GiNaCRA Namespace Reference

Implementation of the class Constraint. More...

Data Structures
struct	SampleList
	Type for a sorted list of RealAlgebraicNumberPtr. More...
struct	CADSettings
	Settings for the CAD class. More...
struct	isLessInLiftingPositions
	Functor comparing two positions of a vector of univariate polynomials. More...
class	CAD
	A collection of methods that lead directly to the computation of the CAD. More...
class	Constraint
	A class representing a condition on a Constraint as to whether its sign is negative (GiNaCRA::NEGATIVE_SIGN), positive (GiNaCRA::POSITVIE_SIGN) or zero (GiNaCRA::ZERO_SIGN). More...
class	Groebner
	Class encapsulating the calculation of Groebner bases. More...
class	MultivariateCoefficient
	A class for a multivariate coefficient providing everything what a GiNaC expression of type power or mul is and, in addition, stores the variables of the monomial (in lexicographic order). More...
class	MultivariateCoefficientMR
	Class encapsulating expressions as coefficients of the terms. More...
class	MultivariateMonomial
	A class for a multivariate monomial providing everything what a GiNaC expression of type power or mul is and, in addition, stores the variables of the monomial (in lexicographic order). More...
class	MultivariateMonomialMR
	A class for a multivariate monomial providing a degree-based representation. More...
class	MultivariatePolynomial
	A class for a multivariate polynomial providing everything what a GiNaC expression of type polynomial is and, in addition, stores the variables of the polynomial (in lexicographic order) as well as the leading term in the variable with the maximal degree. More...
struct	symbol_is_greatereq_tdegree
	Total-degree ordering on symbols w.r.t. More...
class	MultivariatePolynomialFactory
class	MonomMRCompare
	A class for comparing MultivariateMonomials according to a given function. More...
class	MultivariatePolynomialMR
	A class for a multivariate polynomial providing a degree-based representation. More...
class	MultivariateTerm
	A class for a multivariate term providing everything what a GiNaC expression of type power or mul with coefficient is and, in addition, stores the variables of the monomial (in lexicographic order). More...
class	MultivariateTermMR
	A class for a multivariate polynomial providing a degree-based representation. More...
class	OpenInterval
	A class for an open interval providing interval arithmetic operations. More...
class	Polynomial
	A class for a polynomial in general serving as an abstract superclass of both multivariate and univariate polynomials. More...
class	RationalUnivariatePolynomial
	A class for a univariate polynomial providing everything what a GiNaC expression of type polynomial is and in addition, stores the single main variable of the polynomial. More...
class	RealAlgebraicNumber
	This class encapsulates several representations of real algebraic numbers and provides crucial operations such as arithmetic, ordering or sign determination on them. More...
struct	RealAlgebraicNumberPtrHasher
	Hash function for the unordered real-algebraic number pointer set. More...
struct	polynomial_has_nonzero_sign
class	RealAlgebraicNumberFactory
	A class providing useful static methods which produce instances of RealAlgebraicNumberIR. More...
class	RealAlgebraicNumberIR
	An implementation of an real algebraic number providing methods to add, multiply or evaluate their sign on polynomials. More...
class	RealAlgebraicNumberNR
	A real algebraic number exactly represented as a numeric. More...
class	RealAlgebraicPoint
class	CPPUNITSettings
	Collection of CPPUNIT related settings. More...
class	MultivariatePolynomialSettings
	Collection of MultivariatePolynomial related settings. More...
struct	RealAlgebraicNumberSettings
	Collection of RealAlgebraicNumber related settings. More...
class	SpecialQuotientRingMultiplicationTable
	A class providing the multiplication table for the quotient ring modulo a given Groebner basis. More...
class	SymbolDB
	Class encapsulating the global variable and the global parameter list. More...
class	tree_node_
	A node in the tree, combining links to other nodes as well as the actual data. More...
class	tree
class	UnivariatePolynomial
	A class for a univariate polynomial providing everything what a GiNaC expression of type polynomial is and in addition, stores the single main variable of the polynomial. More...
struct	UnivariatePolynomialSetHasher
	Hash function for the unordered univariate polynomial set. More...
struct	UnivariatePolynomialSetEquals
	Comparison function for the unordered univariate polynomial set. More...
class	UnivariatePolynomialSet
	This class encapsulates a set of UnivariatePolynomials and its helping methods. More...
struct	plus_second
class	VariableListPool
	Class saving variable-lists. More...
Typedefs
typedef std::unordered_map < RealAlgebraicNumberPtr, RealAlgebraicNumberPtr, RealAlgebraicNumberPtrHasher >	SampleSimplification
typedef std::pair< unsigned, unsigned >	pui
typedef std::vector< pui > ::const_iterator	vui_cIt
typedef bool(*	MonomOrderingFc )(const MultivariateMonomialMR &, const MultivariateMonomialMR &)
typedef std::set < MultivariateTermMR > ::iterator	sMT_It
typedef std::set < MultivariateTermMR > ::const_iterator	sMT_cIt
typedef std::set < MultivariateTermMR > ::reverse_iterator	sMT_rIt
typedef std::map < GiNaC::symbol, OpenInterval, GiNaC::ex_is_less >	evalintervalmap
typedef std::tr1::shared_ptr < RealAlgebraicNumber >	RealAlgebraicNumberPtr
	smart pointer (shared) to a RealAlgebraicNumber object
typedef std::map< symbol, RealAlgebraicNumberIRPtr, GiNaC::ex_is_less >	evalmap
typedef std::tr1::shared_ptr < RealAlgebraicNumberIR >	RealAlgebraicNumberIRPtr
typedef std::tr1::shared_ptr < RealAlgebraicNumberNR >	RealAlgebraicNumberNRPtr
Enumerations
enum	CADSettingsType {   LOWDEG_CADSETTING, ODDDEG_CADSETTING, EVENDEG_CADSETTING, EAGERLIFTING_CADSETTING,   GROEBNER_CADSETTING, REALROOTCOUNT_CADSETTING, SQUAREFREEELIMINATION_CADSETTING }
	Predefined settings for the CAD procedure. More...
Functions
bool	operator== (const MultivariateCoefficientMR &m1, const MultivariateCoefficientMR &m2)
const MultivariateCoefficientMR	operator* (const MultivariateCoefficientMR &m1, const MultivariateCoefficientMR &m2)
const MultivariateCoefficientMR	operator+ (const MultivariateCoefficientMR &m1, const MultivariateCoefficientMR &m2)
const MultivariateCoefficientMR	operator- (const MultivariateCoefficientMR &m1)
const MultivariateCoefficientMR	operator- (const MultivariateCoefficientMR &m1, const MultivariateCoefficientMR &m2)
const MultivariateCoefficientMR	operator/ (const MultivariateCoefficientMR &m1, const MultivariateCoefficientMR &m2)
std::ostream &	operator<< (std::ostream &os, const MultivariateCoefficientMR &m1)
bool	sort_first (const std::pair< unsigned, unsigned > &p1, const std::pair< unsigned, unsigned > &p2)
bool	compare_first (const std::pair< unsigned, unsigned > &p1, const std::pair< unsigned, unsigned > &p2)
bool	operator== (const MultivariateMonomialMR &lhs, const MultivariateMonomialMR &rhs)
bool	operator!= (const MultivariateMonomialMR &lhs, const MultivariateMonomialMR &rhs)
std::ostream &	operator<< (ostream &os, const MultivariateMonomialMR &rhs)
const MultivariateMonomialMR	operator* (const MultivariateMonomialMR &m1, const MultivariateMonomialMR &m2)
bool	operator!= (const MonomMRCompare &m1, const MonomMRCompare &m2)
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)
bool	operator== (const MultivariateTermMR &t1, const MultivariateTermMR &t2)
const MultivariateTermMR	operator* (const MultivariateTermMR &t1, const MultivariateTermMR &t2)
const MultivariateTermMR	operator* (const MultivariateTermMR &t1, const MultivariateMonomialMR &m1)
const MultivariateTermMR	operator* (const MultivariateMonomialMR &m1, const MultivariateTermMR &t1)
std::ostream &	operator<< (std::ostream &os, const MultivariateTermMR &rhs)
const GiNaC::numeric	abs (const ex &lh)
const OpenInterval	operator+ (const OpenInterval &lh, const OpenInterval &rh)
const OpenInterval	operator- (const OpenInterval &lh, const OpenInterval &rh)
const OpenInterval	operator* (const OpenInterval &lh, const OpenInterval &rh)
const OpenInterval	operator- (const OpenInterval &lh)
const bool	operator== (const OpenInterval &lh, const OpenInterval &rh)
const bool	operator!= (const OpenInterval &lh, const OpenInterval &rh)
const bool	operator<= (const OpenInterval &lh, const OpenInterval &rh)
const bool	operator>= (const OpenInterval &lh, const OpenInterval &rh)
const OpenInterval	operator+ (const OpenInterval &lh, const GiNaC::numeric &rh)
const OpenInterval	operator+ (const GiNaC::numeric &lh, const OpenInterval &rh)
const OpenInterval	operator- (const OpenInterval &lh, const GiNaC::numeric &rh)
const OpenInterval	operator- (const GiNaC::numeric &lh, const OpenInterval &rh)
const OpenInterval	operator* (const OpenInterval &lh, const GiNaC::numeric &rh)
const OpenInterval	operator* (const GiNaC::numeric &lh, const OpenInterval &rh)
const OpenInterval	operator/ (const OpenInterval &lh, const GiNaC::numeric &rh) throw ( overflow_error )
const OpenInterval	operator/ (const GiNaC::numeric &lh, const OpenInterval &rh) throw ( overflow_error )
const UnivariatePolynomial	operator+ (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const UnivariatePolynomial	operator- (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const UnivariatePolynomial	operator* (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const UnivariatePolynomial	operator/ (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const UnivariatePolynomial	operator% (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const RationalUnivariatePolynomial	operator+ (const RationalUnivariatePolynomial &lh, const RationalUnivariatePolynomial &rh)
const RationalUnivariatePolynomial	operator- (const RationalUnivariatePolynomial &lh, const RationalUnivariatePolynomial &rh)
const RationalUnivariatePolynomial	operator* (const RationalUnivariatePolynomial &lh, const RationalUnivariatePolynomial &rh)
const RationalUnivariatePolynomial	operator/ (const RationalUnivariatePolynomial &lh, const RationalUnivariatePolynomial &rh)
const RationalUnivariatePolynomial	operator% (const RationalUnivariatePolynomial &lh, const RationalUnivariatePolynomial &rh)
const UnivariatePolynomial	operator- (const UnivariatePolynomial &lh)
const RationalUnivariatePolynomial	operator- (const RationalUnivariatePolynomial &lh)
const bool	operator== (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
const bool	operator!= (const UnivariatePolynomial &lh, const UnivariatePolynomial &rh)
std::ostream &	operator<< (std::ostream &os, const UnivariatePolynomialSet &s)
RealAlgebraicNumberIR &	operator+ (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator- (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator* (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator/ (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator^ (RealAlgebraicNumberIR &base, int exponent)
RealAlgebraicNumberIR &	operator- (RealAlgebraicNumberIR &lh)
const bool	operator== (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
const bool	operator== (const RealAlgebraicNumberIR &lh, const RealAlgebraicNumberIR &rh)
const bool	operator!= (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
const bool	operator< (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
const bool	operator> (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
const bool	operator<= (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
const bool	operator>= (RealAlgebraicNumberIR &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator+ (const GiNaC::numeric &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator+ (RealAlgebraicNumberIR &lh, const GiNaC::numeric &rh)
RealAlgebraicNumberIR &	operator- (const GiNaC::numeric &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator- (RealAlgebraicNumberIR &lh, const GiNaC::numeric &rh)
RealAlgebraicNumberIR &	operator* (const GiNaC::numeric &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator* (RealAlgebraicNumberIR &lh, const GiNaC::numeric &rh)
RealAlgebraicNumberIR &	operator/ (const GiNaC::numeric &lh, RealAlgebraicNumberIR &rh)
RealAlgebraicNumberIR &	operator/ (RealAlgebraicNumberIR &lh, const GiNaC::numeric &rh)
RealAlgebraicNumberPtr	binaryOperator (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh, RealAlgebraicNumberIR &(*opIRIR)(RealAlgebraicNumberIR &, RealAlgebraicNumberIR &), RealAlgebraicNumberIR &(*opIRNR)(RealAlgebraicNumberIR &, const numeric &), const numeric(*opNRNR)(const numeric &, const numeric &))
RealAlgebraicNumberPtr	operator+ (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh)
RealAlgebraicNumberPtr	operator- (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh)
RealAlgebraicNumberPtr	operator* (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh)
RealAlgebraicNumberPtr	operator/ (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh)
RealAlgebraicNumberPtr	operator^ (const RealAlgebraicNumberPtr &base, int exponent)
RealAlgebraicNumberPtr	operator- (const RealAlgebraicNumberPtr &lh)
const bool	operator== (const RealAlgebraicNumberPtr &a, const RealAlgebraicNumberPtr &b)
const bool	operator!= (const RealAlgebraicNumberPtr &a, const RealAlgebraicNumberPtr &b)
const bool	operator< (const RealAlgebraicNumberPtr &a, const RealAlgebraicNumberPtr &b)
std::ostream &	operator<< (std::ostream &os, const RealAlgebraicNumberPtr &a)
void	print (const RealAlgebraicNumberPtr &a, std::ostream &os)
std::ostream &	operator<< (std::ostream &os, const RealAlgebraicPoint &r)
const bool	operator== (const Constraint &a, const Constraint &b)
std::ostream &	operator<< (std::ostream &os, const Constraint &a)
const GiNaC::numeric	abs (const GiNaC::ex &x)
	This is a wrapping function returning the maximum if the argument is of type GiNaC::numeric or RealAlgebraicNumberIR.
RealAlgebraicNumberPtr	binaryOperator (const RealAlgebraicNumberPtr &lh, const RealAlgebraicNumberPtr &rh, RealAlgebraicNumberIR &(*opIRIR)(RealAlgebraicNumberIR &, RealAlgebraicNumberIR &), RealAlgebraicNumberIR &(*opIRNR)(RealAlgebraicNumberIR &, const GiNaC::numeric &), const GiNaC::numeric(*opNRNR)(const GiNaC::numeric &, const GiNaC::numeric &))
Variables
static const CADSettingsType	DEFAULT_CADSETTING
	The default setting for CAD settings, which is chosen if the CAD object is initialized without any other parameter.

---

Detailed Description

Implementation of the class Constraint.

Implementation of UnivariatePolynomialSet.

Implementation of the class SymbolDB.

Implementation of the class Polynomial.

GiNaCRA - GiNaC Real Algebra package Copyright (C) 2010-2012 Ulrich Loup, Joachim Redies, Sebastian Junges.

A class producing multivariate polynomials.

Author:

Ulrich Loup

Since:

2011-12-05

Version:

2012-04-17

Author:

Ulrich Loup

Since:

2011-05-27

Version:

2011-10-30

See also:

ISBN 0-387-94090-1 and ISBN-13: 978-3642069642

Notation is following http://www.possibility.com/Cpp/CppCodingStandard.html.

This file is part of GiNaCRA.

GiNaCRA is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

GiNaCRA is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with GiNaCRA. If not, see http://www.gnu.org/licenses/. Collection of operators needed within the GiNaC Real Algebra package.

This external declaration and implementation provides a better and standardized overview.

Author:

Ulrich Loup

Since:

2010-09-20

Version:

2012-03-15

Author:

Ulrich Loup

Since:

2011-11-03

Version:

2012-03-19

Notation is following http://www.possibility.com/Cpp/CppCodingStandard.html.

Author:

Joachim Redies

Ulrich Loup

Since:

2011-10-26

Version:

2011-12-29

Author:

Ulrich Loup

Since:

2011-12-07

Version:

2011-12-15

Notation is following http://www.possibility.com/Cpp/CppCodingStandard.html.

Author:

Joachim Redies

Ulrich Loup

Since:

2011-10-03

Version:

2012-05-15

---

Typedef Documentation

typedef std::map<GiNaC::symbol, OpenInterval, GiNaC::ex_is_less> GiNaCRA::evalintervalmap

Definition at line 43 of file OpenInterval.h.

typedef std::map<symbol, RealAlgebraicNumberIRPtr, GiNaC::ex_is_less> GiNaCRA::evalmap

Definition at line 39 of file RealAlgebraicNumberFactory.h.

typedef bool(* GiNaCRA::MonomOrderingFc)(const MultivariateMonomialMR &, const MultivariateMonomialMR &)

Definition at line 43 of file MultivariatePolynomialMR.h.

typedef std::pair<unsigned, unsigned> GiNaCRA::pui

Definition at line 36 of file MultivariateMonomialMR.h.

typedef std::tr1::shared_ptr<RealAlgebraicNumberIR> GiNaCRA::RealAlgebraicNumberIRPtr

Definition at line 334 of file RealAlgebraicNumberIR.h.

typedef std::tr1::shared_ptr<RealAlgebraicNumberNR> GiNaCRA::RealAlgebraicNumberNRPtr

Definition at line 108 of file RealAlgebraicNumberNR.h.

typedef std::tr1::shared_ptr< RealAlgebraicNumber > GiNaCRA::RealAlgebraicNumberPtr

smart pointer (shared) to a RealAlgebraicNumber object

Definition at line 152 of file operators.h.

typedef std::unordered_map<RealAlgebraicNumberPtr, RealAlgebraicNumberPtr, RealAlgebraicNumberPtrHasher> GiNaCRA::SampleSimplification

Definition at line 50 of file CAD.h.

typedef std::set<MultivariateTermMR>::const_iterator GiNaCRA::sMT_cIt

Definition at line 46 of file MultivariatePolynomialMR.h.

typedef std::set<MultivariateTermMR>::iterator GiNaCRA::sMT_It

Definition at line 45 of file MultivariatePolynomialMR.h.

typedef std::set<MultivariateTermMR>::reverse_iterator GiNaCRA::sMT_rIt

Definition at line 47 of file MultivariatePolynomialMR.h.

typedef std::vector<pui>::const_iterator GiNaCRA::vui_cIt

Definition at line 37 of file MultivariateMonomialMR.h.

---

Enumeration Type Documentation

enum GiNaCRA::CADSettingsType

Predefined settings for the CAD procedure.

Implementation of the types is located in CAD.h. Each setting is defined as a power of two in order to use several flags at a time. Note that the order of the flags plays a role: If, e.g., ODDDEG_CADSETTING and EVENDEG_CADSETTING are set, then the last one (EVENDEG_CADSETTING) is used.

Enumerator:

LOWDEG_CADSETTING	low-degree first polynomial order
ODDDEG_CADSETTING	odd-degree first polynomial order
EVENDEG_CADSETTING	even-degree first polynomial order
EAGERLIFTING_CADSETTING	complete search for each lifting position before taking a new one
GROEBNER_CADSETTING	the elimination uses Groebner bases to simplify the levels below the top-most level
REALROOTCOUNT_CADSETTING	the elimination uses real root counting to simplify the bottom-most level
SQUAREFREEELIMINATION_CADSETTING	the elimination uses square-free/separable polynomials in every level

Definition at line 82 of file settings.h.

---

Function Documentation

const GiNaC::numeric GiNaCRA::abs

(

const GiNaC::ex &

x

)

This is a wrapping function returning the maximum if the argument is of type GiNaC::numeric or RealAlgebraicNumberIR.

If it is a RealAlgebraicNumberIR, the function returns the maximum of the absolute values of the interval bounds.

Parameters:

x

Returns:

the absolute value (numeric) / the maximum of the absolute values of the interval bounds (RealAlgebraicNumberIR) / 0 in all other cases

const GiNaC::numeric GiNaCRA::abs

(

const ex &

lh

)

Definition at line 56 of file operators.cpp.

Referenced by GiNaCRA::RationalUnivariatePolynomial::cauchyBound(), GiNaCRA::RationalUnivariatePolynomial::maximumNorm(), GiNaCRA::RationalUnivariatePolynomial::oneNorm(), and GiNaCRA::RealAlgebraicNumberFactory::realRootsEval().

RealAlgebraicNumberPtr GiNaCRA::binaryOperator	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh,
		RealAlgebraicNumberIR &(*)(RealAlgebraicNumberIR &, RealAlgebraicNumberIR &)	opIRIR,
		RealAlgebraicNumberIR &(*)(RealAlgebraicNumberIR &, const GiNaC::numeric &)	opIRNR,
		const GiNaC::numeric(*)(const GiNaC::numeric &, const GiNaC::numeric &)	opNRNR
	)

RealAlgebraicNumberPtr GiNaCRA::binaryOperator	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh,
		RealAlgebraicNumberIR &(*)(RealAlgebraicNumberIR &, RealAlgebraicNumberIR &)	opIRIR,
		RealAlgebraicNumberIR &(*)(RealAlgebraicNumberIR &, const numeric &)	opIRNR,
		const numeric(*)(const numeric &, const numeric &)	opNRNR
	)

Definition at line 425 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumber::isNumeric(), and GiNaCRA::RealAlgebraicNumber::value().

Referenced by operator*(), operator+(), operator-(), and operator/().

bool GiNaCRA::compare_first	(	const std::pair< unsigned, unsigned > &	p1,
		const std::pair< unsigned, unsigned > &	p2
	)

Definition at line 50 of file MultivariateMonomialMR.cpp.

Referenced by GiNaCRA::MultivariateMonomialMR::MultivariateMonomialMR().

bool GiNaCRA::operator!=	(	const MonomMRCompare &	m1,
		const MonomMRCompare &	m2
	)

Definition at line 40 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MonomMRCompare::GetMonomOrdering().

const bool GiNaCRA::operator!=	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 101 of file operators.cpp.

References GiNaCRA::OpenInterval::isEqual().

bool GiNaCRA::operator!=	(	const MultivariateMonomialMR &	lhs,
		const MultivariateMonomialMR &	rhs
	)

Definition at line 162 of file MultivariateMonomialMR.cpp.

const bool GiNaCRA::operator!=	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 252 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::isEqual().

bool GiNaCRA::operator!=	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)

Definition at line 257 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mTerms.

const bool GiNaCRA::operator!=	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 324 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isEqual().

const bool GiNaCRA::operator!=	(	const RealAlgebraicNumberPtr &	a,
		const RealAlgebraicNumberPtr &	b
	)

Definition at line 514 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberFactory::equal().

const UnivariatePolynomial GiNaCRA::operator%	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 200 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::rem().

const RationalUnivariatePolynomial GiNaCRA::operator%	(	const RationalUnivariatePolynomial &	lh,
		const RationalUnivariatePolynomial &	rh
	)

Definition at line 227 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::rem().

const MultivariateCoefficientMR GiNaCRA::operator*	(	const MultivariateCoefficientMR &	m1,
		const MultivariateCoefficientMR &	m2
	)

Definition at line 40 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const OpenInterval GiNaCRA::operator*	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 82 of file operators.cpp.

References GiNaCRA::OpenInterval::mul().

const OpenInterval GiNaCRA::operator*	(	const OpenInterval &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 138 of file operators.cpp.

References GiNaCRA::OpenInterval::left(), and GiNaCRA::OpenInterval::right().

const OpenInterval GiNaCRA::operator*	(	const GiNaC::numeric &	lh,
		const OpenInterval &	rh
	)

Definition at line 147 of file operators.cpp.

const MultivariateTermMR GiNaCRA::operator*	(	const MultivariateTermMR &	t1,
		const MultivariateTermMR &	t2
	)

Definition at line 157 of file MultivariateTermMR.cpp.

References GiNaCRA::MultivariateTermMR::mCoeff.

const MultivariateTermMR GiNaCRA::operator*	(	const MultivariateTermMR &	t1,
		const MultivariateMonomialMR &	m1
	)

Definition at line 162 of file MultivariateTermMR.cpp.

References GiNaCRA::MultivariateTermMR::mCoeff.

const MultivariateTermMR GiNaCRA::operator*	(	const MultivariateMonomialMR &	m1,
		const MultivariateTermMR &	t1
	)

Definition at line 167 of file MultivariateTermMR.cpp.

const UnivariatePolynomial GiNaCRA::operator*	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 190 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::mul().

const RationalUnivariatePolynomial GiNaCRA::operator*	(	const RationalUnivariatePolynomial &	lh,
		const RationalUnivariatePolynomial &	rh
	)

Definition at line 217 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::variable().

const MultivariateMonomialMR GiNaCRA::operator*	(	const MultivariateMonomialMR &	m1,
		const MultivariateMonomialMR &	m2
	)

Definition at line 233 of file MultivariateMonomialMR.cpp.

References GiNaCRA::MultivariateMonomialMR::mExponents, and GiNaCRA::MultivariateMonomialMR::mTotDeg.

RealAlgebraicNumberIR & GiNaCRA::operator*	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 287 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::mul().

RealAlgebraicNumberIR & GiNaCRA::operator*	(	const GiNaC::numeric &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 387 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), GiNaCRA::UnivariatePolynomial::variable(), and GiNaCRA::RealAlgebraicNumberIR::zero().

RealAlgebraicNumberIR & GiNaCRA::operator*	(	RealAlgebraicNumberIR &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 398 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), GiNaCRA::UnivariatePolynomial::variable(), and GiNaCRA::RealAlgebraicNumberIR::zero().

const MultivariatePolynomialMR GiNaCRA::operator*	(	const MultivariatePolynomialMR &	p1,
		const MultivariateTermMR &	t1
	)

Definition at line 449 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mCmp, and GiNaCRA::MultivariatePolynomialMR::mTerms.

const MultivariatePolynomialMR GiNaCRA::operator*	(	const MultivariateTermMR &	t1,
		MultivariatePolynomialMR &	p1
	)

Definition at line 461 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR GiNaCRA::operator*	(	const MultivariatePolynomialMR &	p1,
		const MultivariateMonomialMR &	m1
	)

Definition at line 466 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mCmp, and GiNaCRA::MultivariatePolynomialMR::mTerms.

RealAlgebraicNumberPtr GiNaCRA::operator*	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh
	)

Definition at line 474 of file operators.cpp.

References binaryOperator().

const MultivariatePolynomialMR GiNaCRA::operator*	(	const MultivariateMonomialMR &	m1,
		const MultivariatePolynomialMR &	p1
	)

Definition at line 478 of file MultivariatePolynomialMR.cpp.

const MultivariateCoefficientMR GiNaCRA::operator+	(	const MultivariateCoefficientMR &	m1,
		const MultivariateCoefficientMR &	m2
	)

Definition at line 45 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const OpenInterval GiNaCRA::operator+	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 72 of file operators.cpp.

References GiNaCRA::OpenInterval::add().

const OpenInterval GiNaCRA::operator+	(	const OpenInterval &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 118 of file operators.cpp.

References GiNaCRA::OpenInterval::left(), and GiNaCRA::OpenInterval::right().

const OpenInterval GiNaCRA::operator+	(	const GiNaC::numeric &	lh,
		const OpenInterval &	rh
	)

Definition at line 123 of file operators.cpp.

References GiNaCRA::OpenInterval::left(), and GiNaCRA::OpenInterval::right().

const UnivariatePolynomial GiNaCRA::operator+	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 180 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::add().

const RationalUnivariatePolynomial GiNaCRA::operator+	(	const RationalUnivariatePolynomial &	lh,
		const RationalUnivariatePolynomial &	rh
	)

Definition at line 207 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::variable().

const MultivariatePolynomialMR GiNaCRA::operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)

Definition at line 265 of file MultivariatePolynomialMR.cpp.

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

RealAlgebraicNumberIR & GiNaCRA::operator+	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 276 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::add().

const MultivariatePolynomialMR GiNaCRA::operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariateTermMR &	t1
	)

Definition at line 314 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariateTermMR::getCoeffExpr(), and GiNaCRA::MultivariatePolynomialMR::mTerms.

const MultivariatePolynomialMR GiNaCRA::operator+	(	const MultivariateTermMR &	t1,
		MultivariatePolynomialMR &	p1
	)

Definition at line 342 of file MultivariatePolynomialMR.cpp.

const MultivariatePolynomialMR GiNaCRA::operator+	(	const MultivariatePolynomialMR &	p1,
		const MultivariateMonomialMR &	m1
	)

Definition at line 347 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mTerms.

RealAlgebraicNumberIR & GiNaCRA::operator+	(	const GiNaC::numeric &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 351 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), and GiNaCRA::UnivariatePolynomial::variable().

RealAlgebraicNumberIR & GiNaCRA::operator+	(	RealAlgebraicNumberIR &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 360 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), and GiNaCRA::UnivariatePolynomial::variable().

const MultivariatePolynomialMR GiNaCRA::operator+	(	const MultivariateMonomialMR &	m1,
		const MultivariatePolynomialMR &	p1
	)

Definition at line 376 of file MultivariatePolynomialMR.cpp.

RealAlgebraicNumberPtr GiNaCRA::operator+	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh
	)

Definition at line 464 of file operators.cpp.

References binaryOperator().

const MultivariateCoefficientMR GiNaCRA::operator-

(

const MultivariateCoefficientMR &

m1

)

Definition at line 50 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const MultivariateCoefficientMR GiNaCRA::operator-	(	const MultivariateCoefficientMR &	m1,
		const MultivariateCoefficientMR &	m2
	)

Definition at line 55 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const OpenInterval GiNaCRA::operator-	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 77 of file operators.cpp.

References GiNaCRA::OpenInterval::add(), and GiNaCRA::OpenInterval::minus().

const OpenInterval GiNaCRA::operator-

(

const OpenInterval &

lh

)

Definition at line 89 of file operators.cpp.

References GiNaCRA::OpenInterval::minus().

const OpenInterval GiNaCRA::operator-	(	const OpenInterval &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 128 of file operators.cpp.

const OpenInterval GiNaCRA::operator-	(	const GiNaC::numeric &	lh,
		const OpenInterval &	rh
	)

Definition at line 133 of file operators.cpp.

const UnivariatePolynomial GiNaCRA::operator-	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 185 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::sub().

const RationalUnivariatePolynomial GiNaCRA::operator-	(	const RationalUnivariatePolynomial &	lh,
		const RationalUnivariatePolynomial &	rh
	)

Definition at line 212 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::variable().

const UnivariatePolynomial GiNaCRA::operator-

(

const UnivariatePolynomial &

lh

)

Definition at line 235 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::enabledPolynomialCheck(), and GiNaCRA::UnivariatePolynomial::variable().

const RationalUnivariatePolynomial GiNaCRA::operator-

(

const RationalUnivariatePolynomial &

lh

)

Definition at line 240 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::variable().

RealAlgebraicNumberIR & GiNaCRA::operator-	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 281 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::add(), and GiNaCRA::RealAlgebraicNumberIR::minus().

RealAlgebraicNumberIR & GiNaCRA::operator-

(

RealAlgebraicNumberIR &

lh

)

Definition at line 305 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::minus().

RealAlgebraicNumberIR & GiNaCRA::operator-	(	const GiNaC::numeric &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 369 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), and GiNaCRA::UnivariatePolynomial::variable().

RealAlgebraicNumberIR & GiNaCRA::operator-	(	RealAlgebraicNumberIR &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 378 of file operators.cpp.

References GiNaCRA::RationalUnivariatePolynomial::countRealRoots(), GiNaCRA::RealAlgebraicNumberIR::interval(), GiNaCRA::RealAlgebraicNumberIR::polynomial(), GiNaCRA::RealAlgebraicNumberIR::refine(), and GiNaCRA::UnivariatePolynomial::variable().

const MultivariatePolynomialMR GiNaCRA::operator-	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)

Definition at line 381 of file MultivariatePolynomialMR.cpp.

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

const MultivariatePolynomialMR GiNaCRA::operator-

(

const MultivariatePolynomialMR &

p1

)

Definition at line 432 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mCmp, and GiNaCRA::MultivariatePolynomialMR::mTerms.

RealAlgebraicNumberPtr GiNaCRA::operator-	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh
	)

Definition at line 469 of file operators.cpp.

References binaryOperator().

RealAlgebraicNumberPtr GiNaCRA::operator-

(

const RealAlgebraicNumberPtr &

lh

)

Definition at line 497 of file operators.cpp.

const MultivariateCoefficientMR GiNaCRA::operator/	(	const MultivariateCoefficientMR &	m1,
		const MultivariateCoefficientMR &	m2
	)

Definition at line 60 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const OpenInterval GiNaCRA::operator/	(	const OpenInterval &	lh,
		const GiNaC::numeric &	rh
	)		throw ( overflow_error )

Definition at line 152 of file operators.cpp.

const OpenInterval GiNaCRA::operator/	(	const GiNaC::numeric &	lh,
		const OpenInterval &	rh
	)		throw ( overflow_error )

Definition at line 163 of file operators.cpp.

const UnivariatePolynomial GiNaCRA::operator/	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 195 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::quo().

const RationalUnivariatePolynomial GiNaCRA::operator/	(	const RationalUnivariatePolynomial &	lh,
		const RationalUnivariatePolynomial &	rh
	)

Definition at line 222 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::quo().

RealAlgebraicNumberIR & GiNaCRA::operator/	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 292 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::inverse(), and GiNaCRA::RealAlgebraicNumberIR::mul().

RealAlgebraicNumberIR & GiNaCRA::operator/	(	const GiNaC::numeric &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 409 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::inverse().

RealAlgebraicNumberIR & GiNaCRA::operator/	(	RealAlgebraicNumberIR &	lh,
		const GiNaC::numeric &	rh
	)

Definition at line 414 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::inverse().

RealAlgebraicNumberPtr GiNaCRA::operator/	(	const RealAlgebraicNumberPtr &	lh,
		const RealAlgebraicNumberPtr &	rh
	)

Definition at line 479 of file operators.cpp.

References binaryOperator().

const bool GiNaCRA::operator<	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 329 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isLess().

const bool GiNaCRA::operator<	(	const RealAlgebraicNumberPtr &	a,
		const RealAlgebraicNumberPtr &	b
	)

Definition at line 519 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberFactory::less().

std::ostream& GiNaCRA::operator<<	(	std::ostream &	os,
		const MultivariateCoefficientMR &	m1
	)

Definition at line 65 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

std::ostream& GiNaCRA::operator<<	(	std::ostream &	os,
		const MultivariateMonomialMR &	rhs
	)

Definition at line 167 of file MultivariateMonomialMR.cpp.

References GiNaCRA::MultivariateMonomialMR::mExponents.

std::ostream& GiNaCRA::operator<<	(	std::ostream &	os,
		const MultivariateTermMR &	rhs
	)

Parameters:

os
rhs

Returns:

Definition at line 172 of file MultivariateTermMR.cpp.

References GiNaCRA::MultivariateTermMR::mCoeff.

std::ostream & GiNaCRA::operator<<	(	std::ostream &	os,
		const UnivariatePolynomialSet &	s
	)

Definition at line 261 of file operators.cpp.

std::ostream& GiNaCRA::operator<<	(	std::ostream &	os,
		const MultivariatePolynomialMR &	rhs
	)

Parameters:

os
rhs

Returns:

Definition at line 483 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mTerms.

std::ostream & GiNaCRA::operator<<	(	std::ostream &	os,
		const RealAlgebraicNumberPtr &	a
	)

Definition at line 524 of file operators.cpp.

References print().

std::ostream & GiNaCRA::operator<<	(	std::ostream &	os,
		const RealAlgebraicPoint &	r
	)

Definition at line 550 of file operators.cpp.

References print().

std::ostream & GiNaCRA::operator<<	(	std::ostream &	os,
		const Constraint &	a
	)

Definition at line 572 of file operators.cpp.

References GiNaCRA::Constraint::poly(), GiNaC::POSITIVE_SIGN, GiNaCRA::Constraint::sign(), GiNaCRA::Constraint::variables(), and GiNaC::ZERO_SIGN.

const bool GiNaCRA::operator<=	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 106 of file operators.cpp.

References GiNaCRA::OpenInterval::isLess().

const bool GiNaCRA::operator<=	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 339 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isEqual(), and GiNaCRA::RealAlgebraicNumberIR::isLessWhileUnequal().

bool GiNaCRA::operator==	(	const MultivariateCoefficientMR &	m1,
		const MultivariateCoefficientMR &	m2
	)

Definition at line 35 of file MultivariateCoefficientMR.cpp.

References GiNaCRA::MultivariateCoefficientMR::mCoefficient.

const bool GiNaCRA::operator==	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 96 of file operators.cpp.

References GiNaCRA::OpenInterval::isEqual().

bool GiNaCRA::operator==	(	const MultivariateTermMR &	t1,
		const MultivariateTermMR &	t2
	)

Definition at line 152 of file MultivariateTermMR.cpp.

References GiNaCRA::MultivariateTermMR::mCoeff.

bool GiNaCRA::operator==	(	const MultivariateMonomialMR &	lhs,
		const MultivariateMonomialMR &	rhs
	)

Definition at line 155 of file MultivariateMonomialMR.cpp.

References GiNaCRA::MultivariateMonomialMR::mExponents, and GiNaCRA::MultivariateMonomialMR::mTotDeg.

const bool GiNaCRA::operator==	(	const UnivariatePolynomial &	lh,
		const UnivariatePolynomial &	rh
	)

Definition at line 247 of file operators.cpp.

References GiNaCRA::UnivariatePolynomial::isEqual().

bool GiNaCRA::operator==	(	const MultivariatePolynomialMR &	p1,
		const MultivariatePolynomialMR &	p2
	)

Definition at line 249 of file MultivariatePolynomialMR.cpp.

References GiNaCRA::MultivariatePolynomialMR::mTerms.

const bool GiNaCRA::operator==	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 312 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isEqual().

const bool GiNaCRA::operator==	(	const RealAlgebraicNumberIR &	lh,
		const RealAlgebraicNumberIR &	rh
	)

Definition at line 317 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isEqual().

const bool GiNaCRA::operator==	(	const RealAlgebraicNumberPtr &	a,
		const RealAlgebraicNumberPtr &	b
	)

Definition at line 509 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberFactory::equal().

const bool GiNaCRA::operator==	(	const Constraint &	a,
		const Constraint &	b
	)

Definition at line 565 of file operators.cpp.

References GiNaCRA::Constraint::poly(), and GiNaCRA::Constraint::sign().

const bool GiNaCRA::operator>	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 334 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isEqual(), and GiNaCRA::RealAlgebraicNumberIR::isLessWhileUnequal().

const bool GiNaCRA::operator>=	(	const OpenInterval &	lh,
		const OpenInterval &	rh
	)

Definition at line 111 of file operators.cpp.

References GiNaCRA::OpenInterval::isGreater().

const bool GiNaCRA::operator>=	(	RealAlgebraicNumberIR &	lh,
		RealAlgebraicNumberIR &	rh
	)

Definition at line 344 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::isLess().

RealAlgebraicNumberIR & GiNaCRA::operator^	(	RealAlgebraicNumberIR &	base,
		int	exponent
	)

Definition at line 298 of file operators.cpp.

References GiNaCRA::RealAlgebraicNumberIR::pow().

RealAlgebraicNumberPtr GiNaCRA::operator^	(	const RealAlgebraicNumberPtr &	base,
		int	exponent
	)

Definition at line 484 of file operators.cpp.

void GiNaCRA::print	(	const RealAlgebraicNumberPtr &	a,
		std::ostream &	os
	)

Definition at line 532 of file operators.cpp.

Referenced by GiNaCRA::CAD::liftCheck(), operator<<(), GiNaCRA::CAD::printSampleTree(), and GiNaCRA::SampleList::simplify().

bool GiNaCRA::sort_first	(	const std::pair< unsigned, unsigned > &	p1,
		const std::pair< unsigned, unsigned > &	p2
	)

Definition at line 45 of file MultivariateMonomialMR.cpp.

Referenced by GiNaCRA::MultivariateMonomialMR::MultivariateMonomialMR().

---

Variable Documentation

const CADSettingsType GiNaCRA::DEFAULT_CADSETTING [static]

The default setting for CAD settings, which is chosen if the CAD object is initialized without any other parameter.

Definition at line 101 of file settings.h.