Provides the differential type for differentiation of expression trees. More...

#include <differential.hpp>

Inheritance diagram for bertini::node::Differential:

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

int	Degree (VariableGroup const &vars) const override

std::shared_ptr< Node >	Differentiate (std::shared_ptr< Variable > const &v=nullptr) const override

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

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

bool	IsHomogeneous (VariableGroup const &vars) const override

std::vector< int >	MultiDegree (VariableGroup const &vars) const override

void	precision (unsigned int prec) const override

void	print (std::ostream &target) const override

void	Reset () const override

Public Member Functions inherited from bertini::node::NamedSymbol
const std::string &	name () const

void	name (const std::string &new_name)

	NamedSymbol (const std::string &new_name)

void	print (std::ostream &target) const override

Public Member Functions inherited from bertini::node::Symbol
unsigned	EliminateOnes () override
	A transform function, which eliminates nodes from the tree.

unsigned	EliminateZeros () override
	A transform function, which eliminates nodes from the tree.

Public Member Functions inherited from bertini::node::Node
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

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

bool	IsPolynomial (VariableGroup const &v) const

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

Protected Member Functions
void	FreshEval_d (dbl &evaluation_value, std::shared_ptr< Variable > const &diff_variable) const override

dbl	FreshEval_d (std::shared_ptr< Variable > const &diff_variable) const override

void	FreshEval_mp (mpfr_complex &evaluation_value, std::shared_ptr< Variable > const &diff_variable) const override

mpfr_complex	FreshEval_mp (std::shared_ptr< Variable > const &diff_variable) const override

Protected Member Functions inherited from bertini::node::Node
void	ResetStoredValues () const

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

Provides the differential type for differentiation of expression trees.

This class represents differentials. These are produced in the course of differentiation of a non-constant expression tree.

Member Function Documentation

◆ Degree() [1/2]

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

overridevirtual

Compute the degree with respect to a single variable. For differentials, the degree is 0.

Implements bertini::node::Node.

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◆ Degree() [2/2]

int bertini::node::Differential::Degree ( VariableGroup const & vars ) const

overridevirtual

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.

Implements bertini::node::Node.

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◆ Differentiate()

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

overridevirtual

Differentiates a number.

Implements bertini::node::Node.

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◆ FreshEval_d() [1/2]

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

overrideprotectedvirtual

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.

Implements bertini::node::Node.

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◆ FreshEval_d() [2/2]

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

overrideprotectedvirtual

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.

Implements bertini::node::Node.

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◆ FreshEval_mp() [1/2]

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

overrideprotectedvirtual

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.

Implements bertini::node::Node.

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◆ FreshEval_mp() [2/2]

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

overrideprotectedvirtual

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.

Implements bertini::node::Node.

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◆ Homogenize()

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

overridevirtual

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.

Implements bertini::node::Node.

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◆ IsHomogeneous() [1/2]

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

overridevirtual

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.

Implements bertini::node::Node.

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◆ IsHomogeneous() [2/2]

bool bertini::node::Differential::IsHomogeneous ( VariableGroup const & vars ) const

overridevirtual

Check for homogeneity, with respect to a variable group.

Implements bertini::node::Node.

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◆ MultiDegree()

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

overridevirtual

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.

Implements bertini::node::Node.

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◆ precision()

void bertini::node::Differential::precision ( unsigned int prec ) const

overridevirtual

Change the precision of this variable-precision tree node.

Parameters

prec	the number of digits to change precision to.

Implements bertini::node::Node.

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◆ print()

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

overridevirtual

Virtual method for printing Nodes to arbitrary output streams.

Implements bertini::node::Node.

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◆ Reset()

void bertini::node::Differential::Reset ( ) const

overridevirtual

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

Implements bertini::node::Node.

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

differential.hpp
differential.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Degree() [1/2]

◆ Degree() [2/2]

◆ Differentiate()

◆ FreshEval_d() [1/2]

◆ FreshEval_d() [2/2]

◆ FreshEval_mp() [1/2]

◆ FreshEval_mp() [2/2]

◆ Homogenize()

◆ IsHomogeneous() [1/2]

◆ IsHomogeneous() [2/2]

◆ MultiDegree()

◆ precision()

◆ print()

◆ Reset()