The fundamental polynomial system class for Bertini2. More...

#include <system.hpp>

Inheritance diagram for bertini::System:

Public Member Functions
void	AddConstant (Fn const &C)

void	AddConstants (std::vector< Fn > const &C)

void	AddFunction (Fn const &F)

void	AddFunction (Nd const &F, std::string const &name="unnamed_function")

void	AddFunctions (std::vector< Fn > const &F)

void	AddHomVariableGroup (VariableGroup const &v)

void	AddImplicitParameter (Var const &v)

void	AddImplicitParameters (VariableGroup const &v)

void	AddParameter (Fn const &F)

void	AddParameters (std::vector< Fn > const &F)

void	AddPathVariable (Var const &v)

void	AddSubfunction (Fn const &F)

void	AddSubfunctions (std::vector< Fn > const &F)

void	AddUngroupedVariable (Var const &v)

void	AddUngroupedVariables (VariableGroup const &v)

void	AddVariableGroup (VariableGroup const &v)

VariableGroup const &	AffineVariableGroup (size_t index) const
	Get an affine variable group the class has defined.

template<typename T>
Vec< T >	DehomogenizePoint (Vec< T > const &x) const
	Dehomogenize a point, using the variable grouping / structure of the system.

void	Differentiate () const
	Compute and internally store the symbolic Jacobian of the system.

template<typename T>
Vec< T >	Eval () const
	Evaluate the system using the previously set variable (and time) values, creating vector of function values.

template<typename Derived>
Derived::PlainObject	Eval (const Eigen::MatrixBase< Derived > &variable_values) const
	Evaluate the system, provided the system has no path variable defined.

template<typename Derived, typename T>
Vec< T >	Eval (const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const

template<typename T>
void	EvalInPlace (Vec< T > &function_values) const
	Evaluate the system using the previously set variable (and time) values, in place.

template<typename T, typename Derived>
void	EvalInPlace (Vec< T > &function_values, const Eigen::MatrixBase< Derived > &variable_values) const
	Evaluate the system, provided the system has no path variable defined, in place.

template<typename Derived, typename T>
void	EvalInPlace (Vec< T > &function_values, const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const

auto	Function (unsigned index) const
	Get a function by its index.

auto	GetNaturalFunctions () const
	Get the functions.

bool	HavePathVariable () const

void	Homogenize ()

auto	HomVariableGroups () const

bool	IsHomogeneous () const

bool	IsPolynomial () const

template<typename T>
Mat< T >	Jacobian () const

template<typename Derived, typename T>
Mat< T >	Jacobian (const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const

template<typename T>
Mat< T >	Jacobian (const Vec< T > &variable_values) const

template<typename T>
void	JacobianInPlace (Mat< T > &J) const
	Evaluate the Jacobian matrix of the system, using the previous space and time values, in place.

template<typename Derived, typename T>
void	JacobianInPlace (Mat< T > &J, const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const

template<typename T>
void	JacobianInPlace (Mat< T > &J, const Vec< T > &variable_values) const

size_t	NumConstants () const

size_t	NumHomVariableGroups () const

size_t	NumHomVariables () const

size_t	NumImplicitParameters () const

size_t	NumNaturalFunctions () const

size_t	NumNaturalVariables () const

size_t	NumParameters () const

size_t	NumPatches () const

size_t	NumTotalFunctions () const

size_t	NumTotalVariableGroups () const

size_t	NumUngroupedVariables () const

size_t	NumVariableGroups () const

size_t	NumVariables () const

System &	operator= (const System &other)
	The assignment operator.

System &	operator= (System &&other)=default
	The move assignment operator.

unsigned	precision () const
	Get the current precision of a system.

void	precision (unsigned new_precision) const

void	Reset () const
	A complete reset of the system, so that all of functions, space derivatives, and time derivatives will all be re-evaluated.

void	ResetFunctions () const
	Force re-evaluation of the system next eval of functions. If something has changed in the system, call this.

void	ResetJacobian () const
	Force re-evaluation of the system next eval of Jacobians. If something has changed in the system, call this.

template<typename T>
void	SetImplicitParameters (Vec< T > new_values) const

template<typename T>
void	SetPathVariable (T const &new_value) const

template<typename T>
void	SetVariables (const Vec< T > &new_values) const

	System ()
	The default constructor for a system.

	System (std::string const &input)
	The copy operator, creates a system from a string using the Bertini parser for Bertini classic syntax.

	System (System &&other)
	The move copy operator.

	System (System const &other)
	The copy operator.

template<typename T>
Vec< T >	TimeDerivative () const
	Compute the time-derivative of a system.

template<typename Derived, typename T>
Vec< T >	TimeDerivative (const Eigen::MatrixBase< Derived > &variable_values) const
	Compute the time-derivative of a system.

template<typename Derived, typename T>
Vec< T >	TimeDerivative (const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const
	Compute the time-derivative of a system.

template<typename Derived, typename T>
void	TimeDerivativeInPlace (Vec< T > &ds_dt, const Eigen::MatrixBase< Derived > &variable_values, const T &path_variable_value) const
	Compute the time-derivative of a system.

auto	VariableGroups () const

std::vector< unsigned >	VariableGroupSizes () const
	Get the sizes of the variable groups, according to the current ordering.

VariableGroup	VariableOrdering () const

const VariableGroup &	Variables () const

Friends
void	swap (System &a, System &b)

Detailed Description

The fundamental polynomial system class for Bertini2.

Other System types are derived from this, but this class is not abstract.

Constructor & Destructor Documentation

◆ System() [1/4]

bertini::System::System ( )

inline

The default constructor for a system.

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◆ System() [2/4]

bertini::System::System ( std::string const & input )

inlineexplicit

The copy operator, creates a system from a string using the Bertini parser for Bertini classic syntax.

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◆ System() [3/4]

bertini::System::System ( System const & other )

The copy operator.

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◆ System() [4/4]

bertini::System::System ( System && other )

inline

The move copy operator.

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Member Function Documentation

◆ AddConstant()

void bertini::System::AddConstant ( Fn const & C )

Add a constant function to the system. Constants must not depend on anything which can vary – they're constant!

Parameters

C	The constant to add.

◆ AddConstants()

void bertini::System::AddConstants ( std::vector< Fn > const & C )

Add some constant functions to the system. Constants must not depend on anything which can vary – they're constant!

Parameters

C	The constants to add.

◆ AddFunction() [1/2]

void bertini::System::AddFunction ( Fn const & F )

Add a function to the system.

Parameters

F	The function to add.

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◆ AddFunction() [2/2]

void bertini::System::AddFunction	(	Nd const &	F,
		std::string const &	name = "unnamed_function" )

Add a function to the system.

Parameters

F	The function to add.
name	The name of the function

◆ AddFunctions()

void bertini::System::AddFunctions ( std::vector< Fn > const & F )

Add some functions to the system.

Parameters

F	The functions to add.

◆ AddHomVariableGroup()

void bertini::System::AddHomVariableGroup ( VariableGroup const & v )

Add a homogeneous (projective) variable group to the system. The system must be homogeneous with respect to this group, though this is not verified at the time of this call.

Parameters

v	The variable group to add.

◆ AddImplicitParameter()

void bertini::System::AddImplicitParameter ( Var const & v )

Add an implicit parameter to the system. Implicit parameters are advanced by the tracker akin to variable advancement.

Parameters

v	The implicit parameter to add.

◆ AddImplicitParameters()

void bertini::System::AddImplicitParameters ( VariableGroup const & v )

Add some implicit parameters to the system. Implicit parameters are advanced by the tracker akin to variable advancement.

Parameters

v	The implicit parameters to add.

◆ AddParameter()

void bertini::System::AddParameter ( Fn const & F )

Add an explicit parameter to the system. Explicit parameters should depend only on the path variable, though this is not checked in this function.

Parameters

F	The parameter to add.

◆ AddParameters()

void bertini::System::AddParameters ( std::vector< Fn > const & F )

Add some explicit parameters to the system. Explicit parameters should depend only on the path variable, though this is not checked in this function.

Parameters

F	The parameters to add.

◆ AddPathVariable()

void bertini::System::AddPathVariable ( Var const & v )

Add a variable as the Path Variable to a System. Will overwrite any previously declared path variable.

Parameters

v	The new path variable.

◆ AddSubfunction()

void bertini::System::AddSubfunction ( Fn const & F )

Add a subfunction to the system.

Tacks them onto the end of the system.

Parameters

F	The subfunction to add.

◆ AddSubfunctions()

void bertini::System::AddSubfunctions ( std::vector< Fn > const & F )

Add some subfunctions to the system.

Tacks them onto the end of the system.

Parameters

F	The subfunctions to add.

◆ AddUngroupedVariable()

void bertini::System::AddUngroupedVariable ( Var const & v )

Add variables to the system which are in neither a regular variable group, nor in a homogeneous group. This is likely used for user-defined systems, Classic userhomotopy: 1;.

Parameters

v	The variable to add.

◆ AddUngroupedVariables()

void bertini::System::AddUngroupedVariables ( VariableGroup const & v )

Add variables to the system which are in neither a regular variable group, nor in a homogeneous group. This is likely used for user-defined systems, Classic userhomotopy: 1;.

Parameters

v	The variables to add.

◆ AddVariableGroup()

void bertini::System::AddVariableGroup ( VariableGroup const & v )

Add a variable group to the system. The system may be homogenized with respect to this variable group, though this is not done at the time of this call.

Parameters

v	The variable group to add.

◆ AffineVariableGroup()

VariableGroup const & bertini::System::AffineVariableGroup ( size_t index ) const

inline

Get an affine variable group the class has defined.

It is up to you to ensure this group exists.

◆ DehomogenizePoint()

template<typename T>

Vec< T > bertini::System::DehomogenizePoint ( Vec< T > const & x ) const

inline

Dehomogenize a point, using the variable grouping / structure of the system.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime_error,if there is a mismatch between the number of variables in the input point, and the total number of var

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◆ Differentiate()

void bertini::System::Differentiate ( ) const

Compute and internally store the symbolic Jacobian of the system.

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◆ Eval() [1/3]

template<typename T>

Vec< T > bertini::System::Eval ( ) const

inline

Evaluate the system using the previously set variable (and time) values, creating vector of function values.

It is up to YOU to ensure that the system's variables (and path variable) has been set prior to this function call.

Returns: The function values of the system

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◆ Eval() [2/3]

template<typename Derived>

Derived::PlainObject bertini::System::Eval ( const Eigen::MatrixBase< Derived > & variable_values ) const

inline

Evaluate the system, provided the system has no path variable defined.

Causes the current variable values to be set in the system. Resets the function tree's stored numbers.

Exceptions

std::runtime_error,if a path variable IS defined, but you didn't pass it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values The values of the variables, for the evaluation.

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◆ Eval() [3/3]

template<typename Derived, typename T>

Vec< T > bertini::System::Eval	(	const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Evaluate the system, provided a path variable is defined for the system.

Exceptions

std::runtime_error,if a path variable is NOT defined, and you passed it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values	The values of the variables, for the evaluation.
path_variable_value	The current value of the path variable.

Todo: The Eval() function for systems has the unfortunate side effect of resetting constant functions. Modify the System class so that only certain parts of the tree get reset.

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◆ EvalInPlace() [1/3]

template<typename T>

void bertini::System::EvalInPlace ( Vec< T > & function_values ) const

inline

Evaluate the system using the previously set variable (and time) values, in place.

It is up to YOU to ensure that the system's variables (and path variable) has been set prior to this function call.

Returns: The function values of the system

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◆ EvalInPlace() [2/3]

template<typename T, typename Derived>

void bertini::System::EvalInPlace	(	Vec< T > &	function_values,
		const Eigen::MatrixBase< Derived > &	variable_values ) const

inline

Evaluate the system, provided the system has no path variable defined, in place.

Causes the current variable values to be set in the system. Resets the function tree's stored numbers.

Exceptions

std::runtime_error,if a path variable IS defined, but you didn't pass it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values The values of the variables, for the evaluation.

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◆ EvalInPlace() [3/3]

template<typename Derived, typename T>

void bertini::System::EvalInPlace	(	Vec< T > &	function_values,
		const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Evaluate the system, provided a path variable is defined for the system, in place.

Exceptions

std::runtime_error,if a path variable is NOT defined, and you passed it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values	The values of the variables, for the evaluation.
path_variable_value	The current value of the path variable.

Todo: The Eval() function for systems has the unfortunate side effect of resetting constant functions. Modify the System class so that only certain parts of the tree get reset.

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◆ Function()

auto bertini::System::Function ( unsigned index ) const

inline

Get a function by its index.

This is just as scary as you think it is. It is up to you to make sure the function at this index exists.

◆ GetNaturalFunctions()

auto bertini::System::GetNaturalFunctions ( ) const

inline

Get the functions.

◆ HavePathVariable()

bool bertini::System::HavePathVariable ( ) const

Query whether a path variable is set for this system

Returns: true if have a path variable, false if not.

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◆ Homogenize()

void bertini::System::Homogenize ( )

Homogenize the system, adding new homogenizing variables for each VariableGroup defined for the system.

Exceptions

std::runtime_error,if the system is not polynomial, has a mismatch on the number of homogenizing variables and the number of variable groups (this would result from a partially homogenized system), or the homogenizing variable names somehow get screwed up by having duplicates.

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◆ HomVariableGroups()

auto bertini::System::HomVariableGroups ( ) const

inline

Get the homogeneous (projective) variable groups in the problem.

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◆ IsHomogeneous()

bool bertini::System::IsHomogeneous ( ) const

Checks whether a system is homogeneous, overall. This means with respect to each variable group (including homogenizing variable if defined), homogeneous variable group, and ungrouped variables, if defined.

Exceptions

std::runtime_error,if the number of homogenizing variables does not match the number of variable_groups.

Returns: true if homogeneous, false if not

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◆ IsPolynomial()

bool bertini::System::IsPolynomial ( ) const

Checks whether a system is polynomial, overall. This means with respect to each variable group (including homogenizing variable if defined), homogeneous variable group, and ungrouped variables, if defined.

Exceptions

std::runtime_error,if the number of homogenizing variables does not match the number of variable_groups.

Returns: true if polynomial, false if not.

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◆ Jacobian() [1/3]

template<typename T>

Mat< T > bertini::System::Jacobian ( ) const

inline

Evaluate the Jacobian matrix of the system, using the previous space and time values.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

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◆ Jacobian() [2/3]

template<typename Derived, typename T>

Mat< T > bertini::System::Jacobian	(	const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Evaluate the Jacobian of the system, provided a path variable is defined for the system.

Exceptions

std::runtime_error,if a path variable is NOT defined, and you passed it a value. Also throws if the number of variables doesn't match.

Returns: The Jacobian matrix.

Parameters

variable_values	The values of the variables, for the evaluation.
path_variable_value	The current value of the path variable.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

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◆ Jacobian() [3/3]

template<typename T>

Mat< T > bertini::System::Jacobian ( const Vec< T > & variable_values ) const

inline

Evaluate the Jacobian matrix of the system, provided the system has no path variable defined.

Exceptions

std::runtime_error,if a path variable IS defined, but you didn't pass it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values The values of the variables, for the evaluation.

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◆ JacobianInPlace() [1/3]

template<typename T>

void bertini::System::JacobianInPlace ( Mat< T > & J ) const

inline

Evaluate the Jacobian matrix of the system, using the previous space and time values, in place.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

This is analogous to J = sys.JacobianInPlace();

The input matrix must have the correct size already

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◆ JacobianInPlace() [2/3]

template<typename Derived, typename T>

void bertini::System::JacobianInPlace	(	Mat< T > &	J,
		const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Evaluate the Jacobian of the system, provided a path variable is defined for the system, in place.

Exceptions

std::runtime_error,if a path variable is NOT defined, and you passed it a value. Also throws if the number of variables doesn't match.

Returns: The Jacobian matrix.

Parameters

variable_values	The values of the variables, for the evaluation.
path_variable_value	The current value of the path variable.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

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◆ JacobianInPlace() [3/3]

template<typename T>

void bertini::System::JacobianInPlace	(	Mat< T > &	J,
		const Vec< T > &	variable_values ) const

inline

Evaluate the Jacobian matrix of the system, provided the system has no path variable defined.

Exceptions

std::runtime_error,if a path variable IS defined, but you didn't pass it a value. Also throws if the number of variables doesn't match.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

variable_values The values of the variables, for the evaluation.

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◆ NumConstants()

size_t bertini::System::NumConstants ( ) const

Get the number of constants in this system

◆ NumHomVariableGroups()

size_t bertini::System::NumHomVariableGroups ( ) const

Get the number of homogeneous variable groups in the system

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◆ NumHomVariables()

size_t bertini::System::NumHomVariables ( ) const

Get the number of homogenizing variables in this system

◆ NumImplicitParameters()

size_t bertini::System::NumImplicitParameters ( ) const

Get the number of implicit parameters in this system

◆ NumNaturalFunctions()

size_t bertini::System::NumNaturalFunctions ( ) const

Get the number of functions in this system, excluding patches.

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◆ NumNaturalVariables()

size_t bertini::System::NumNaturalVariables ( ) const

Get the number of variables in this system, NOT including homogenizing variables.

◆ NumParameters()

size_t bertini::System::NumParameters ( ) const

Get the number of explicit parameters in this system

◆ NumPatches()

size_t bertini::System::NumPatches ( ) const

inline

Get the number of patches in this system.

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◆ NumTotalFunctions()

size_t bertini::System::NumTotalFunctions ( ) const

Get the total number of functions, including patches

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◆ NumTotalVariableGroups()

size_t bertini::System::NumTotalVariableGroups ( ) const

Get the total number of variable groups in the system, including both affine and homogenous. Ignores the ungrouped variables, because they are not in any group.

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◆ NumUngroupedVariables()

size_t bertini::System::NumUngroupedVariables ( ) const

get the number of variables which are ungrouped.

◆ NumVariableGroups()

size_t bertini::System::NumVariableGroups ( ) const

Get the number of affine variable groups in the system

◆ NumVariables()

size_t bertini::System::NumVariables ( ) const

Get the total number of variables in this system, including homogenizing variables.

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◆ operator=() [1/2]

System & bertini::System::operator= ( const System & other )

The assignment operator.

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◆ operator=() [2/2]

System & bertini::System::operator= ( System && other )

default

The move assignment operator.

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◆ precision() [1/2]

unsigned bertini::System::precision ( ) const

inline

Get the current precision of a system.

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◆ precision() [2/2]

void bertini::System::precision ( unsigned new_precision ) const

Change the precision of the entire system's functions, subfunctions, and all other nodes.

Parameters

new_precision The new precision, in digits, to work in. This only affects the mpfr_complex types, not double. To use low-precision (doubles), use that number type in the templated functions.

◆ Reset()

void bertini::System::Reset ( ) const

inline

A complete reset of the system, so that all of functions, space derivatives, and time derivatives will all be re-evaluated.

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◆ ResetFunctions()

void bertini::System::ResetFunctions ( ) const

inline

Force re-evaluation of the system next eval of functions. If something has changed in the system, call this.

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◆ ResetJacobian()

void bertini::System::ResetJacobian ( ) const

inline

Force re-evaluation of the system next eval of Jacobians. If something has changed in the system, call this.

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◆ SetImplicitParameters()

template<typename T>

void bertini::System::SetImplicitParameters ( Vec< T > new_values ) const

inline

For a system with implicitly defined parameters, set their values. The values are determined externally to the system, and are tracked along with the variables.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

new_values The new updated values for the implicit parameters.

◆ SetPathVariable()

template<typename T>

void bertini::System::SetPathVariable ( T const & new_value ) const

inline

Set the current value of the path variable.

Exceptions

std::runtime_error,if a path variable is not defined.

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Parameters

new_value The new updated values for the path variable.

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◆ SetVariables()

template<typename T>

void bertini::System::SetVariables ( const Vec< T > & new_values ) const

inline

Set the values of the variables to be equal to the input values

Template Parameters

T	the number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime_error if the number of variables doesn't match.

The ordering of the variables matters.

The AffHomUng ordering is 1) variable groups, with homogenizing variable first. 2) homogeneous variable groups. 3) ungrouped variables. The FIFO ordering uses the order in which the variable groups were added.

The path variable is not considered a variable for this operation. It is set separately.

Parameters

new_values The new updated values for the variables.

See also: SetPathVariable; Variables

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◆ TimeDerivative() [1/3]

template<typename T>

Vec< T > bertini::System::TimeDerivative ( ) const

inline

Compute the time-derivative of a system.

If \(S\) is the system, and \(t\) is the path variable this computes \(\frac{dS}{dt}\).

Template Parameters

T	The number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime error if the system does not have a path variable defined.

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◆ TimeDerivative() [2/3]

template<typename Derived, typename T>

Vec< T > bertini::System::TimeDerivative ( const Eigen::MatrixBase< Derived > & variable_values ) const

inline

Compute the time-derivative of a system.

If \(S\) is the system, and \(t\) is the path variable this computes \(\frac{dS}{dt}\).

Template Parameters

T	The number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime error if the system does not have a path variable defined.

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◆ TimeDerivative() [3/3]

template<typename Derived, typename T>

Vec< T > bertini::System::TimeDerivative	(	const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Compute the time-derivative of a system.

If \(S\) is the system, and \(t\) is the path variable this computes \(\frac{dS}{dt}\).

Template Parameters

T	The number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime error if the system does not have a path variable defined.

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◆ TimeDerivativeInPlace()

template<typename Derived, typename T>

void bertini::System::TimeDerivativeInPlace	(	Vec< T > &	ds_dt,
		const Eigen::MatrixBase< Derived > &	variable_values,
		const T &	path_variable_value ) const

inline

Compute the time-derivative of a system.

If \(S\) is the system, and \(t\) is the path variable this computes \(\frac{dS}{dt}\).

Template Parameters

T	The number-type for return. Probably dbl=std::complex<double>, or mpfr_complex=bertini::mpfr_complex.

Exceptions

std::runtime error if the system does not have a path variable defined.

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◆ VariableGroups()

auto bertini::System::VariableGroups ( ) const

inline

Get the affine variable groups in the problem.

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◆ VariableGroupSizes()

std::vector< unsigned > bertini::System::VariableGroupSizes ( ) const

inline

Get the sizes of the variable groups, according to the current ordering.

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◆ VariableOrdering()

VariableGroup bertini::System::VariableOrdering ( ) const

Order the variables, by the order in which the groups were added.

This function returns the variables in First In First Out (FIFO) ordering.

Homogenizing variables precede affine variable groups, so that groups always are grouped together.

This function freshly constructs the ordering every time. If you want to use the cached value,

See also: Variables.

Exceptions

std::runtime_error,if there is a mismatch between the number of homogenizing variables and the number of variable_groups. This would happen if a system is homogenized, and then more stuff is added to it.

◆ Variables()

const VariableGroup & bertini::System::Variables ( ) const

Get the variables in the problem.

Returns the variable ordering, constructing it if necessary.

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Friends And Related Symbol Documentation

◆ swap

void swap	(	System &	a,
		System &	b )

friend

The free swap function for systems.

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

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ System() [1/4]

◆ System() [2/4]

◆ System() [3/4]

◆ System() [4/4]

Member Function Documentation

◆ AddConstant()

◆ AddConstants()

◆ AddFunction() [1/2]

◆ AddFunction() [2/2]

◆ AddFunctions()

◆ AddHomVariableGroup()

◆ AddImplicitParameter()

◆ AddImplicitParameters()

◆ AddParameter()

◆ AddParameters()

◆ AddPathVariable()

◆ AddSubfunction()

◆ AddSubfunctions()

◆ AddUngroupedVariable()

◆ AddUngroupedVariables()

◆ AddVariableGroup()

◆ AffineVariableGroup()

◆ DehomogenizePoint()

◆ Differentiate()

◆ Eval() [1/3]

◆ Eval() [2/3]

◆ Eval() [3/3]

◆ EvalInPlace() [1/3]

◆ EvalInPlace() [2/3]

◆ EvalInPlace() [3/3]

◆ Function()

◆ GetNaturalFunctions()

◆ HavePathVariable()

◆ Homogenize()

◆ HomVariableGroups()

◆ IsHomogeneous()

◆ IsPolynomial()

◆ Jacobian() [1/3]

◆ Jacobian() [2/3]

◆ Jacobian() [3/3]

◆ JacobianInPlace() [1/3]

◆ JacobianInPlace() [2/3]

◆ JacobianInPlace() [3/3]

◆ NumConstants()

◆ NumHomVariableGroups()

◆ NumHomVariables()

◆ NumImplicitParameters()

◆ NumNaturalFunctions()

◆ NumNaturalVariables()

◆ NumParameters()

◆ NumPatches()

◆ NumTotalFunctions()

◆ NumTotalVariableGroups()

◆ NumUngroupedVariables()

◆ NumVariableGroups()

◆ NumVariables()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ precision() [1/2]

◆ precision() [2/2]

◆ Reset()

◆ ResetFunctions()

◆ ResetJacobian()

◆ SetImplicitParameters()

◆ SetPathVariable()

◆ SetVariables()

◆ TimeDerivative() [1/3]

◆ TimeDerivative() [2/3]

◆ TimeDerivative() [3/3]

◆ TimeDerivativeInPlace()

◆ VariableGroups()

◆ VariableGroupSizes()

◆ VariableOrdering()

◆ Variables()

Friends And Related Symbol Documentation

◆ swap