Series class. More...

#include <piranha/series.hpp>

Inheritance diagram for piranha::series< Cf, Key, Derived >:

Collaboration diagram for piranha::series< Cf, Key, Derived >:

Public Types
using	term_type = term< Cf, Key >
	Alias for term type.

using	size_type = typename container_type::size_type
	Size type. More...

using	const_iterator = const_iterator_impl
	Const iterator. More...

Public Member Functions
	series ()=default
	Defaulted default constructor.

	series (const series &)=default
	Defaulted copy constructor. More...

	series (series &&)=default
	Defaulted move constructor.

template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>
	series (const T &x)
	Generic constructor. More...

	~series ()
	Trivial destructor.

series &	operator= (const series &other)
	Copy-assignment operator. More...

series &	operator= (series &&other)=default
	Move assignment operator. More...

template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>
series &	operator= (const T &x)
	Generic assignment operator. More...

size_type	size () const
	Series size. More...

bool	empty () const
	Empty test. More...

bool	is_single_coefficient () const
	Test for single-coefficient series. More...

template<bool Sign, typename T , insert_enabler< T > = 0>
void	insert (T &&term)
	Insert term. More...

template<typename T , insert_enabler< T > = 0>
void	insert (T &&term)
	Insert generic term with `Sign = true`. More...

Derived	operator+ () const
	Identity operator. More...

Derived	operator- () const
	Negation operator. More...

void	negate ()
	Negate series in-place. More...

template<typename T , typename U = Derived>
pow_ret_type< T, U >	pow (const T &x) const
	Exponentiation. More...

template<typename Series = Derived>
partial_type< Series >	partial (const std::string &name) const
	Partial derivative. More...

const_iterator	begin () const
	Begin iterator. More...

const_iterator	end () const
	End iterator. More...

Derived	filter (std::function< bool(const std::pair< typename term_type::cf_type, Derived > &)> func) const
	Term filtering. More...

Derived	transform (std::function< std::pair< typename term_type::cf_type, Derived >(const std::pair< typename term_type::cf_type, Derived > &)> func) const
	Term transformation. More...

Derived	trim () const
	Trim. More...

void	print_tex (std::ostream &os) const
	Print in TeX mode. More...

std::size_t	hash () const
	Hash value. More...

template<typename T = Derived, is_identical_enabler< T > = 0>
bool	is_identical (const Derived &other) const
	Check for identical series. More...

const symbol_fset &	get_symbol_set () const
	Symbol set getter. More...

void	set_symbol_set (const symbol_fset &args)
	Symbol set setter. More...

Table-querying methods
Methods to query the properties of the internal container used to store the terms.
sparsity_info_type	table_sparsity () const
	Table sparsity. More...

double	table_load_factor () const
	Table load factor. More...

size_type	table_bucket_count () const
	Table bucket count. More...

Low-level interface
Low-level methods.
container_type &	_container ()
	Get a mutable reference to the container of terms. More...

const container_type &	_container () const
	Get a const reference to the container of terms. More...

Static Public Member Functions
template<typename T = Derived, is_identical_enabler< T > = 0>
static void	clear_pow_cache ()
	Clear the internal cache of natural powers. More...

template<typename F , typename Series = Derived, custom_partial_enabler< F, Series > = 0>
static void	register_custom_derivative (const std::string &name, F func)
	Register custom partial derivative. More...

template<typename Series = Derived, typename Partial = partial_type<Series>>
static void	unregister_custom_derivative (const std::string &name)
	Unregister custom partial derivative. More...

template<typename Series = Derived, typename Partial = partial_type<Series>>
static void	unregister_all_custom_derivatives ()
	Unregister all custom partial derivatives. More...

Protected Types
using	container_type = hash_set< term_type >
	Container type for terms.

Protected Attributes
symbol_fset	m_symbol_set
	Symbol set.

container_type	m_container
	Terms container.

Friends
std::ostream &	operator<< (std::ostream &os, const series &s)
	Overloaded stream operator for piranha::series. More...

Detailed Description

template<typename Cf, typename Key, typename Derived>
class piranha::series< Cf, Key, Derived >

Series class.

This class contains the arithmetic and comparison operator overloads for piranha::series instances via the parent class piranha::series_operators.

Type requirements

Cf and Key must be suitable for use in piranha::term.
Derived must derive from piranha::series of Cf, Key and Derived.
Derived must satisfy piranha::is_series.
Derived must satisfy piranha::is_container_element.

Exception safety guarantee

Unless otherwise specified, this class provides the strong exception safety guarantee for all operations.

Move semantics

Moved-from series are left in a state equivalent to an empty series.

Definition at line 45 of file series_fwd.hpp.

Member Typedef Documentation

◆ const_iterator

template<typename Cf, typename Key, typename Derived>

using piranha::series< Cf, Key, Derived >::const_iterator = const_iterator_impl

Const iterator.

Iterator type that can be used to iterate over the terms of the series. The object returned upon dereferentiation is an std::pair in which the first element is a copy of the coefficient of the term, the second element a single-term instance of Derived constructed from the term's key and a unitary coefficient.

This iterator is an input iterator which additionally offers the multi-pass guarantee.

See also: piranha::series::begin() and piranha::series::end().

Definition at line 1994 of file series.hpp.

◆ size_type

template<typename Cf, typename Key, typename Derived>

using piranha::series< Cf, Key, Derived >::size_type = typename container_type::size_type

Size type.

Used to represent the number of terms in the series. Equivalent to piranha::hash_set::size_type.

Definition at line 1981 of file series.hpp.

Constructor & Destructor Documentation

◆ series() [1/2]

template<typename Cf, typename Key, typename Derived>

piranha::series< Cf, Key, Derived >::series ( const series< Cf, Key, Derived > & )

default

Defaulted copy constructor.

Exceptions

unspecified any exception thrown by the copy constructor of piranha::hash_set.

◆ series() [2/2]

template<typename Cf, typename Key, typename Derived>

template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>

piranha::series< Cf, Key, Derived >::series ( const T & x )

inlineexplicit

Generic constructor.

Note: This constructor is enabled only if T does not derive from the calling piranha::series instance and the algorithm outlined below is supported by the involved types.

The generic construction algorithm works as follows:

if T is a series with the same series recursion index as this, then the symbol set of x is copied into this and all terms from x are inserted into this. The terms of x are converted to term_type via the binary constructor of piranha::term, and the keys of x are converted to the key type of term_type via a converting constructor, if available (see piranha::key_is_convertible);
else, if the recursion index of T is less than the recursion index of this:
- x is used to construct a new term as follows:
  - x is used to construct a coefficient via piranha::convert_to;
  - an empty arguments set will be used to construct a key;
  - coefficient and key are used to construct the new term instance;
- the new term is inserted into this;
otherwise, the constructor is disabled.

Parameters

x	object to construct from.

Exceptions

unspecified

any exception thrown by:

the copy assignment operator of piranha::symbol_fset,
the construction of a coefficient from x or of a key from piranha::symbol_fset,
the construction of a term from a coefficient-key pair,
insert().

Definition at line 2033 of file series.hpp.

Member Function Documentation

◆ _container() [1/2]

template<typename Cf, typename Key, typename Derived>

container_type& piranha::series< Cf, Key, Derived >::_container ( )

inline

Get a mutable reference to the container of terms.

Returns: a reference to the internal container of terms.

Definition at line 2788 of file series.hpp.

◆ _container() [2/2]

template<typename Cf, typename Key, typename Derived>

const container_type& piranha::series< Cf, Key, Derived >::_container ( ) const

inline

Get a const reference to the container of terms.

Returns: a const reference to the internal container of terms.

Definition at line 2796 of file series.hpp.

◆ begin()

template<typename Cf, typename Key, typename Derived>

const_iterator piranha::series< Cf, Key, Derived >::begin ( ) const

inline

Begin iterator.

Return an iterator to the first term of the series. The returned iterator will provide, when dereferenced, an std::pair in which the first element is a copy of the coefficient of the term, whereas the second element is a single-term instance of Derived built from the term's key and a unitary coefficient.

Note that terms are stored unordered in the series, hence it is not defined which particular term will be returned by calling this method. The only guarantee is that the iterator can be used to transverse all the series' terms until piranha::series::end() is eventually reached.

Calling any non-const method on the series will invalidate the iterators obtained via piranha::series::begin() and piranha::series::end().

Returns: an iterator to the first term of the series.

Exceptions

unspecified

any exception thrown by:

construction and assignment of piranha::symbol_fset,
insert(),
construction of term, coefficient and key instances.

Definition at line 2504 of file series.hpp.

◆ clear_pow_cache()

template<typename Cf, typename Key, typename Derived>

template<typename T = Derived, is_identical_enabler< T > = 0>

static void piranha::series< Cf, Key, Derived >::clear_pow_cache ( )

inlinestatic

Clear the internal cache of natural powers.

This method can be used to clear the cache of natural powers of series maintained by piranha::series::pow().

Exceptions

unspecified any exception thrown by threading primitives.

Definition at line 2371 of file series.hpp.

◆ empty()

template<typename Cf, typename Key, typename Derived>

bool piranha::series< Cf, Key, Derived >::empty ( ) const

inline

Empty test.

Returns: true if size() is nonzero, false otherwise.

Definition at line 2103 of file series.hpp.

◆ end()

template<typename Cf, typename Key, typename Derived>

const_iterator piranha::series< Cf, Key, Derived >::end ( ) const

inline

End iterator.

Return an iterator one past the last term of the series. See the documentation of piranha::series::begin() on how the returned iterator can be used.

Returns: an iterator to the end of the series.

Exceptions

unspecified

any exception thrown by:

construction and assignment of piranha::symbol_fset,
insert(),
construction of term, coefficient and key instances.

Definition at line 2523 of file series.hpp.

◆ filter()

template<typename Cf, typename Key, typename Derived>

Derived piranha::series< Cf, Key, Derived >::filter ( std::function< bool(const std::pair< typename term_type::cf_type, Derived > &)> func ) const

inline

Term filtering.

This method will apply the functor func to each term in the series, and produce a return series containing all terms in this for which func returns true. Terms are passed to func in the format resulting from dereferencing the iterators obtained via piranha::series::begin().

Parameters

func	filtering functor.

Returns: filtered series.

Exceptions

unspecified

any exception thrown by:

the call operator of func,
insert(),
the assignment operator of piranha::symbol_fset,
term, coefficient, key construction.

Definition at line 2547 of file series.hpp.

◆ get_symbol_set()

template<typename Cf, typename Key, typename Derived>

const symbol_fset& piranha::series< Cf, Key, Derived >::get_symbol_set ( ) const

inline

Symbol set getter.

Returns: const reference to the piranha::symbol_fset associated to the series.

Definition at line 2762 of file series.hpp.

◆ hash()

template<typename Cf, typename Key, typename Derived>

std::size_t piranha::series< Cf, Key, Derived >::hash ( ) const

inline

Hash value.

The hash value for a series is zero if the series is empty, otherwise it is computed by adding the hash values of all terms. This ensures that two identical series in which the terms are stored in different order still produce the same hash value.

Note, however, that the arguments of the series are not considered in the hash value and that, in general, two series that compare equal according to operator==() will not have the same hash value (as the equality operator merges the arguments of two series before actually performing the comparison). Instead of operator==(), is_identical() should be used for storing series as keys in associative containers.

Returns: a hash value for the series.

Exceptions

unspecified any exception thrown by computing the hash of a term.

Definition at line 2730 of file series.hpp.

◆ insert() [1/2]

template<typename Cf, typename Key, typename Derived>

template<bool Sign, typename T , insert_enabler< T > = 0>

void piranha::series< Cf, Key, Derived >::insert ( T && term )

inline

Insert term.

Note: This method is enabled only if the decay type of T is piranha::series::term_type.

This method will insert term into the series using internally piranha::hash_set::insert.

The insertion algorithm proceeds as follows:

if the term is not compatible for insertion, an std::invalid_argument exception is thrown;
if the term is ignorable, the method will return without performing any insertion;
if the term is already in the series, then:
- its coefficient is added (if Sign is true) or subtracted (if Sign is false) to the existing term's coefficient;
- if, after the addition/subtraction the existing term is ignorable, it will be erased;
else:
- the term is inserted into the term container and, if Sign is false, its coefficient is negated.

After any modification to an existing term in the series (e.g., via insertion with negative Sign or via in-place addition or subtraction of existing coefficients), the term will be checked again for compatibility and ignorability, and, in case the term has become incompatible or ignorable, it will be erased from the series.

The exception safety guarantee upon insertion is that the series will be left in an undefined but valid state. Such a guarantee relies on the fact that the addition/subtraction and negation methods of the coefficient type will leave the coefficient in a valid (possibly undefined) state in face of exceptions.

Parameters

term	term to be inserted.

Exceptions

unspecified	any exception thrown by: piranha::hash_set::insert(), piranha::hash_set::find(), piranha::hash_set::erase(), piranha::math::negate(), in-place addition/subtraction on coefficient types.
std::invalid_argument	if `term` is incompatible.

Definition at line 2161 of file series.hpp.

◆ insert() [2/2]

template<typename Cf, typename Key, typename Derived>

template<typename T , insert_enabler< T > = 0>

void piranha::series< Cf, Key, Derived >::insert ( T && term )

inline

Insert generic term with Sign = true.

Note: This method is enabled only if the decay type of T is piranha::series::term_type.

Convenience wrapper for the generic insert() method, with Sign set to true.

Parameters

term	term to be inserted.

Exceptions

unspecified any exception thrown by generic insert().

Definition at line 2177 of file series.hpp.

◆ is_identical()

template<typename Cf, typename Key, typename Derived>

template<typename T = Derived, is_identical_enabler< T > = 0>

bool piranha::series< Cf, Key, Derived >::is_identical ( const Derived & other ) const

inline

Check for identical series.

Note: This method is enabled only if Derived is equality-comparable.

This method will return true if the symbol sets of this and other are the same, and other == *this.

Parameters

other argument for the comparison.

Returns: true if this and other are identical, false otherwise.

Exceptions

unspecified any exception thrown by the comparison operator of Derived.

Definition at line 2754 of file series.hpp.

◆ is_single_coefficient()

template<typename Cf, typename Key, typename Derived>

bool piranha::series< Cf, Key, Derived >::is_single_coefficient ( ) const

inline

Test for single-coefficient series.

A series is considered to be single-coefficient when it is symbolically equivalent to a coefficient. That is, the series is either empty (in which case it is considered to be equivalent to a coefficient constructed from zero) or consisting of a single term with unitary key (in which case the series is considered equivalent to its only coefficient).

Returns: true in case of single-coefficient series, false otherwise.

Exceptions

unspecified any exception thrown by the is_unitary() method of the key type.

Definition at line 2118 of file series.hpp.

◆ negate()

template<typename Cf, typename Key, typename Derived>

void piranha::series< Cf, Key, Derived >::negate ( )

inline

Negate series in-place.

This method will call math::negate() on the coefficients of all terms. In case of exceptions, the basic exception safety guarantee is provided.

If any term becomes ignorable or incompatible after negation, it will be erased from the series.

Exceptions

unspecified any exception thrown by math::negate() on the coefficient type.

Definition at line 2214 of file series.hpp.

◆ operator+()

template<typename Cf, typename Key, typename Derived>

Derived piranha::series< Cf, Key, Derived >::operator+ ( ) const

inline

Identity operator.

Returns: copy of this, cast to Derived.

Exceptions

unspecified any exception thrown by the copy constructor.

Definition at line 2187 of file series.hpp.

◆ operator-()

template<typename Cf, typename Key, typename Derived>

Derived piranha::series< Cf, Key, Derived >::operator- ( ) const

inline

Negation operator.

Returns: a copy of this on which negate() has been called.

Exceptions

unspecified

any exception thrown by:

negate(),
the copy constructor of Derived.

Definition at line 2199 of file series.hpp.

◆ operator=() [1/3]

template<typename Cf, typename Key, typename Derived>

series& piranha::series< Cf, Key, Derived >::operator= ( const series< Cf, Key, Derived > & other )

inline

Copy-assignment operator.

Parameters

other assignment argument.

Returns: reference to this.

Exceptions

unspecified any exception thrown by the copy constructor.

Definition at line 2055 of file series.hpp.

◆ operator=() [2/3]

template<typename Cf, typename Key, typename Derived>

series& piranha::series< Cf, Key, Derived >::operator= ( series< Cf, Key, Derived > && other )

default

Move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator=() [3/3]

template<typename Cf, typename Key, typename Derived>

template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>

series& piranha::series< Cf, Key, Derived >::operator= ( const T & x )

inline

Generic assignment operator.

Note: This operator is enabled only if the corresponding generic constructor from x is enabled.

Generic assignment is equivalent to assignment to a piranha::series constructed via the generic constructor.

Parameters

x	assignment argument.

Returns: reference to this.

Exceptions

unspecified any exception thrown by the generic constructor.

Definition at line 2085 of file series.hpp.

◆ partial()

template<typename Cf, typename Key, typename Derived>

template<typename Series = Derived>

partial_type<Series> piranha::series< Cf, Key, Derived >::partial ( const std::string & name ) const

inline

Partial derivative.

Note: This method is enabled only if the coefficient and key are differentiable (i.e., they satisfy the piranha::is_differentiable and piranha::key_is_differentiable type traits), and if the arithmetic operations needed to compute the partial derivative are supported by all the involved types.

This method will return the partial derivative of this with respect to the variable called name. The method will construct the return value from the output of the differentiation methods of coefficient and key, and via arithmetic and/or term insertion operations.

Note that, contrary to the specialisation of piranha::math::partial() for series types, this method will not take into account custom derivatives registered via piranha::series::register_custom_derivative().

Parameters

name	name of the argument with respect to which the derivative will be calculated.

Returns: partial derivative of this with respect to the symbol name.

Exceptions

unspecified

any exception thrown by:

the differentiation methods of coefficient and key,
term construction and insertion,
arithmetic operations on the involved types,
construction of the return type.

Definition at line 2405 of file series.hpp.

◆ pow()

template<typename Cf, typename Key, typename Derived>

template<typename T , typename U = Derived>

pow_ret_type<T, U> piranha::series< Cf, Key, Derived >::pow ( const T & x ) const

inline

Exponentiation.

Note: This method is enabled only if the algorithm outlined here is supported by the involved types.

Return this raised to the x-th power. The type of the result is either the calling series type, or the calling series type rebound to the type resulting from the exponentiation of the coefficient of the calling type to the power of x. The exponentiation algorithm proceeds as follows:

if the series is single-coefficient, the result is a single-coefficient series in which the coefficient is the original coefficient (or zero, if the calling series is empty) raised to the power of x;
if x is zero (as established by piranha::math::is_zero()), a series with a single term with unitary key and coefficient constructed from the integer numeral "1" is returned (i.e., any series raised to the power of zero is 1 - including empty series);
if x represents a non-negative integral value, the return value is constructed via repeated multiplications;
otherwise, an exception will be raised.

An internal thread-safe cache of natural powers of series is maintained in order to improve performance during, e.g., substitution operations. This cache can be cleared with clear_pow_cache().

Parameters

x exponent.

Returns: this raised to the power of x.

Exceptions

std::invalid_argument	if exponentiation is computed via repeated series multiplications and `x` does not represent a non-negative integer.
unspecified	any exception thrown by: series, term, coefficient and key construction, insert(), is_single_coefficient(), piranha::math::pow(), piranha::math::is_zero() and piranha::safe_cast(), series multiplication, memory errors in standard containers, threading primitives, hash() or is_identical().

Definition at line 2304 of file series.hpp.

◆ print_tex()

template<typename Cf, typename Key, typename Derived>

void piranha::series< Cf, Key, Derived >::print_tex ( std::ostream & os ) const

inline

Print in TeX mode.

Print series to stream os in TeX mode. The representation is constructed in the same way as explained in piranha::series::operator<<(), but using piranha::print_tex_coefficient() and the key's TeX printing method instead of the plain printing functions.

Parameters

os	target stream.

Exceptions

unspecified

any exception thrown by:

piranha::print_tex_coefficient(),
the TeX printing method of the key type,
memory allocation errors in standard containers,
piranha::settings::get_max_term_output(),
streaming to os or to instances of std::ostringstream.

See also: operator<<().

Definition at line 2654 of file series.hpp.

◆ register_custom_derivative()

template<typename Cf, typename Key, typename Derived>

template<typename F , typename Series = Derived, custom_partial_enabler< F, Series > = 0>

static void piranha::series< Cf, Key, Derived >::register_custom_derivative	(	const std::string &	name,
		F	func
	)

inlinestatic

Register custom partial derivative.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived, and if F is a type that can be used to construct std::function<partial_type(const Derived &), where partial_type is the type resulting from the partial derivative of Derived.

Register a copy of a callable func associated to the symbol name for use by piranha::math::partial(). func will be used to compute the partial derivative of instances of type Derived with respect to name in place of the default partial differentiation algorithm.

It is safe to call this method from multiple threads.

Parameters

name	symbol for which the custom partial derivative function will be registered.
func	custom partial derivative function.

Exceptions

unspecified

any exception thrown by:

failure(s) in threading primitives,
lookup and insertion operations on std::unordered_map,
construction and move-assignment of std::function.

Definition at line 2432 of file series.hpp.

◆ set_symbol_set()

template<typename Cf, typename Key, typename Derived>

void piranha::series< Cf, Key, Derived >::set_symbol_set ( const symbol_fset & args )

inline

Symbol set setter.

Parameters

args	piranha::symbol_fset that will be associated to the series.

Exceptions

std::invalid_argument	if the series is not empty.
unspecified	any exception thrown by the copy assignment operator of piranha::symbol_fset.

Definition at line 2773 of file series.hpp.

◆ size()

template<typename Cf, typename Key, typename Derived>

size_type piranha::series< Cf, Key, Derived >::size ( ) const

inline

Series size.

Returns: the number of terms in the series.

Definition at line 2095 of file series.hpp.

◆ table_bucket_count()

template<typename Cf, typename Key, typename Derived>

size_type piranha::series< Cf, Key, Derived >::table_bucket_count ( ) const

inline

Table bucket count.

Returns: the bucket count of the internal container.

Definition at line 2263 of file series.hpp.

◆ table_load_factor()

template<typename Cf, typename Key, typename Derived>

double piranha::series< Cf, Key, Derived >::table_load_factor ( ) const

inline

Table load factor.

Will call piranha::hash_set::load_factor() on the internal terms container and return the result.

Returns: the load factor of the internal container.

Definition at line 2255 of file series.hpp.

◆ table_sparsity()

template<typename Cf, typename Key, typename Derived>

sparsity_info_type piranha::series< Cf, Key, Derived >::table_sparsity ( ) const

inline

Table sparsity.

Will call piranha::hash_set::evaluate_sparsity() on the internal terms container and return the result.

Returns: the output of piranha::hash_set::evaluate_sparsity().

Exceptions

unspecified any exception thrown by piranha::hash_set::evaluate_sparsity().

Definition at line 2244 of file series.hpp.

◆ transform()

template<typename Cf, typename Key, typename Derived>

Derived piranha::series< Cf, Key, Derived >::transform ( std::function< std::pair< typename term_type::cf_type, Derived >(const std::pair< typename term_type::cf_type, Derived > &)> func ) const

inline

Term transformation.

This method will apply the functor func to each term in the series, and will use the return value of the functor to construct a new series. Terms are passed to func in the same format resulting from dereferencing the iterators obtained via piranha::series::begin(), and func is expected to produce a return value of the same type.

The return series is first initialised as an empty series. For each input term t, the return value of func is used to construct a new temporary series from the multiplication of t.first and t.second. Each temporary series is then added to the return value series.

This method requires the coefficient type to be multipliable by Derived.

Parameters

func	transforming functor.

Returns: transformed series.

Exceptions

unspecified

any exception thrown by:

the call operator of func,
insert(),
the assignment operator of piranha::symbol_fset,
term, coefficient, key construction,
series multiplication and addition.

Definition at line 2585 of file series.hpp.

◆ trim()

template<typename Cf, typename Key, typename Derived>

Derived piranha::series< Cf, Key, Derived >::trim ( ) const

inline

Trim.

This method will return a series mathematically equivalent to this in which discardable arguments have been removed from the internal set of symbols. Which symbols are removed depends on the trimming method trim_identify() of the key type (e.g., in a polynomial a symbol can be discarded if its exponent is zero in all monomials).

If the coefficient type is an instance of piranha::series, trim() will be called recursively on the coefficients while building the return value.

Returns: trimmed version of this.

Exceptions

unspecified

any exception thrown by:

piranha::safe_cast(),
operations on piranha::symbol_fset,
the trimming methods of coefficient and/or key,
insert(),
term, coefficient and key type construction.

Definition at line 2619 of file series.hpp.

◆ unregister_all_custom_derivatives()

template<typename Cf, typename Key, typename Derived>

template<typename Series = Derived, typename Partial = partial_type<Series>>

static void piranha::series< Cf, Key, Derived >::unregister_all_custom_derivatives ( )

inlinestatic

Unregister all custom partial derivatives.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived.

Will unregister all custom derivatives currently registered via register_custom_derivative(). It is safe to call this method from multiple threads.

Exceptions

unspecified any exception thrown by failure(s) in threading primitives.

Definition at line 2478 of file series.hpp.

◆ unregister_custom_derivative()

template<typename Cf, typename Key, typename Derived>

template<typename Series = Derived, typename Partial = partial_type<Series>>

static void piranha::series< Cf, Key, Derived >::unregister_custom_derivative ( const std::string & name )

inlinestatic

Unregister custom partial derivative.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived.

Unregister the custom partial derivative function associated to the symbol name. If no custom partial derivative was previously registered using register_custom_derivative(), calling this function will be a no-op.

It is safe to call this method from multiple threads.

Parameters

name	symbol for which the custom partial derivative function will be unregistered.

Exceptions

unspecified

any exception thrown by:

failure(s) in threading primitives,
lookup and erase operations on std::unordered_map.

Definition at line 2459 of file series.hpp.

Friends And Related Function Documentation

◆ operator<<

template<typename Cf, typename Key, typename Derived>

std::ostream& operator<<	(	std::ostream &	os,
		const series< Cf, Key, Derived > &	s
	)

friend

Overloaded stream operator for piranha::series.

Will direct to stream a human-readable representation of the series.

The human-readable representation of the series is built as follows:

the coefficient and key of each term are printed adjacent to each other separated by the character "*", the former via the piranha::print_coefficient() function, the latter via its print() method;
terms are separated by a "+" sign.

The following additional transformations take place on the printed output:

if the printed output of a coefficient is the string "1" and the printed output of its key is not empty, the coefficient and the "*" sign are not printed;
if the printed output of a coefficient is the string "-1" and the printed output of its key is not empty, the printed output of the coefficient is transformed into "-" and the sign "*" is not printed;
if the key output is empty, the sign "*" is not printed;
the sequence of characters "+-" is transformed into "-";
at most piranha::settings::get_max_term_output() terms are printed, and terms in excess are represented with ellipsis "..." at the end of the output; if piranha::settings::get_max_term_output() is zero, all the terms will be printed.

Note that the print order of the terms will be undefined.

Parameters

os	target stream.
s	piranha::series argument.

Returns: reference to os.

Exceptions

unspecified

any exception thrown by:

piranha::print_coefficient(),
the print() method of the key type,
memory allocation errors in standard containers,
piranha::settings::get_max_term_output(),
streaming to os or to instances of std::ostringstream.

Definition at line 2699 of file series.hpp.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Attributes

Friends

Detailed Description

template<typename Cf, typename Key, typename Derived> class piranha::series< Cf, Key, Derived >

Type requirements

Exception safety guarantee

Move semantics

Member Typedef Documentation

◆ const_iterator

◆ size_type

Constructor & Destructor Documentation

◆ series() [1/2]

◆ series() [2/2]

Member Function Documentation

◆ _container() [1/2]

◆ _container() [2/2]

◆ begin()

◆ clear_pow_cache()

◆ empty()

◆ end()

◆ filter()

◆ get_symbol_set()

◆ hash()

◆ insert() [1/2]

◆ insert() [2/2]

◆ is_identical()

◆ is_single_coefficient()

◆ negate()

◆ operator+()

◆ operator-()

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ partial()

◆ pow()

◆ print_tex()

◆ register_custom_derivative()

◆ set_symbol_set()

◆ size()

◆ table_bucket_count()

◆ table_load_factor()

◆ table_sparsity()

◆ transform()

◆ trim()

◆ unregister_all_custom_derivatives()

◆ unregister_custom_derivative()

Friends And Related Function Documentation

◆ operator<<

template<typename Cf, typename Key, typename Derived>
class piranha::series< Cf, Key, Derived >