Oasis::Expression Class Reference

An expression. More...

#include <Oasis/Expression.hpp>

Inheritance diagram for Oasis::Expression:

Public Member Functions
virtual auto	Copy () const -> std::unique_ptr< Expression >=0
	Copies this expression.
virtual auto	Differentiate (const Expression &) const -> std::unique_ptr< Expression >
	Tries to differentiate this function.
virtual auto	Equals (const Expression &other) const -> bool=0
	Compares this expression to another expression for equality.
auto	FindZeros () const -> std::vector< std::unique_ptr< Expression > >
	The FindZeros function finds all rational real zeros, and up to 2 irrational/complex zeros of a polynomial.
virtual auto	GetCategory () const -> uint32_t
	Gets the category of this expression.
virtual auto	GetType () const -> ExpressionType
	Gets the type of this expression.
virtual auto	Generalize () const -> std::unique_ptr< Expression >
	Converts this expression to a more general expression.
virtual auto	Integrate (const Expression &) const -> std::unique_ptr< Expression >
	Attempts to integrate this expression using integration rules.
virtual auto	IntegrateWithBounds (const Expression &, const Expression &, const Expression &) -> std::unique_ptr< Expression >
	Attempts to integrate this expression using integration rules.
template<IExpression T>
bool	Is () const
	Gets whether this expression is of a specific type.
template<template< typename > typename T>
bool	Is () const
template<template< typename, typename > typename T>
bool	Is () const
virtual auto	Simplify () const -> std::unique_ptr< Expression >
	Simplifies this expression.
virtual auto	StructurallyEquivalent (const Expression &other) const -> bool=0
	Checks whether this expression is structurally equivalent to another expression.
virtual auto	Substitute (const Expression &var, const Expression &val) -> std::unique_ptr< Expression >=0
virtual void	Serialize (SerializationVisitor &visitor) const =0
	This function serializes the expression object.
virtual	~Expression ()=default

Detailed Description

An expression.

Expressions are a tree-like structure that represent mathematical expressions. They can be evaluated, simplified, and compared for equality. They are immutable, and all operations on them return a new expression.

Constructor & Destructor Documentation

~Expression()

virtual Oasis::Expression::~Expression ( )

virtualdefault

Member Function Documentation

Copy()

virtual auto Oasis::Expression::Copy ( ) const -> std::unique_ptr< Expression >

pure virtual

Copies this expression.

Returns

A copy of this expression.

Implemented in Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::BoundedUnaryExpression< DerivedT, OperandT, LowerBoundT, UpperBoundT >, Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, Oasis::LeafExpression< Variable >, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, and Oasis::UnaryExpression< Negate, OperandT >.

Differentiate()

auto Oasis::Expression::Differentiate ( const Expression & ) const -> std::unique_ptr<Expression>

virtual

Tries to differentiate this function.

Returns

the differentiated expression.

Reimplemented in Oasis::Matrix, Oasis::Real, Oasis::Variable, Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::BoundedUnaryExpression< DerivedT, OperandT, LowerBoundT, UpperBoundT >, Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, Oasis::LeafExpression< Variable >, Oasis::Magnitude< OperandT >, and Oasis::Negate< OperandT >.

Equals()

virtual auto Oasis::Expression::Equals ( const Expression & other ) const -> bool

pure virtual

Compares this expression to another expression for equality.

Two expressions are equal if they are structurally equivalent and have the same value. While this method considers the associativity and commutativity of expressions, it does not simplify the expressions before comparing them. For example, Add<Real>(Real(1), Real(2)) and Add<Real>(Real(2), Real(1)) are not equal, despite being structurally equivalent.

Parameters

other

The other expression.

Returns

Whether the two expressions are equal.

Implemented in Oasis::Undefined, Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::BoundedUnaryExpression< DerivedT, OperandT, LowerBoundT, UpperBoundT >, Oasis::EulerNumber, Oasis::Imaginary, Oasis::Matrix, Oasis::Pi, Oasis::Real, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, Oasis::UnaryExpression< Negate, OperandT >, and Oasis::Variable.

FindZeros()

auto Oasis::Expression::FindZeros

(

)

const -> std::vector<std::unique_ptr<Expression>>

The FindZeros function finds all rational real zeros, and up to 2 irrational/complex zeros of a polynomial.

The FindZeros function finds all rational zeros of a polynomial.

Currently assumes an expression of the form a+bx+cx^2+dx^3+... where a, b, c, d are a integers.

Template Parameters

origonalExpresion

The expression for which all the factors will be found.

Generalize()

auto Oasis::Expression::Generalize ( ) const -> std::unique_ptr<Expression>

virtual

Converts this expression to a more general expression.

Some expressions may explicitly specify the type of their operands. For example, a Divide<Real> expression may only accept Real operands. This function converts the expression to a more general expression, such as Divide<Expression>, which accepts any expression as an operand.

Returns

The generalized expression.

Reimplemented in Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, and Oasis::UnaryExpression< Negate, OperandT >.

GetCategory()

auto Oasis::Expression::GetCategory ( ) const -> uint32_t

virtual

Gets the category of this expression.

Returns

The category of this expression.

GetType()

auto Oasis::Expression::GetType ( ) const -> ExpressionType

virtual

Gets the type of this expression.

Returns

The type of this expression.

Integrate()

auto Oasis::Expression::Integrate ( const Expression & variable ) const -> std::unique_ptr<Expression>

virtual

Attempts to integrate this expression using integration rules.

Returns

An indefinite integral of the expression added to a constant

Reimplemented in Oasis::Magnitude< OperandT >, Oasis::Matrix, Oasis::Real, Oasis::Variable, Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, and Oasis::LeafExpression< Variable >.

IntegrateWithBounds()

auto Oasis::Expression::IntegrateWithBounds ( const Expression & variable, const Expression & , const Expression &  ) -> std::unique_ptr<Expression>

virtual

Attempts to integrate this expression using integration rules.

Returns

A solved definite integral of the expression

Is() [1/3]

template<IExpression T>

bool Oasis::Expression::Is ( ) const

inline

Gets whether this expression is of a specific type.

Template Parameters

T	The type to check against.

Returns

true if this expression is of type T, false otherwise.

Is() [2/3]

template<template< typename > typename T>

bool Oasis::Expression::Is ( ) const

inline

Is() [3/3]

template<template< typename, typename > typename T>

bool Oasis::Expression::Is ( ) const

inline

Serialize()

virtual void Oasis::Expression::Serialize ( SerializationVisitor & visitor ) const

pure virtual

This function serializes the expression object.

Parameters

visitor

The serializer class object to write the Expression data.

Implemented in Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::BoundedUnaryExpression< DerivedT, OperandT, LowerBoundT, UpperBoundT >, Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, Oasis::LeafExpression< Variable >, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, and Oasis::UnaryExpression< Negate, OperandT >.

Simplify()

auto Oasis::Expression::Simplify ( ) const -> std::unique_ptr<Expression>

virtual

Simplifies this expression.

Returns

The simplified expression.

Reimplemented in Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::Magnitude< OperandT >, and Oasis::Negate< OperandT >.

StructurallyEquivalent()

virtual auto Oasis::Expression::StructurallyEquivalent ( const Expression & other ) const -> bool

pure virtual

Checks whether this expression is structurally equivalent to another expression.

Two expressions are structurally equivalent if the share the same tree structure. For example, Add<Real>(Real(1), Real(2)) and Add<Real>(Real(2), Real(1)) are structurally equivalent despite having different values.

Parameters

other

The other expression.

Returns

Whether the two expressions are structurally equivalent.

Implemented in Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, Oasis::LeafExpression< Variable >, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, and Oasis::UnaryExpression< Negate, OperandT >.

Substitute()

virtual auto Oasis::Expression::Substitute ( const Expression & var, const Expression & val ) -> std::unique_ptr< Expression >

pure virtual

Implemented in Oasis::LeafExpression< DerivedT >, Oasis::LeafExpression< EulerNumber >, Oasis::LeafExpression< Imaginary >, Oasis::LeafExpression< Matrix >, Oasis::LeafExpression< Pi >, Oasis::LeafExpression< Real >, Oasis::LeafExpression< Undefined >, Oasis::LeafExpression< Variable >, Oasis::BinaryExpression< DerivedT, MostSigOpT, LeastSigOpT >, Oasis::BinaryExpression< Add, Expression, Expression >, Oasis::BinaryExpression< Derivative, Expression, Expression >, Oasis::BinaryExpression< Divide, Expression, Expression >, Oasis::BinaryExpression< Exponent, Expression, Expression >, Oasis::BinaryExpression< Integral, Expression, Expression >, Oasis::BinaryExpression< Log, Expression, Expression >, Oasis::BinaryExpression< Multiply, Expression, Expression >, Oasis::BinaryExpression< Subtract, Expression, Expression >, Oasis::BoundedBinaryExpression< DerivedT, MostSigOpT, LeastSigOpT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< DefiniteIntegral, OperandT, VariableT, LowerBoundT, UpperBoundT >, Oasis::BoundedBinaryExpression< Summation, OperandT, IncrementingVarT, LowerBoundT, UpperBoundT >, Oasis::BoundedUnaryExpression< DerivedT, OperandT, LowerBoundT, UpperBoundT >, Oasis::UnaryExpression< DerivedT, OperandT >, Oasis::UnaryExpression< Magnitude, OperandT >, Oasis::UnaryExpression< Negate, OperandT >, and Oasis::Variable.

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

• include/Oasis/Expression.hpp
• src/Expression.cpp