The general-purpose multivariate polynomial class. More...

#include <MultivariatePolynomial.h>

Inheritance diagram for carl::MultivariatePolynomial< Coeff, Ordering, Policies >:

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Collaboration diagram for carl::MultivariatePolynomial< Coeff, Ordering, Policies >:

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Public Types
enum class	ConstructorOperation { ADD , SUB , MUL , DIV }

using	OrderedBy = Ordering
	The ordering of the terms. More...

using	TermType = Term< Coeff >
	Type of the terms. More...

using	MonomType = Monomial
	Type of the monomials within the terms. More...

using	CoeffType = Coeff
	Type of the coefficients. More...

using	Policy = Policies
	Policies for this monomial. More...

using	NumberType = typename UnderlyingNumberType< Coeff >::type
	Number type within the coefficients. More...

using	IntNumberType = typename IntegralType< NumberType >::type
	Integer type associated with the number type. More...

using	PolyType = MultivariatePolynomial< Coeff, Ordering, Policies >

using	CACHE = void
	The type of the cache. Multivariate polynomials do not need a cache, we set it to something. More...

using	TermsType = std::vector< Term< Coeff > >
	Type our terms vector.f. More...

using	RootType = typename UnivariatePolynomial< NumberType >::RootType

template<typename C , typename T >
using	EnableIfNotSame = typename std::enable_if<!std::is_same< C, T >::value, T >::type

Public Member Functions
	~MultivariatePolynomial () noexcept=default

bool	isOrdered () const
	Check if the terms are ordered. More...

void	reset_ordered () const

void	makeOrdered () const
	Ensure that the terms are ordered. More...

const Term< Coeff > &	lterm () const
	The leading term. More...

Term< Coeff > &	lterm ()

const Coeff &	lcoeff () const
	Returns the coefficient of the leading term. More...

const Monomial::Arg &	lmon () const
	The leading monomial. More...

MultivariatePolynomial	lcoeff (Variable::Arg var) const
	Returns the leading coefficient with respect to the given variable. More...

const Term< Coeff > &	trailingTerm () const
	Give the last term according to Ordering. More...

Term< Coeff > &	trailingTerm ()

std::size_t	total_degree () const
	Calculates the max. More...

std::size_t	degree (Variable::Arg var) const
	Calculates the degree of this polynomial with respect to the given variable. More...

MultivariatePolynomial	coeff (Variable::Arg var, std::size_t exp) const
	Calculates the coefficient of var^exp. More...

bool	is_zero () const
	Check if the polynomial is zero. More...

bool	is_one () const

bool	is_constant () const
	Check if the polynomial is constant. More...

bool	is_number () const
	Check if the polynomial is a number, i.e., a constant. More...

bool	is_variable () const

bool	is_linear () const
	Check if the polynomial is linear. More...

std::size_t	nr_terms () const
	Calculate the number of terms. More...

std::size_t	size () const

bool	has_constant_term () const
	Check if the polynomial has a constant term that is not zero. More...

bool	integer_valued () const

const Coeff &	constant_part () const
	Retrieve the constant term of this polynomial or zero, if there is no constant term. More...

auto	begin () const

auto	end () const

auto	rbegin () const

auto	rend () const

auto	erase_term (typename TermsType::iterator pos)

const TermsType &	terms () const

TermsType &	terms ()

MultivariatePolynomial	tail (bool makeFullyOrdered=false) const
	For the polynomial p, the function calculates a polynomial p - lt(p). More...

MultivariatePolynomial &	strip_lterm ()
	Drops the leading term. More...

bool	has_single_variable () const

Variable	single_variable () const
	For terms with exactly one variable, get this variable. More...

const CoeffType &	coefficient () const

const PolyType &	polynomial () const

bool	is_univariate () const
	Checks whether only one variable occurs. More...

bool	is_tsos () const
	Checks whether the polynomial is a trivial sum of squares. More...

bool	has (Variable v) const

bool	is_reducible_identity () const

void	subtractProduct (const Term< Coeff > &factor, const MultivariatePolynomial &p)
	Subtract a term times a polynomial from this polynomial. More...

void	addTerm (const Term< Coeff > &term)
	Adds a single term without using a TermAdditionManager or changing the ordering status. More...

bool	sqrt (MultivariatePolynomial &res) const
	Calculates the square of this multivariate polynomial if it is a square. More...

Coeff	coprime_factor () const

template<typename C = Coeff, EnableIf< is_subset_of_rationals_type< C >> = dummy>
Coeff	coprime_factor_without_constant () const

MultivariatePolynomial	coprime_coefficients () const

MultivariatePolynomial	coprime_coefficients_sign_preserving () const

MultivariatePolynomial	normalize () const
	For a polynomial p, returns p/lc(p) More...

bool	divides (const MultivariatePolynomial &b) const

MultivariatePolynomial< typename IntegralType< Coeff >::type, Ordering, Policies >	to_integer_domain () const

const Term< Coeff > &	operator[] (std::size_t index) const

MultivariatePolynomial	mod (const typename IntegralType< Coeff >::type &modulo) const

template<typename C = Coeff, EnableIf< is_number_type< C >> = dummy>
Coeff	numeric_content () const

template<typename C = Coeff, DisableIf< is_number_type< C >> = dummy>
UnderlyingNumberType< C >::type	numeric_content () const

template<typename C = Coeff, EnableIf< is_number_type< C >> = dummy>
IntNumberType	main_denom () const

MultivariatePolynomial	operator- () const

template<bool findConstantTerm = true, bool findLeadingTerm = true>
void	makeMinimallyOrdered () const
	Make sure that the terms are at least minimally ordered. More...

bool	is_consistent () const
	Asserts that this polynomial complies with the requirements and assumptions for MultivariatePolynomial objects. More...

void	setReason (unsigned index)

BitVector	getReasons () const

void	setReasons (const BitVector &) const

Constructors
	MultivariatePolynomial ()

	MultivariatePolynomial (const MultivariatePolynomial< Coeff, Ordering, Policies > &p)

	MultivariatePolynomial (MultivariatePolynomial< Coeff, Ordering, Policies > &&p)

MultivariatePolynomial &	operator= (const MultivariatePolynomial &p)

MultivariatePolynomial &	operator= (MultivariatePolynomial &&p) noexcept

	MultivariatePolynomial (int c)

template<typename C = Coeff>
	MultivariatePolynomial (EnableIfNotSame< C, sint > c)

template<typename C = Coeff>
	MultivariatePolynomial (EnableIfNotSame< C, uint > c)

	MultivariatePolynomial (const Coeff &c)

	MultivariatePolynomial (Variable::Arg v)

	MultivariatePolynomial (const Term< Coeff > &t)

	MultivariatePolynomial (const std::shared_ptr< const Monomial > &m)

	MultivariatePolynomial (const UnivariatePolynomial< MultivariatePolynomial< Coeff, Ordering, Policy >> &pol)

	MultivariatePolynomial (const UnivariatePolynomial< Coeff > &p)

template<class OtherPolicies , DisableIf< std::is_same< Policies, OtherPolicies >> = dummy>
	MultivariatePolynomial (const MultivariatePolynomial< Coeff, Ordering, OtherPolicies > &p)

	MultivariatePolynomial (TermsType &&terms, bool duplicates=true, bool ordered=false)

	MultivariatePolynomial (const TermsType &terms, bool duplicates=true, bool ordered=false)

	MultivariatePolynomial (const std::initializer_list< Term< Coeff >> &terms)

	MultivariatePolynomial (const std::initializer_list< Variable > &terms)

	MultivariatePolynomial (const std::pair< ConstructorOperation, std::vector< MultivariatePolynomial >> &p)

	MultivariatePolynomial (ConstructorOperation op, const std::vector< MultivariatePolynomial > &operands)

In-place addition operators
MultivariatePolynomial &	operator+= (const MultivariatePolynomial &rhs)
	Add something to this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator+= (const TermType &rhs)
	Add something to this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator+= (const std::shared_ptr< const TermType > &rhs)
	Add something to this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator+= (const Monomial::Arg &rhs)
	Add something to this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator+= (Variable rhs)
	Add something to this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator+= (const Coeff &rhs)
	Add something to this polynomial and return the changed polynomial. More...

In-place subtraction operators
MultivariatePolynomial &	operator-= (const MultivariatePolynomial &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator-= (const Term< Coeff > &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator-= (const Monomial::Arg &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator-= (Variable::Arg rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

MultivariatePolynomial &	operator-= (const Coeff &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

In-place multiplication operators
MultivariatePolynomial &	operator*= (const MultivariatePolynomial &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

MultivariatePolynomial &	operator*= (const Term< Coeff > &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

MultivariatePolynomial &	operator*= (const Monomial::Arg &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

MultivariatePolynomial &	operator*= (Variable::Arg rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

MultivariatePolynomial &	operator*= (const Coeff &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

In-place division operators
MultivariatePolynomial &	operator/= (const MultivariatePolynomial &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

MultivariatePolynomial &	operator/= (const Term< Coeff > &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

MultivariatePolynomial &	operator/= (const Monomial::Arg &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

MultivariatePolynomial &	operator/= (Variable::Arg rhs)
	Divide this polynomial by something and return the changed polynomial. More...

MultivariatePolynomial &	operator/= (const Coeff &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

Static Public Member Functions
static bool	compareByLeadingTerm (const MultivariatePolynomial &p1, const MultivariatePolynomial &p2)

static bool	compareByNrTerms (const MultivariatePolynomial &p1, const MultivariatePolynomial &p2)

Static Public Attributes
static TermAdditionManager< MultivariatePolynomial, Ordering >	mTermAdditionManager

static const bool	searchLinear = true
	Linear searching means that we search linearly for a term instead of applying e.g. More...

static const bool	has_reasons = ReasonsAdaptor::has_reasons

Private Member Functions
void	makeMinimallyOrdered (typename TermsType::iterator &lterm, typename TermsType::iterator &cterm) const
	Make sure that the terms are at least minimally ordered. More...

Private Attributes
TermsType	mTerms
	A vector of all terms. More...

bool	mOrdered
	Flag that indicates if the terms are ordered. More...

Friends
template<typename Polynomial , typename Order >
class	TermAdditionManager

std::ostream &	operator<< (std::ostream &os, ConstructorOperation op)

Division operators
template<typename C , typename O , typename P >
MultivariatePolynomial< C, O, P >	operator/ (const MultivariatePolynomial< C, O, P > &lhs, const MultivariatePolynomial< C, O, P > &rhs)
	Perform a division involving a polynomial. More...

template<typename C , typename O , typename P >
MultivariatePolynomial< C, O, P >	operator/ (const MultivariatePolynomial< C, O, P > &lhs, unsigned long rhs)
	Perform a division involving a polynomial. More...

Detailed Description

template<typename Coeff, typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>
class carl::MultivariatePolynomial< Coeff, Ordering, Policies >

The general-purpose multivariate polynomial class.

It is represented as a sum of terms, being a coefficient and a monomial.

A polynomial is always minimally ordered. By that, we mean that the leading term and the constant term (if there is any) are at the correct positions. For some operations, the terms may be fully ordered. isOrdered() checks if the polynomial is fully ordered while makeOrdered() makes the polynomial fully ordered.

Definition at line 42 of file MultivariatePolynomial.h.

Member Typedef Documentation

◆ CACHE

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::CACHE = void

The type of the cache. Multivariate polynomials do not need a cache, we set it to something.

Definition at line 64 of file MultivariatePolynomial.h.

◆ CoeffType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::CoeffType = Coeff

Type of the coefficients.

Definition at line 54 of file MultivariatePolynomial.h.

◆ EnableIfNotSame

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C , typename T >

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::EnableIfNotSame = typename std::enable_if<!std::is_same<C,T>::value,T>::type

Definition at line 71 of file MultivariatePolynomial.h.

◆ IntNumberType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::IntNumberType = typename IntegralType<NumberType>::type

Integer type associated with the number type.

Definition at line 60 of file MultivariatePolynomial.h.

◆ MonomType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MonomType = Monomial

Type of the monomials within the terms.

Definition at line 52 of file MultivariatePolynomial.h.

◆ NumberType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::NumberType = typename UnderlyingNumberType<Coeff>::type

Number type within the coefficients.

Definition at line 58 of file MultivariatePolynomial.h.

◆ OrderedBy

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::OrderedBy = Ordering

The ordering of the terms.

Definition at line 48 of file MultivariatePolynomial.h.

◆ Policy

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::Policy = Policies

Policies for this monomial.

Definition at line 56 of file MultivariatePolynomial.h.

◆ PolyType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::PolyType = MultivariatePolynomial<Coeff, Ordering, Policies>

Definition at line 62 of file MultivariatePolynomial.h.

◆ RootType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::RootType = typename UnivariatePolynomial<NumberType>::RootType

Definition at line 68 of file MultivariatePolynomial.h.

◆ TermsType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::TermsType = std::vector<Term<Coeff> >

Type our terms vector.f.

Definition at line 66 of file MultivariatePolynomial.h.

◆ TermType

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

using carl::MultivariatePolynomial< Coeff, Ordering, Policies >::TermType = Term<Coeff>

Type of the terms.

Definition at line 50 of file MultivariatePolynomial.h.

Member Enumeration Documentation

◆ ConstructorOperation

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

enum carl::MultivariatePolynomial::ConstructorOperation

strong

Enumerator
ADD
SUB
MUL
DIV

Definition at line 82 of file MultivariatePolynomial.h.

Constructor & Destructor Documentation

◆ MultivariatePolynomial() [1/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( )

◆ MultivariatePolynomial() [2/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const MultivariatePolynomial< Coeff, Ordering, Policies > & p )

◆ MultivariatePolynomial() [3/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( MultivariatePolynomial< Coeff, Ordering, Policies > && p )

◆ MultivariatePolynomial() [4/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( int c )

inlineexplicit

Definition at line 100 of file MultivariatePolynomial.h.

◆ MultivariatePolynomial() [5/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( EnableIfNotSame< C, sint > c )

explicit

◆ MultivariatePolynomial() [6/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( EnableIfNotSame< C, uint > c )

explicit

◆ MultivariatePolynomial() [7/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const Coeff & c )

explicit

◆ MultivariatePolynomial() [8/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( Variable::Arg v )

explicit

◆ MultivariatePolynomial() [9/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const Term< Coeff > & t )

explicit

◆ MultivariatePolynomial() [10/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const std::shared_ptr< const Monomial > & m )

explicit

◆ MultivariatePolynomial() [11/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const UnivariatePolynomial< MultivariatePolynomial< Coeff, Ordering, Policy >> & pol )

explicit

◆ MultivariatePolynomial() [12/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const UnivariatePolynomial< Coeff > & p )

explicit

◆ MultivariatePolynomial() [13/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<class OtherPolicies , DisableIf< std::is_same< Policies, OtherPolicies >> = dummy>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const MultivariatePolynomial< Coeff, Ordering, OtherPolicies > & p )

explicit

◆ MultivariatePolynomial() [14/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial	(	TermsType &&	terms,
		bool	duplicates = `true`,
		bool	ordered = `false`
	)

explicit

◆ MultivariatePolynomial() [15/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial	(	const TermsType &	terms,
		bool	duplicates = `true`,
		bool	ordered = `false`
	)

explicit

◆ MultivariatePolynomial() [16/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const std::initializer_list< Term< Coeff >> & terms )

◆ MultivariatePolynomial() [17/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const std::initializer_list< Variable > & terms )

◆ MultivariatePolynomial() [18/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial ( const std::pair< ConstructorOperation, std::vector< MultivariatePolynomial< Coeff, Ordering, Policies > >> & p )

explicit

◆ MultivariatePolynomial() [19/19]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::MultivariatePolynomial	(	ConstructorOperation	op,
		const std::vector< MultivariatePolynomial< Coeff, Ordering, Policies > > &	operands
	)

explicit

◆ ~MultivariatePolynomial()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

carl::MultivariatePolynomial< Coeff, Ordering, Policies >::~MultivariatePolynomial ( )

defaultnoexcept

Member Function Documentation

◆ addTerm()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::addTerm ( const Term< Coeff > & term )

Adds a single term without using a TermAdditionManager or changing the ordering status.

Parameters

term Term.

◆ begin()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

auto carl::MultivariatePolynomial< Coeff, Ordering, Policies >::begin ( ) const

inline

Definition at line 310 of file MultivariatePolynomial.h.

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◆ coeff()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coeff	(	Variable::Arg	var,
		std::size_t	exp
	)		const

inline

Calculates the coefficient of var^exp.

Parameters

var	Variable.
exp	Exponent.

Returns: Coefficient of var^exp.

Definition at line 221 of file MultivariatePolynomial.h.

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◆ coefficient()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const CoeffType& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coefficient ( ) const

inline

Returns: Coefficient of the polynomial (this makes only sense for polynomials storing the gcd of all coefficients separately)

Definition at line 365 of file MultivariatePolynomial.h.

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◆ compareByLeadingTerm()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

static bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::compareByLeadingTerm	(	const MultivariatePolynomial< Coeff, Ordering, Policies > &	p1,
		const MultivariatePolynomial< Coeff, Ordering, Policies > &	p2
	)

inlinestatic

Definition at line 551 of file MultivariatePolynomial.h.

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◆ compareByNrTerms()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

static bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::compareByNrTerms	(	const MultivariatePolynomial< Coeff, Ordering, Policies > &	p1,
		const MultivariatePolynomial< Coeff, Ordering, Policies > &	p2
	)

inlinestatic

Definition at line 556 of file MultivariatePolynomial.h.

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◆ constant_part()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Coeff& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::constant_part ( ) const

Retrieve the constant term of this polynomial or zero, if there is no constant term.

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◆ coprime_coefficients()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coprime_coefficients ( ) const

Returns: p * p.coprime_factor()

See also: coprime_factor()

◆ coprime_coefficients_sign_preserving()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coprime_coefficients_sign_preserving ( ) const

Returns: p * |p.coprime_factor()|

See also: coprime_coefficients()

◆ coprime_factor()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

Coeff carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coprime_factor ( ) const

Returns: The lcm of the denominators of the coefficients in p divided by the gcd of numerators of the coefficients in p.

◆ coprime_factor_without_constant()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff, EnableIf< is_subset_of_rationals_type< C >> = dummy>

Coeff carl::MultivariatePolynomial< Coeff, Ordering, Policies >::coprime_factor_without_constant ( ) const

Returns: The lcm of the denominators of the coefficients (without the constant one) in p divided by the gcd of numerators of the coefficients in p.

◆ degree()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

std::size_t carl::MultivariatePolynomial< Coeff, Ordering, Policies >::degree ( Variable::Arg var ) const

inline

Calculates the degree of this polynomial with respect to the given variable.

Parameters

var Variable.

Returns: Degree w.r.t. var.

Definition at line 205 of file MultivariatePolynomial.h.

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◆ divides()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::divides ( const MultivariatePolynomial< Coeff, Ordering, Policies > & b ) const

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◆ end()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

auto carl::MultivariatePolynomial< Coeff, Ordering, Policies >::end ( ) const

inline

Definition at line 313 of file MultivariatePolynomial.h.

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◆ erase_term()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

auto carl::MultivariatePolynomial< Coeff, Ordering, Policies >::erase_term ( typename TermsType::iterator pos )

inline

Todo:: find new lterm or constant term

Definition at line 323 of file MultivariatePolynomial.h.

◆ getReasons()

BitVector carl::NoReasons::getReasons ( ) const

inlineinherited

Definition at line 17 of file ReasonsAdaptor.h.

◆ has()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::has ( Variable v ) const

inline

Parameters

v	The variable to check for its occurrence.

Returns: true, if the variable occurs in this term.

Definition at line 397 of file MultivariatePolynomial.h.

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◆ has_constant_term()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::has_constant_term ( ) const

inline

Check if the polynomial has a constant term that is not zero.

Definition at line 292 of file MultivariatePolynomial.h.

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◆ has_single_variable()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::has_single_variable ( ) const

inline

Definition at line 350 of file MultivariatePolynomial.h.

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◆ integer_valued()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::integer_valued ( ) const

inline

Returns: true, if the image of this polynomial is integer-valued.

Definition at line 299 of file MultivariatePolynomial.h.

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◆ is_consistent()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_consistent ( ) const

Asserts that this polynomial complies with the requirements and assumptions for MultivariatePolynomial objects.

All terms are actually valid and not nullptr or alike
Only the trailing term may be constant.

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◆ is_constant()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_constant ( ) const

inline

Check if the polynomial is constant.

Definition at line 254 of file MultivariatePolynomial.h.

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◆ is_linear()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_linear ( ) const

Check if the polynomial is linear.

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◆ is_number()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_number ( ) const

inline

Check if the polynomial is a number, i.e., a constant.

Definition at line 260 of file MultivariatePolynomial.h.

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◆ is_one()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_one ( ) const

inline

Returns

Definition at line 248 of file MultivariatePolynomial.h.

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◆ is_reducible_identity()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_reducible_identity ( ) const

◆ is_tsos()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_tsos ( ) const

inline

Checks whether the polynomial is a trivial sum of squares.

Returns: true if polynomial is of the form \sum a_im_i^2 with a_i > 0 for all i.

Definition at line 387 of file MultivariatePolynomial.h.

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◆ is_univariate()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_univariate ( ) const

Checks whether only one variable occurs.

Returns: Notice that it might be better to use the variable information if several pieces of information are requested.

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◆ is_variable()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_variable ( ) const

inline

Returns: true, if this polynomial consists just of one variable (with coefficient 1).

Definition at line 266 of file MultivariatePolynomial.h.

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◆ is_zero()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::is_zero ( ) const

inline

Check if the polynomial is zero.

Definition at line 240 of file MultivariatePolynomial.h.

◆ isOrdered()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::isOrdered ( ) const

inline

Check if the terms are ordered.

Returns: If terms are ordered.

Definition at line 127 of file MultivariatePolynomial.h.

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◆ lcoeff() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Coeff& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::lcoeff ( ) const

inline

Returns the coefficient of the leading term.

Notice that this is not defined for zero polynomials.

Returns: Leading coefficient.

Definition at line 161 of file MultivariatePolynomial.h.

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◆ lcoeff() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::lcoeff ( Variable::Arg var ) const

inline

Returns the leading coefficient with respect to the given variable.

Parameters

var Variable.

Returns: Leading coefficient.

Definition at line 176 of file MultivariatePolynomial.h.

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◆ lmon()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Monomial::Arg& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::lmon ( ) const

inline

The leading monomial.

Returns: monomial of leading term.

Definition at line 168 of file MultivariatePolynomial.h.

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◆ lterm() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

Term<Coeff>& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::lterm ( )

inline

Definition at line 152 of file MultivariatePolynomial.h.

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◆ lterm() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Term<Coeff>& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::lterm ( ) const

inline

The leading term.

Returns: leading term.

Definition at line 148 of file MultivariatePolynomial.h.

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◆ main_denom()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff, EnableIf< is_number_type< C >> = dummy>

IntNumberType carl::MultivariatePolynomial< Coeff, Ordering, Policies >::main_denom ( ) const

◆ makeMinimallyOrdered() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<bool findConstantTerm = true, bool findLeadingTerm = true>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::makeMinimallyOrdered ( ) const

Make sure that the terms are at least minimally ordered.

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◆ makeMinimallyOrdered() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::makeMinimallyOrdered	(	typename TermsType::iterator &	lterm,
		typename TermsType::iterator &	cterm
	)		const

private

Make sure that the terms are at least minimally ordered.

Iterators to the important terms are given as arguments, so that we don't need to scan the whole vector.

Parameters

lterm	Iterator to leading term.
cterm	Iterator to constant term.

◆ makeOrdered()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::makeOrdered ( ) const

inline

Ensure that the terms are ordered.

Definition at line 136 of file MultivariatePolynomial.h.

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◆ mod()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::mod ( const typename IntegralType< Coeff >::type & modulo ) const

◆ normalize()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::normalize ( ) const

For a polynomial p, returns p/lc(p)

Returns

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◆ nr_terms()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

std::size_t carl::MultivariatePolynomial< Coeff, Ordering, Policies >::nr_terms ( ) const

inline

Calculate the number of terms.

Definition at line 277 of file MultivariatePolynomial.h.

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◆ numeric_content() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff, EnableIf< is_number_type< C >> = dummy>

Coeff carl::MultivariatePolynomial< Coeff, Ordering, Policies >::numeric_content ( ) const

◆ numeric_content() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C = Coeff, DisableIf< is_number_type< C >> = dummy>

UnderlyingNumberType<C>::type carl::MultivariatePolynomial< Coeff, Ordering, Policies >::numeric_content ( ) const

◆ operator*=() [1/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator*= ( const Coeff & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [2/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator*= ( const Monomial::Arg & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [3/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator*= ( const MultivariatePolynomial< Coeff, Ordering, Policies > & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [4/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator*= ( const Term< Coeff > & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [5/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator*= ( Variable::Arg rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [1/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( const Coeff & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [2/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( const Monomial::Arg & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [3/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( const MultivariatePolynomial< Coeff, Ordering, Policies > & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [4/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( const std::shared_ptr< const TermType > & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [5/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( const TermType & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [6/6]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator+= ( Variable rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator- ( ) const

◆ operator-=() [1/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator-= ( const Coeff & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-=() [2/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator-= ( const Monomial::Arg & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-=() [3/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator-= ( const MultivariatePolynomial< Coeff, Ordering, Policies > & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-=() [4/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator-= ( const Term< Coeff > & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-=() [5/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator-= ( Variable::Arg rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [1/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator/= ( const Coeff & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [2/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator/= ( const Monomial::Arg & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [3/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator/= ( const MultivariatePolynomial< Coeff, Ordering, Policies > & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [4/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator/= ( const Term< Coeff > & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [5/5]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator/= ( Variable::Arg rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator=() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator= ( const MultivariatePolynomial< Coeff, Ordering, Policies > & p )

◆ operator=() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator= ( MultivariatePolynomial< Coeff, Ordering, Policies > && p )

noexcept

◆ operator[]()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Term<Coeff>& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::operator[] ( std::size_t index ) const

inline

Definition at line 460 of file MultivariatePolynomial.h.

◆ polynomial()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const PolyType& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::polynomial ( ) const

inline

Returns: The coprimeCoefficients of this polyomial, if this is stored internally, otherwise this polynomial.

Definition at line 372 of file MultivariatePolynomial.h.

◆ rbegin()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

auto carl::MultivariatePolynomial< Coeff, Ordering, Policies >::rbegin ( ) const

inline

Definition at line 316 of file MultivariatePolynomial.h.

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◆ rend()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

auto carl::MultivariatePolynomial< Coeff, Ordering, Policies >::rend ( ) const

inline

Definition at line 319 of file MultivariatePolynomial.h.

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◆ reset_ordered()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::reset_ordered ( ) const

inline

Definition at line 130 of file MultivariatePolynomial.h.

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◆ setReason()

void carl::NoReasons::setReason ( unsigned index )

inherited

◆ setReasons()

void carl::NoReasons::setReasons ( const BitVector & ) const

inlineinherited

Definition at line 18 of file ReasonsAdaptor.h.

◆ single_variable()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

Variable carl::MultivariatePolynomial< Coeff, Ordering, Policies >::single_variable ( ) const

inline

For terms with exactly one variable, get this variable.

Returns: The only variable occuring in the term.

Definition at line 358 of file MultivariatePolynomial.h.

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◆ size()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

std::size_t carl::MultivariatePolynomial< Coeff, Ordering, Policies >::size ( ) const

inline

Returns: A rough estimation of the size of this polynomial being the number of its terms. (Note, that this method is required, as it is provided of other polynomials not necessarily being straightforward.)

Definition at line 285 of file MultivariatePolynomial.h.

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◆ sqrt()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::sqrt ( MultivariatePolynomial< Coeff, Ordering, Policies > & res ) const

Calculates the square of this multivariate polynomial if it is a square.

Parameters

res	Used to store the result in.

Returns: true, if this multivariate polynomial is a square; false, otherwise.

◆ strip_lterm()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::strip_lterm ( )

Drops the leading term.

The function assumes the polynomial to be nonzero, otherwise the leading term is not defined.

Returns: A reference to this.

Todo:: find new lterm

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◆ subtractProduct()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

void carl::MultivariatePolynomial< Coeff, Ordering, Policies >::subtractProduct	(	const Term< Coeff > &	factor,
		const MultivariatePolynomial< Coeff, Ordering, Policies > &	p
	)

Subtract a term times a polynomial from this polynomial.

Parameters

factor	Term.
p	Polynomial.

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◆ tail()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial carl::MultivariatePolynomial< Coeff, Ordering, Policies >::tail ( bool makeFullyOrdered = false ) const

For the polynomial p, the function calculates a polynomial p - lt(p).

The function assumes the polynomial to be nonzero, otherwise, lt(p) is not defined.

Returns: A new polynomial p - lt(p).

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◆ terms() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

TermsType& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::terms ( )

inline

Definition at line 332 of file MultivariatePolynomial.h.

◆ terms() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const TermsType& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::terms ( ) const

inline

Definition at line 329 of file MultivariatePolynomial.h.

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◆ to_integer_domain()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

MultivariatePolynomial<typename IntegralType<Coeff>::type, Ordering, Policies> carl::MultivariatePolynomial< Coeff, Ordering, Policies >::to_integer_domain ( ) const

◆ total_degree()

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

std::size_t carl::MultivariatePolynomial< Coeff, Ordering, Policies >::total_degree ( ) const

Calculates the max.

degree over all monomials occurring in the polynomial. As the degree of the zero polynomial is $-\infty$ , we assert that this polynomial is not zero. This must be checked by the caller before calling this method.

See also: [3], page 48

Returns: Total degree.

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◆ trailingTerm() [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

Term<Coeff>& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::trailingTerm ( )

inline

Definition at line 187 of file MultivariatePolynomial.h.

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◆ trailingTerm() [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

const Term<Coeff>& carl::MultivariatePolynomial< Coeff, Ordering, Policies >::trailingTerm ( ) const

inline

Give the last term according to Ordering.

Notice that if there is a constant part, it is always trailing.

Definition at line 183 of file MultivariatePolynomial.h.

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Friends And Related Function Documentation

◆ operator/ [1/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C , typename O , typename P >

MultivariatePolynomial<C,O,P> operator/	(	const MultivariatePolynomial< C, O, P > &	lhs,
		const MultivariatePolynomial< C, O, P > &	rhs
	)

friend

Perform a division involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs / rhs

Definition at line 242 of file Division.h.

◆ operator/ [2/2]

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename C , typename O , typename P >

MultivariatePolynomial<C,O,P> operator/	(	const MultivariatePolynomial< C, O, P > &	lhs,
		unsigned long	rhs
	)

friend

Perform a division involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs / rhs

◆ operator<<

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

std::ostream& operator<<	(	std::ostream &	os,
		ConstructorOperation	op
	)

friend

Definition at line 83 of file MultivariatePolynomial.h.

◆ TermAdditionManager

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

template<typename Polynomial , typename Order >

friend class TermAdditionManager

friend

Definition at line 45 of file MultivariatePolynomial.h.

Field Documentation

◆ has_reasons

template<typename ReasonsAdaptor = NoReasons, typename Allocator = NoAllocator>

const bool carl::StdMultivariatePolynomialPolicies< ReasonsAdaptor, Allocator >::has_reasons = ReasonsAdaptor::has_reasons

staticinherited

Definition at line 31 of file MultivariatePolynomialPolicy.h.

◆ mOrdered

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

bool carl::MultivariatePolynomial< Coeff, Ordering, Policies >::mOrdered

mutableprivate

Flag that indicates if the terms are ordered.

Definition at line 77 of file MultivariatePolynomial.h.

◆ mTermAdditionManager

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

TermAdditionManager<MultivariatePolynomial,Ordering> carl::MultivariatePolynomial< Coeff, Ordering, Policies >::mTermAdditionManager

static

Definition at line 80 of file MultivariatePolynomial.h.

◆ mTerms

template<typename Coeff , typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>

TermsType carl::MultivariatePolynomial< Coeff, Ordering, Policies >::mTerms

mutableprivate

A vector of all terms.

Definition at line 75 of file MultivariatePolynomial.h.

◆ searchLinear

template<typename ReasonsAdaptor = NoReasons, typename Allocator = NoAllocator>

const bool carl::StdMultivariatePolynomialPolicies< ReasonsAdaptor, Allocator >::searchLinear = true

staticinherited

Linear searching means that we search linearly for a term instead of applying e.g.

binary search. Although the worst-case complexity is worse, for polynomials with a small nr of terms, this should be better.

Definition at line 28 of file MultivariatePolynomialPolicy.h.

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

carl-arith/numbers/typetraits.h
carl-arith/poly/umvpoly/MultivariatePolynomial.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

template<typename Coeff, typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>> class carl::MultivariatePolynomial< Coeff, Ordering, Policies >

Member Typedef Documentation

◆ CACHE

◆ CoeffType

◆ EnableIfNotSame

◆ IntNumberType

◆ MonomType

◆ NumberType

◆ OrderedBy

◆ Policy

◆ PolyType

◆ RootType

◆ TermsType

◆ TermType

Member Enumeration Documentation

◆ ConstructorOperation

Constructor & Destructor Documentation

◆ MultivariatePolynomial() [1/19]

◆ MultivariatePolynomial() [2/19]

◆ MultivariatePolynomial() [3/19]

◆ MultivariatePolynomial() [4/19]

◆ MultivariatePolynomial() [5/19]

◆ MultivariatePolynomial() [6/19]

◆ MultivariatePolynomial() [7/19]

◆ MultivariatePolynomial() [8/19]

◆ MultivariatePolynomial() [9/19]

◆ MultivariatePolynomial() [10/19]

◆ MultivariatePolynomial() [11/19]

◆ MultivariatePolynomial() [12/19]

◆ MultivariatePolynomial() [13/19]

◆ MultivariatePolynomial() [14/19]

◆ MultivariatePolynomial() [15/19]

◆ MultivariatePolynomial() [16/19]

◆ MultivariatePolynomial() [17/19]

◆ MultivariatePolynomial() [18/19]

◆ MultivariatePolynomial() [19/19]

◆ ~MultivariatePolynomial()

Member Function Documentation

◆ addTerm()

◆ begin()

◆ coeff()

◆ coefficient()

◆ compareByLeadingTerm()

◆ compareByNrTerms()

◆ constant_part()

◆ coprime_coefficients()

◆ coprime_coefficients_sign_preserving()

◆ coprime_factor()

◆ coprime_factor_without_constant()

◆ degree()

◆ divides()

◆ end()

◆ erase_term()

◆ getReasons()

◆ has()

◆ has_constant_term()

◆ has_single_variable()

◆ integer_valued()

◆ is_consistent()

◆ is_constant()

◆ is_linear()

◆ is_number()

◆ is_one()

◆ is_reducible_identity()

◆ is_tsos()

◆ is_univariate()

◆ is_variable()

◆ is_zero()

◆ isOrdered()

◆ lcoeff() [1/2]

◆ lcoeff() [2/2]

◆ lmon()

template<typename Coeff, typename Ordering = GrLexOrdering, typename Policies = StdMultivariatePolynomialPolicies<>>
class carl::MultivariatePolynomial< Coeff, Ordering, Policies >