &t1) const
Static Public Member Functions
static const MultivariatePolynomialMR	SPol (const MultivariatePolynomialMR &p1, const MultivariatePolynomialMR &p2)
	Calculates the S-polynomial of p1 and p2.
static bool	sortByLeadingTerm (const MultivariatePolynomialMR &m1, const MultivariatePolynomialMR &m2)
Protected Attributes
MonomMRCompare	mCmp
	Ordering of Terms.
std::set< MultivariateTermMR, MonomMRCompare >	mTerms
	Set of Terms.
Friends
bool	operator== (const MultivariatePolynomialMR &p1, const MultivariatePolynomialMR &p2)
bool	operator!= (const MultivariatePolynomialMR &p1, const MultivariatePolynomialMR &p2)
const MultivariatePolynomialMR	operator+ (const MultivariatePolynomialMR &p1, const MultivariatePolynomialMR &p2)
const MultivariatePolynomialMR	operator+ (const MultivariatePolynomialMR &p1, const MultivariateTermMR &t1)
const MultivariatePolynomialMR	operator+ (const MultivariateTermMR &t1, MultivariatePolynomialMR &p1)
const MultivariatePolynomialMR	operator+ (const MultivariatePolynomialMR &p1, const MultivariateMonomialMR &m1)
const MultivariatePolynomialMR	operator+ (const MultivariateMonomialMR &m1, const MultivariatePolynomialMR &p1)
const MultivariatePolynomialMR	operator- (const MultivariatePolynomialMR &p1, const MultivariatePolynomialMR &p2)
const MultivariatePolynomialMR	operator- (const MultivariatePolynomialMR &p1)
const MultivariatePolynomialMR	operator* (const MultivariatePolynomialMR &p1, const MultivariateTermMR &t1)
const MultivariatePolynomialMR	operator* (const MultivariateTermMR &t1, MultivariatePolynomialMR &p1)
const MultivariatePolynomialMR	operator* (const MultivariatePolynomialMR &p1, const MultivariateMonomialMR &m1)
const MultivariatePolynomialMR	operator* (const MultivariateMonomialMR &m1, const MultivariatePolynomialMR &p1)
std::ostream &	operator<< (std::ostream &os, const MultivariatePolynomialMR &rhs)

Detailed Description

A class for a multivariate polynomial providing a degree-based representation.

Author:: Sebastian Junges

Since:: 2011-11-26

Version:: 2012-01-31

Definition at line 106 of file MultivariatePolynomialMR.h.

Constructor & Destructor Documentation

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR ( )

Definition at line 45 of file MultivariatePolynomialMR.cpp.

Referenced by CalculateRemainder(), normalized(), SPol(), and truncLT().

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR ( const MonomMRCompare & comp )

Parameters:

comp

Definition at line 50 of file MultivariatePolynomialMR.cpp.

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR	(	const MultivariateTermMR &	t1,
		const MonomMRCompare &	comp
	)

Parameters:

t1
comp

Definition at line 55 of file MultivariatePolynomialMR.cpp.

References mTerms.

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR	(	const MultivariateTermMR &	t1,
		const MultivariateTermMR &	t2,
		const MonomMRCompare &	comp
	)

Parameters:

t1
t2
comp

Definition at line 62 of file MultivariatePolynomialMR.cpp.

References mTerms.

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR	(	sMT_It	begin,
		sMT_It	last,
		const MonomMRCompare &	comp
	)

Parameters:

begin
last
comp

Definition at line 70 of file MultivariatePolynomialMR.cpp.

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR	(	const GiNaC::ex &	expr,
		const MonomMRCompare &	cmp
	)

Constructs a multivariate polynomial with standard variables using graded degree lexicographic monomial ordering.

Parameters:

expr	a polynomial
cmp	the ordering

Definition at line 106 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::VariableListPool::getVariables(), GiNaC::is_constant(), and mTerms.

GiNaCRA::MultivariatePolynomialMR::MultivariatePolynomialMR	(	const sMT_It	begin1,
		const sMT_It	last1,
		const sMT_It	begin2,
		const sMT_It	last2,
		const MonomMRCompare &	comp
	)

Creates an object with the sum of the given terms.

Parameters:

begin1
last1
begin2
last2
comp	Monomial Ordering. Note that if this is different from the order of the sets 1 and 2, the creation of the object is slow.

Definition at line 75 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MonomMRCompare::GetMonomOrdering(), mCmp, and mTerms.

Member Function Documentation

MultivariatePolynomialMR GiNaCRA::MultivariatePolynomialMR::CalculateRemainder	(	std::list< MultivariatePolynomialMR >::const_iterator	ideallistBegin,
		std::list< MultivariatePolynomialMR >::const_iterator	ideallistEnd
	)		const

Calculates the remainder with respect to the ideal.

Parameters:

ideallistBegin
ideallistEnd

Returns:

Definition at line 517 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariateTermMR::divby(), isZero(), lterm(), mCmp, mTerms, and MultivariatePolynomialMR().

Referenced by GiNaCRA::Groebner::solve().

MonomMRCompare GiNaCRA::MultivariatePolynomialMR::getMonomOrder ( ) const [inline]

Definition at line 166 of file MultivariatePolynomialMR.h.

References mCmp.

Referenced by SPol().

MonomOrderingFc GiNaCRA::MultivariatePolynomialMR::getMonomOrderFunction ( ) const [inline]

Returns:

Definition at line 161 of file MultivariatePolynomialMR.h.

References GiNaCRA::MonomMRCompare::GetMonomOrdering(), and mCmp.

Referenced by sortByLeadingTerm().

bool GiNaCRA::MultivariatePolynomialMR::isConstant ( ) const [inline]

Definition at line 180 of file MultivariatePolynomialMR.h.

References mTerms.

Referenced by GiNaCRA::Groebner::solve().

bool GiNaCRA::MultivariatePolynomialMR::isZero ( ) const [inline]

Checks whether there are any terms.

Returns:: true, if zero

Definition at line 175 of file MultivariatePolynomialMR.h.

References mTerms.

Referenced by CalculateRemainder(), lmon(), lterm(), and GiNaCRA::Groebner::solve().

GiNaC::ex GiNaCRA::MultivariatePolynomialMR::lcoeff ( ) const [inline]

Returns:: the coefficient of the leading term

Definition at line 211 of file MultivariatePolynomialMR.h.

References mTerms.

Referenced by normalized().

MultivariateMonomialMR GiNaCRA::MultivariatePolynomialMR::lmon ( ) const [inline]

Returns:: The leading monomial with respect to the current ordering

Definition at line 188 of file MultivariatePolynomialMR.h.

References isZero(), and mTerms.

Referenced by sortByLeadingTerm(), and SPol().

MultivariateTermMR GiNaCRA::MultivariatePolynomialMR::lterm ( ) const [inline]

Returns:: the leading term with respect to the current ordering

Definition at line 201 of file MultivariatePolynomialMR.h.

References isZero(), and mTerms.

Referenced by CalculateRemainder(), and SPol().

MultivariatePolynomialMR GiNaCRA::MultivariatePolynomialMR::multiply ( const MultivariateTermMR & t1 ) const [inline]

Parameters:

t1

Returns:

Definition at line 293 of file MultivariatePolynomialMR.h.

Referenced by SPol().

MultivariatePolynomialMR GiNaCRA::MultivariatePolynomialMR::normalized ( )

Definition at line 555 of file MultivariatePolynomialMR.cpp.

References lcoeff(), mCmp, mTerms, and MultivariatePolynomialMR().

unsigned GiNaCRA::MultivariatePolynomialMR::nrOfTerms ( ) const [inline]

Returns:: the number of terms

Runtime complexity:: constant

Definition at line 220 of file MultivariatePolynomialMR.h.

References mTerms.

Referenced by SPol().

static bool GiNaCRA::MultivariatePolynomialMR::sortByLeadingTerm	(	const MultivariatePolynomialMR &	m1,
		const MultivariatePolynomialMR &	m2
	)		`[inline, static]`

Definition at line 298 of file MultivariatePolynomialMR.h.

References getMonomOrderFunction(), and lmon().

Referenced by GiNaCRA::Groebner::addPolynomial(), and GiNaCRA::Groebner::Groebner().

const MultivariatePolynomialMR GiNaCRA::MultivariatePolynomialMR::SPol	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)		`[static]`

Calculates the S-polynomial of p1 and p2.

Parameters:

p1
p2

Returns:: S-Polynomial

Definition at line 492 of file MultivariatePolynomialMR.cpp.

References getMonomOrder(), GiNaCRA::MultivariateTermMR::lcmdivt(), lmon(), lterm(), mCmp, multiply(), MultivariatePolynomialMR(), nrOfTerms(), and truncLT().

Referenced by GiNaCRA::Groebner::solve().

GiNaC::ex GiNaCRA::MultivariatePolynomialMR::toEx ( ) const

GiNaC expression representing the same multivariate polynomial.

Returns:

Definition at line 239 of file MultivariatePolynomialMR.cpp.

References mTerms.

const MultivariatePolynomialMR GiNaCRA::MultivariatePolynomialMR::truncLT ( ) const [inline]

Returns:: a MultivariatePolynomial without the leading term.

Definition at line 229 of file MultivariatePolynomialMR.h.

References mCmp, mTerms, and MultivariatePolynomialMR().

Referenced by SPol().

Friends And Related Function Documentation

bool operator!=	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)		`[friend]`

Definition at line 257 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator*	(	const MultivariatePolynomialMR &	p1,
		const MultivariateTermMR &	t1
	)		`[friend]`

Definition at line 449 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator*	(	const MultivariateTermMR &	t1,
		MultivariatePolynomialMR &	p1
	)		`[friend]`

Definition at line 461 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator*	(	const MultivariatePolynomialMR &	p1,
		const MultivariateMonomialMR &	m1
	)		`[friend]`

Definition at line 466 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator*	(	const MultivariateMonomialMR &	m1,
		const MultivariatePolynomialMR &	p1
	)		`[friend]`

Definition at line 478 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)		`[friend]`

Definition at line 265 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariateTermMR &	t1
	)		`[friend]`

Definition at line 314 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator+	(	const MultivariateTermMR &	t1,
		MultivariatePolynomialMR &	p1
	)		`[friend]`

Definition at line 342 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariateMonomialMR &	m1
	)		`[friend]`

Definition at line 347 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator+	(	const MultivariateMonomialMR &	m1,
		const MultivariatePolynomialMR &	p1
	)		`[friend]`

Definition at line 376 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator-	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)		`[friend]`

Definition at line 381 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR operator- ( const MultivariatePolynomialMR & p1 ) [friend]

Definition at line 432 of file MultivariatePolynomialMR.cpp.

std::ostream& operator<<	(	std::ostream &	os,
		const MultivariatePolynomialMR &	rhs
	)		`[friend]`

Parameters:

os
rhs

Returns:

Definition at line 483 of file MultivariatePolynomialMR.cpp.

bool operator==	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)		`[friend]`

Definition at line 249 of file MultivariatePolynomialMR.cpp.

Field Documentation

MonomMRCompare GiNaCRA::MultivariatePolynomialMR::mCmp [protected]

Ordering of Terms.

Definition at line 305 of file MultivariatePolynomialMR.h.

Referenced by CalculateRemainder(), getMonomOrder(), getMonomOrderFunction(), MultivariatePolynomialMR(), normalized(), GiNaCRA::operator*(), GiNaCRA::operator+(), GiNaCRA::operator-(), SPol(), and truncLT().

std::set<MultivariateTermMR, MonomMRCompare> GiNaCRA::MultivariatePolynomialMR::mTerms [protected]

Set of Terms.

Definition at line 307 of file MultivariatePolynomialMR.h.

Referenced by CalculateRemainder(), isConstant(), isZero(), lcoeff(), lmon(), lterm(), MultivariatePolynomialMR(), normalized(), nrOfTerms(), GiNaCRA::operator!=(), GiNaCRA::operator*(), GiNaCRA::operator+(), GiNaCRA::operator-(), GiNaCRA::operator<<(), GiNaCRA::operator==(), toEx(), and truncLT().

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

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Field Documentation