Drake
Polynomial Class Reference

Represents symbolic polynomials. More...

#include <common/symbolic_polynomial.h>

Public Types

using MapType = std::unordered_map< Monomial, Expression >
 

Public Member Functions

 Polynomial ()=default
 Constructs a zero polynomial. More...
 
 Polynomial (MapType init)
 Constructs a polynomial from a map, MonomialExpression. More...
 
 Polynomial (const Monomial &m)
 Constructs a polynomial from a monomial m. More...
 
 Polynomial (const Expression &e)
 Constructs a polynomial from an expression e. More...
 
 Polynomial (const Expression &e, const Variables &indeterminates)
 Constructs a polynomial from an expression e by decomposing it with respect to indeterminates. More...
 
Variables indeterminates () const
 Returns the indeterminates of this polynomial. More...
 
Variables decision_variables () const
 Returns the decision variables of this polynomial. More...
 
int Degree (const Variable &v) const
 Returns the highest degree of this polynomial in a variable v. More...
 
int TotalDegree () const
 Returns the total degree of this polynomial. More...
 
const MapTypemonomial_to_coefficient_map () const
 Returns the mapping from a Monomial to its corresponding coefficient of this polynomial. More...
 
Expression ToExpression () const
 Returns an equivalent symbolic expression of this polynomial. More...
 
Polynomial Differentiate (const Variable &x) const
 Differentiates this polynomial with respect to the variable x. More...
 
template<typename Derived >
Eigen::Matrix< Polynomial, 1, Derived::RowsAtCompileTime > Jacobian (const Eigen::MatrixBase< Derived > &vars) const
 Computes the Jacobian matrix J of the polynomial with respect to vars. More...
 
PolynomialAddProduct (const Expression &coeff, const Monomial &m)
 Adds coeff * m to this polynomial. More...
 
Polynomialoperator+= (const Polynomial &p)
 
Polynomialoperator+= (const Monomial &m)
 
Polynomialoperator+= (double c)
 
Polynomialoperator-= (const Polynomial &p)
 
Polynomialoperator-= (const Monomial &m)
 
Polynomialoperator-= (double c)
 
Polynomialoperator*= (const Polynomial &p)
 
Polynomialoperator*= (const Monomial &m)
 
Polynomialoperator*= (double c)
 
bool EqualTo (const Polynomial &p) const
 Returns true if this polynomial and p are structurally equal. More...
 
Formula operator== (Polynomial p) const
 Returns a symbolic formula representing the condition where this polynomial and p are the same. More...
 
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
 Polynomial (const Polynomial &)=default
 
Polynomialoperator= (const Polynomial &)=default
 
 Polynomial (Polynomial &&)=default
 
Polynomialoperator= (Polynomial &&)=default
 

Detailed Description

Represents symbolic polynomials.

A symbolic polynomial keeps a mapping from a monomial of indeterminates to its coefficient in a symbolic expression.

A polynomial p has to satisfy an invariant such that p.decision_variables() ∩ p.indeterminates() = ∅. We have CheckInvariant() method to check the invariant.

Note that arithmetic operations (+,-,*) between a Polynomial and a Variable are not provided. The problem is that Variable class has no intrinsic information if a variable is a decision variable or an indeterminate while we need this information to perform arithmetic operations over Polynomials.

Member Typedef Documentation

using MapType = std::unordered_map<Monomial, Expression>

Constructor & Destructor Documentation

Polynomial ( )
default

Constructs a zero polynomial.

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Polynomial ( const Polynomial )
default
Polynomial ( Polynomial &&  )
default
Polynomial ( MapType  init)
explicit

Constructs a polynomial from a map, MonomialExpression.

Polynomial ( const Monomial m)

Constructs a polynomial from a monomial m.

Note that all variables in m are considered as indeterminates.

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Polynomial ( const Expression e)
explicit

Constructs a polynomial from an expression e.

Note that all variables in e are considered as indeterminates.

Exceptions
std::runtime_errorif e is not a polynomial.

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Polynomial ( const Expression e,
const Variables indeterminates 
)

Constructs a polynomial from an expression e by decomposing it with respect to indeterminates.

Exceptions
std::runtime_errorif e is not a polynomial in indeterminates.

Member Function Documentation

Polynomial & AddProduct ( const Expression coeff,
const Monomial m 
)

Adds coeff * m to this polynomial.

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Variables decision_variables ( ) const

Returns the decision variables of this polynomial.

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int Degree ( const Variable v) const

Returns the highest degree of this polynomial in a variable v.

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Polynomial Differentiate ( const Variable x) const

Differentiates this polynomial with respect to the variable x.

Note that a variable x can be either a decision variable or an indeterminate.

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bool EqualTo ( const Polynomial p) const

Returns true if this polynomial and p are structurally equal.

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Variables indeterminates ( ) const

Returns the indeterminates of this polynomial.

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Eigen::Matrix<Polynomial, 1, Derived::RowsAtCompileTime> Jacobian ( const Eigen::MatrixBase< Derived > &  vars) const
inline

Computes the Jacobian matrix J of the polynomial with respect to vars.

J(0,i) contains ∂f/∂vars(i).

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const Polynomial::MapType & monomial_to_coefficient_map ( ) const

Returns the mapping from a Monomial to its corresponding coefficient of this polynomial.

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Polynomial & operator*= ( const Polynomial p)

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Polynomial & operator*= ( const Monomial m)
Polynomial & operator*= ( double  c)
Polynomial & operator+= ( const Polynomial p)

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Polynomial & operator+= ( const Monomial m)

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Polynomial & operator+= ( double  c)

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Polynomial & operator-= ( const Polynomial p)

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Polynomial & operator-= ( const Monomial m)

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Polynomial & operator-= ( double  c)

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Polynomial& operator= ( const Polynomial )
default
Polynomial& operator= ( Polynomial &&  )
default
Formula operator== ( Polynomial  p) const

Returns a symbolic formula representing the condition where this polynomial and p are the same.

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Expression ToExpression ( ) const

Returns an equivalent symbolic expression of this polynomial.

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int TotalDegree ( ) const

Returns the total degree of this polynomial.

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