Abstract base class for the Bertini hybrid-precision (double-multiple) expression tree. More...

#include <node.hpp>

Inheritance diagram for bertini::node::Node:

Collaboration diagram for bertini::node::Node:

Public Member Functions
virtual int	Degree (std::shared_ptr< Variable > const &v=nullptr) const =0

virtual int	Degree (VariableGroup const &vars) const =0

virtual std::shared_ptr< Node >	Differentiate (std::shared_ptr< Variable > const &v=nullptr) const =0
	Compute the derivative with respect to a single variable.

virtual unsigned	EliminateOnes ()=0
	A transform function, which eliminates nodes from the tree.

virtual unsigned	EliminateZeros ()=0
	A transform function, which eliminates nodes from the tree.

template<typename T>
T	Eval (std::shared_ptr< Variable > const &diff_variable=nullptr) const

template<typename T>
void	EvalInPlace (T &eval_value, std::shared_ptr< Variable > const &diff_variable=nullptr) const

virtual void	Homogenize (VariableGroup const &vars, std::shared_ptr< Variable > const &homvar)=0

virtual bool	IsHomogeneous (std::shared_ptr< Variable > const &v=nullptr) const =0

virtual bool	IsHomogeneous (VariableGroup const &vars) const =0

bool	IsPolynomial (std::shared_ptr< Variable > const &v=nullptr) const

bool	IsPolynomial (VariableGroup const &v) const

virtual std::vector< int >	MultiDegree (VariableGroup const &vars) const =0

virtual void	precision (unsigned int prec) const =0

virtual void	print (std::ostream &target) const =0

virtual unsigned	ReduceDepth ()
	A mutating function which finds ways to reduce the depth of the tree.

virtual void	Reset () const =0

Protected Member Functions
virtual void	FreshEval_d (dbl &evaluation_value, std::shared_ptr< Variable > const &) const =0

virtual dbl	FreshEval_d (std::shared_ptr< Variable > const &) const =0

virtual void	FreshEval_mp (mpfr_complex &evaluation_value, std::shared_ptr< Variable > const &) const =0

virtual mpfr_complex	FreshEval_mp (std::shared_ptr< Variable > const &) const =0

void	ResetStoredValues () const

Friends
std::ostream &	operator<< (std::ostream &out, const Node &N)

Additional Inherited Members
Static Protected Member Functions inherited from bertini::VisitableBase< RetT, CatchAll >
template<typename T>
static VisitReturnType	AcceptBase (T &visited, VisitorBase &guest)
	Abstract method for how to accept a visitor.

Detailed Description

Abstract base class for the Bertini hybrid-precision (double-multiple) expression tree.

An interface for all nodes in a function tree, and for a function object as well. Almost all methods that will be called on a node must be declared in this class. The main evaluation method is defined in this class.

Bertini function trees are created using std::shared_ptr's to Node base class, generally.

Member Function Documentation

◆ Degree() [1/2]

virtual int bertini::node::Node::Degree ( std::shared_ptr< Variable > const & v = nullptr ) const

pure virtual

Compute the degree, optionally with respect to a single variable.

Parameters

v	Shared pointer to variable with respect to which you want to compute the degree of the Node.

Returns: The degree. Will be negative if the Node is non-polynomial.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::ExpOperator, bertini::node::IntegerPowerOperator, bertini::node::LinearProduct, bertini::node::LogOperator, bertini::node::MultOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SqrtOperator, bertini::node::SumOperator, bertini::node::TrigOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ Degree() [2/2]

virtual int bertini::node::Node::Degree ( VariableGroup const & vars ) const

pure virtual

Compute the overall degree with respect to a variable group.

Parameters

vars	A group of variables.

Returns: The degree. Will be negative if the Node is non-polynomial.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::LinearProduct, bertini::node::MultOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SumOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ Differentiate()

virtual std::shared_ptr< Node > bertini::node::Node::Differentiate ( std::shared_ptr< Variable > const & v = nullptr ) const

pure virtual

Compute the derivative with respect to a single variable.

Virtual method for differentiating the node. If no variable is passed, produces a Jacobian tree when all is said and done, which is used for evaluating the Jacobian.

Returns: The result of differentiation. Jacobian or regular Node depending on what you passed in.

◆ EliminateOnes()

virtual unsigned bertini::node::Node::EliminateOnes ( )

pure virtual

A transform function, which eliminates nodes from the tree.

A better implementation of this would use a generic Transform. If you know how to do this, please rewrite the Nodes so they can transform to our whim, and submit a PR.

Returns: The number of nodes eliminated

See also: EliminateZeros

Implemented in bertini::node::ArcCosOperator, bertini::node::ArcSinOperator, bertini::node::ArcTanOperator, bertini::node::CosOperator, bertini::node::ExpOperator, bertini::node::IntegerPowerOperator, bertini::node::LinearProduct, bertini::node::LogOperator, bertini::node::MultOperator, bertini::node::NegateOperator, bertini::node::PowerOperator, bertini::node::SinOperator, bertini::node::SqrtOperator, bertini::node::SumOperator, bertini::node::Symbol, and bertini::node::TanOperator.

◆ EliminateZeros()

virtual unsigned bertini::node::Node::EliminateZeros ( )

pure virtual

A transform function, which eliminates nodes from the tree.

A better implementation of this would use a generic Transform. If you know how to do this, please rewrite the Nodes so they can transform to our whim, and submit a PR.

Returns: The number of nodes eliminated

See also: EliminateOnes

Implemented in bertini::node::LinearProduct, bertini::node::NegateOperator, bertini::node::SqrtOperator, bertini::node::SumOperator, and bertini::node::Symbol.

◆ Eval()

template<typename T>

T bertini::node::Node::Eval ( std::shared_ptr< Variable > const & diff_variable = nullptr ) const

inline

Evaluate the node. If flag false, just return value, if flag true run the specific FreshEval of the node, then set flag to false.

Template type is type of value you want returned.

Returns: The value of the node.

Template Parameters

T	The number type for return. Must be one of the types stored in the Node class, currently dbl and mpfr_complex.

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◆ EvalInPlace()

template<typename T>

void bertini::node::Node::EvalInPlace	(	T &	eval_value,
		std::shared_ptr< Variable > const &	diff_variable = nullptr ) const

Evaluate the node in place. If flag false, just return value, if flag true run the specific FreshEval of the node, then set flag to false.

Template type is type of value you want returned.

Returns: The value of the node.

Template Parameters

T	The number type for return. Must be one of the types stored in the Node class, currently dbl and mpfr_complex.

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◆ FreshEval_d() [1/2]

virtual void bertini::node::Node::FreshEval_d	(	dbl &	evaluation_value,
		std::shared_ptr< Variable > const &	) const

protectedpure virtual

Overridden code for specific node types, for how to evaluate themselves. Called from the wrapper EvalInPlace<>() call from Node, if so required (by resetting, etc).

If we had the ability to use template virtual functions, we would have. However, this is impossible with current C++ without using experimental libraries, so we have two copies – because there are two number types for Nodes, dbl and mpfr_complex.

◆ FreshEval_d() [2/2]

virtual dbl bertini::node::Node::FreshEval_d ( std::shared_ptr< Variable > const & ) const

protectedpure virtual

Overridden code for specific node types, for how to evaluate themselves. Called from the wrapper Eval<>() call from Node, if so required (by resetting, etc).

If we had the ability to use template virtual functions, we would have. However, this is impossible with current C++ without using experimental libraries, so we have two copies – because there are two number types for Nodes, dbl and mpfr_complex.

◆ FreshEval_mp() [1/2]

virtual void bertini::node::Node::FreshEval_mp	(	mpfr_complex &	evaluation_value,
		std::shared_ptr< Variable > const &	) const

protectedpure virtual

Overridden code for specific node types, for how to evaluate themselves. Called from the wrapper Eval<>() call from Node, if so required (by resetting, etc).

If we had the ability to use template virtual functions, we would have. However, this is impossible with current C++ without using experimental libraries, so we have two copies – because there are two number types for Nodes, dbl and mpfr_complex.

◆ FreshEval_mp() [2/2]

virtual mpfr_complex bertini::node::Node::FreshEval_mp ( std::shared_ptr< Variable > const & ) const

protectedpure virtual

Overridden code for specific node types, for how to evaluate themselves. Called from the wrapper Eval<>() call from Node, if so required (by resetting, etc).

If we had the ability to use template virtual functions, we would have. However, this is impossible with current C++ without using experimental libraries, so we have two copies – because there are two number types for Nodes, dbl and mpfr_complex.

◆ Homogenize()

virtual void bertini::node::Node::Homogenize	(	VariableGroup const &	vars,
		std::shared_ptr< Variable > const &	homvar )

pure virtual

Homogenize a tree, inputting a variable group holding the non-homogeneous variables, and the new homogenizing variable. The homvar may be an element of the variable group, that's perfectly ok.

Parameters

homvar	The homogenizing variable, which is multiplied against terms with degree deficiency with repect to other terms.
vars	A group of variables, with respect to which you wish to homogenize.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::LinearProduct, bertini::node::MultOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SumOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ IsHomogeneous() [1/2]

virtual bool bertini::node::Node::IsHomogeneous ( std::shared_ptr< Variable > const & v = nullptr ) const

pure virtual

Check for homogeneity, absolutely with respect to all variables, including path variables and all other variable types, or with respect to a single varaible, if passed.

Returns: True if it is homogeneous, false if not.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::IntegerPowerOperator, bertini::node::LinearProduct, bertini::node::MultOperator, bertini::node::NegateOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SumOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ IsHomogeneous() [2/2]

virtual bool bertini::node::Node::IsHomogeneous ( VariableGroup const & vars ) const

pure virtual

Check for homogeneity, with respect to a variable group.

Returns: True if it is homogeneous, false if not.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::IntegerPowerOperator, bertini::node::LinearProduct, bertini::node::MultOperator, bertini::node::NegateOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SumOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ IsPolynomial() [1/2]

bool bertini::node::Node::IsPolynomial ( std::shared_ptr< Variable > const & v = nullptr ) const

Check if a Node is polynomial – it has degree at least 0. Negative degrees indicate non-polynomial.

Returns: True if it is polynomial, false if not.

◆ IsPolynomial() [2/2]

bool bertini::node::Node::IsPolynomial ( VariableGroup const & v ) const

Check if a Node is polynomial – it has degree at least 0. Negative degrees indicate non-polynomial.

Returns: True if it is polynomial, false if not.

◆ MultiDegree()

virtual std::vector< int > bertini::node::Node::MultiDegree ( VariableGroup const & vars ) const

pure virtual

Compute the multidegree with respect to a variable group. This is for homogenization, and testing for homogeneity.

Returns: A vector containing the degrees. Negative entries indicate non-polynomiality.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::LinearProduct, bertini::node::MultOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::SumOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ precision()

virtual void bertini::node::Node::precision ( unsigned int prec ) const

pure virtual

Change the precision of this variable-precision tree node.

Parameters

prec	the number of digits to change precision to.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::LinearProduct, bertini::node::NaryOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

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◆ print()

virtual void bertini::node::Node::print ( std::ostream & target ) const

pure virtual

Virtual method for printing Nodes to arbitrary output streams.

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◆ ReduceDepth()

virtual unsigned bertini::node::Node::ReduceDepth ( )

virtual

A mutating function which finds ways to reduce the depth of the tree.

Note: The default implementation is empty, and does literally nothing.

Reimplemented in bertini::node::MultOperator, and bertini::node::SumOperator.

◆ Reset()

virtual void bertini::node::Node::Reset ( ) const

pure virtual

Tells code to run a fresh eval on node next time.

Implemented in bertini::node::Differential, bertini::node::DiffLinear, bertini::node::LinearProduct, bertini::node::NaryOperator, bertini::node::Number, bertini::node::PowerOperator, bertini::node::UnaryOperator, and bertini::node::Variable.

◆ ResetStoredValues()

void bertini::node::Node::ResetStoredValues ( ) const

protected

Set the stored values for the Node to indicate a fresh eval on the next pass. This is so that Nodes which are referred to more than once, are only evaluated once. The first evaluation is fresh, and then the indicator for fresh/stored is set to stored. Subsequent evaluation calls simply return the stored number.

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Friends And Related Symbol Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		const Node &	N )

friend

a single layer of indirection, though which to call the overridden virtual print() method which must be defined for each non-abstract Node type.

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

node.hpp

Public Member Functions

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Degree() [1/2]

◆ Degree() [2/2]

◆ Differentiate()

◆ EliminateOnes()

◆ EliminateZeros()

◆ Eval()

◆ EvalInPlace()

◆ FreshEval_d() [1/2]

◆ FreshEval_d() [2/2]

◆ FreshEval_mp() [1/2]

◆ FreshEval_mp() [2/2]

◆ Homogenize()

◆ IsHomogeneous() [1/2]

◆ IsHomogeneous() [2/2]

◆ IsPolynomial() [1/2]

◆ IsPolynomial() [2/2]

◆ MultiDegree()

◆ precision()

◆ print()

◆ ReduceDepth()

◆ Reset()

◆ ResetStoredValues()

Friends And Related Symbol Documentation

◆ operator<<