RationalFunction Class Reference

Detailed Description

Represents symbolic rational function.

A function f(x) is a rational function, if f(x) = p(x) / q(x), where both p(x) and q(x) are polynomials of x. Note that rational functions are closed under (+, -, x, /). One application of rational function is in polynomial optimization, where we represent (or approximate) functions using rational functions, and then convert the constraint f(x) = h(x) (where h(x) is a polynomial) to a polynomial constraint p(x) - q(x) * h(x) = 0, or convert the inequality constraint f(x) >= h(x) as p(x) - q(x) * h(x) >= 0 if we know q(x) > 0.

This class represents a special subset of the symbolic::Expression. While a symbolic::Expression can represent a rational function, extracting the numerator and denominator, generally, is quite difficult; for instance, from p1(x) / q1(x) + p2(x) / q2(x) + ... + pn(x) / qn(x). This class's explicit structure facilitates this decomposition.

#include <drake/common/symbolic/rational_function.h>

Public Member Functions
	RationalFunction ()
	Constructs a zero rational function 0 / 1.
	RationalFunction (Polynomial numerator, Polynomial denominator)
	Constructs the rational function: numerator / denominator.
	RationalFunction (const Polynomial &p)
	Constructs the rational function: p / 1.
	RationalFunction (const Monomial &m)
	Constructs the rational function: m / 1 for any type which can be cast to a monomial.
	RationalFunction (double c)
	Constructs the rational function: c / 1.
double	Evaluate (const Environment &env) const
	Evaluates this rational function under a given environment env.
	~RationalFunction ()=default
const Polynomial &	numerator () const
	Getter for the numerator.
const Polynomial &	denominator () const
	Getter for the denominator.
RationalFunction &	operator+= (const RationalFunction &f)
RationalFunction &	operator+= (const Polynomial &p)
RationalFunction &	operator+= (const Monomial &m)
RationalFunction &	operator+= (double c)
RationalFunction &	operator-= (const RationalFunction &f)
RationalFunction &	operator-= (const Polynomial &p)
RationalFunction &	operator-= (const Monomial &m)
RationalFunction &	operator-= (double c)
RationalFunction &	operator*= (const RationalFunction &f)
RationalFunction &	operator*= (const Polynomial &p)
RationalFunction &	operator*= (const Monomial &m)
RationalFunction &	operator*= (double c)
RationalFunction &	operator/= (const RationalFunction &f)
RationalFunction &	operator/= (const Polynomial &p)
RationalFunction &	operator/= (const Monomial &m)
RationalFunction &	operator/= (double c)
bool	EqualTo (const RationalFunction &f) const
	Returns true if this rational function and f are structurally equal.
Formula	operator== (const RationalFunction &f) const
	Returns a symbolic formula representing the condition where this rational function and f are the same.
Formula	operator!= (const RationalFunction &f) const
	Returns a symbolic formula representing the condition where this rational function and f are not the same.
Expression	ToExpression () const
	Returns an equivalent symbolic expression of this rational function.
void	SetIndeterminates (const Variables &new_indeterminates)
	Sets the indeterminates of the numerator and denominator polynomials.
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	RationalFunction (const RationalFunction &)=default
RationalFunction &	operator= (const RationalFunction &)=default
	RationalFunction (RationalFunction &&)=default
RationalFunction &	operator= (RationalFunction &&)=default

Friends
RationalFunction	operator- (RationalFunction f)
	Unary minus operation for rational function.
std::ostream &	operator<< (std::ostream &, const RationalFunction &f)

Constructor & Destructor Documentation

RationalFunction() [1/7]

RationalFunction

(

)

Constructs a zero rational function 0 / 1.

RationalFunction() [2/7]

RationalFunction ( const RationalFunction & )

default

RationalFunction() [3/7]

RationalFunction ( RationalFunction && )

default

RationalFunction() [4/7]

RationalFunction	(	Polynomial	numerator,
		Polynomial	denominator )

Constructs the rational function: numerator / denominator.

Parameters

numerator	The numerator of the fraction.
denominator	The denominator of the fraction.

Precondition

denominator is not equal to zero.

None of the indeterminates in the numerator can be decision variables in the denominator; similarly none of the indeterminates in the denominator can be decision variables in the numerator.

RationalFunction() [5/7]

RationalFunction ( const Polynomial & p )

explicit

Constructs the rational function: p / 1.

Note that we use 1 as the denominator.

Parameters

p	The numerator of the rational function.

RationalFunction() [6/7]

RationalFunction ( const Monomial & m )

explicit

Constructs the rational function: m / 1 for any type which can be cast to a monomial.

Parameters

m	The numerator of the rational function.

RationalFunction() [7/7]

RationalFunction ( double c )

explicit

Constructs the rational function: c / 1.

Note that we use 1 as the denominator.

Parameters

c	The numerator of the rational function.

~RationalFunction()

~RationalFunction ( )

default

Member Function Documentation

denominator()

const Polynomial & denominator ( ) const

nodiscard

Getter for the denominator.

EqualTo()

bool EqualTo ( const RationalFunction & f ) const

nodiscard

Returns true if this rational function and f are structurally equal.

Evaluate()

double Evaluate ( const Environment & env ) const

nodiscard

Evaluates this rational function under a given environment env.

Exceptions

std::exception

if there is a variable in this rational function whose assignment is not provided by env.

numerator()

const Polynomial & numerator ( ) const

nodiscard

Getter for the numerator.

operator!=()

Formula operator!=

(

const RationalFunction &

f

)

const

Returns a symbolic formula representing the condition where this rational function and f are not the same.

operator*=() [1/4]

RationalFunction & operator*=

(

const Monomial &

m

)

operator*=() [2/4]

RationalFunction & operator*=

(

const Polynomial &

p

)

operator*=() [3/4]

RationalFunction & operator*=

(

const RationalFunction &

f

)

operator*=() [4/4]

RationalFunction & operator*=

(

double

c

)

operator+=() [1/4]

RationalFunction & operator+=

(

const Monomial &

m

)

operator+=() [2/4]

RationalFunction & operator+=

(

const Polynomial &

p

)

operator+=() [3/4]

RationalFunction & operator+=

(

const RationalFunction &

f

)

operator+=() [4/4]

RationalFunction & operator+=

(

double

c

)

operator-=() [1/4]

RationalFunction & operator-=

(

const Monomial &

m

)

operator-=() [2/4]

RationalFunction & operator-=

(

const Polynomial &

p

)

operator-=() [3/4]

RationalFunction & operator-=

(

const RationalFunction &

f

)

operator-=() [4/4]

RationalFunction & operator-=

(

double

c

)

operator/=() [1/4]

RationalFunction & operator/=

(

const Monomial &

m

)

operator/=() [2/4]

RationalFunction & operator/=

(

const Polynomial &

p

)

Exceptions

std::exception

if the divisor is structurally equal to zero. Note that this does not guarantee that the denominator of the result is not zero after expansion.

operator/=() [3/4]

RationalFunction & operator/=

(

const RationalFunction &

f

)

Exceptions

std::exception

if the numerator of the divisor is structurally equal to zero. Note that this does not guarantee that the denominator of the result is not zero after expansion.

operator/=() [4/4]

RationalFunction & operator/=

(

double

c

)

Exceptions

std::exception

if c is 0

operator=() [1/2]

RationalFunction & operator= ( const RationalFunction & )

default

operator=() [2/2]

RationalFunction & operator= ( RationalFunction && )

default

operator==()

Formula operator==

(

const RationalFunction &

f

)

const

Returns a symbolic formula representing the condition where this rational function and f are the same.

If f1 = p1 / q1, f2 = p2 / q2, then f1 == f2 <=> p1 * q2 == p2 * q1

SetIndeterminates()

void SetIndeterminates

(

const Variables &

new_indeterminates

)

Sets the indeterminates of the numerator and denominator polynomials.

ToExpression()

Expression ToExpression ( ) const

nodiscard

Returns an equivalent symbolic expression of this rational function.

Friends And Related Symbol Documentation

operator-

RationalFunction operator- ( RationalFunction f )

friend

Unary minus operation for rational function.

if f(x) = p(x) / q(x), then -f(x) = (-p(x)) / q(x)

operator<<

std::ostream & operator<< ( std::ostream & , const RationalFunction & f )

friend

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

• drake/common/symbolic/rational_function.h