Divisor class. More...

#include <piranha/divisor.hpp>

Public Types
using	value_type = T
	Alias for `T`.

using	container_type = hash_set< p_type, p_type_hasher >
	Underlying container type.

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

Public Member Functions
	divisor ()=default
	Defaulted default constructor. More...

	divisor (const divisor &)=default
	Defaulted copy constructor.

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

	divisor (const divisor &other, const symbol_fset &args)
	Converting constructor. More...

	divisor (const symbol_fset &)
	Constructor from piranha::symbol_fset. More...

	~divisor ()
	Trivial destructor.

divisor &	operator= (const divisor &other)=default
	Copy assignment operator. More...

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

template<typename It , typename Exponent , insert_enabler< It, Exponent > = 0>
void	insert (It begin, It end, const Exponent &e)
	Create and insert a term from range and exponent. More...

size_type	size () const
	Size. More...

const container_type &	_container () const
	Const access to the internal container. More...

container_type &	_container ()
	Mutable access to the internal container. More...

void	clear ()
	Clear. More...

bool	operator== (const divisor &other) const
	Equality operator. More...

bool	operator!= (const divisor &other) const
	Inequality operator. More...

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

bool	is_compatible (const symbol_fset &args) const noexcept
	Compatibility check. More...

bool	is_zero (const symbol_fset &) const noexcept
	Zero check. More...

bool	is_unitary (const symbol_fset &) const
	Check if divisor is unitary. More...

divisor	merge_symbols (const symbol_idx_fmap< symbol_fset > &ins_map, const symbol_fset &args) const
	Merge symbols. More...

void	print (std::ostream &os, const symbol_fset &args) const
	Print to stream. More...

void	print_tex (std::ostream &os, const symbol_fset &args) const
	Print to stream in TeX mode. More...

template<typename U >
eval_type< U >	evaluate (const std::vector< U > &values, const symbol_fset &args) const
	Evaluation. More...

void	trim_identify (std::vector< char > &trim_mask, const symbol_fset &args) const
	Identify symbols that can be trimmed. More...

divisor	trim (const std::vector< char > &trim_mask, const symbol_fset &args) const
	Trim. More...

std::pair< divisor, divisor >	split (const symbol_idx &p, const symbol_fset &args) const
	Split divisor. More...

template<typename Stream , msgpack_pack_enabler< Stream > = 0>
void	msgpack_pack (msgpack::packer< Stream > &p, msgpack_format f, const symbol_fset &args) const
	Pack in msgpack format. More...

template<typename U = divisor, msgpack_convert_enabler< U > = 0>
void	msgpack_convert (const msgpack::object &o, msgpack_format f, const symbol_fset &args)
	Convert from msgpack object. More...

Static Public Member Functions
template<typename Cf , multiply_enabler< Cf > = 0>
static void	multiply (std::array< term< Cf, divisor >, multiply_arity > &res, const term< Cf, divisor > &t1, const term< Cf, divisor > &t2, const symbol_fset &args)
	Multiply terms with a divisor key. More...

Static Public Attributes
static const std::size_t	multiply_arity = 1u
	Arity of the multiply() method.

Detailed Description

template<typename T>
class piranha::divisor< T >

Divisor class.

This class is used to represent keys of the form

\[ \prod_j\frac{1}{\left(a_{0,j}x_0+a_{1,j}x_1+\ldots+a_{n,j}x_n\right)^{e_j}}, \]

where \( a_{i,j} \) are integers, \( x_i \) are symbols, and \( e_j \) are positive integers. The type of \( a_{i,j} \) and \( e_j \) is T. The terms of the product are stored in a piranha::hash_set and they are guaranteed to be in a canonical form defined by the following properties:

if T is a C++ integral type, the values of \( a_{i,j} \) and \( e_j \) are within implementation-defined ranges,
\( e_j \) is always strictly positive,
the first nonzero \( a_{i,j} \) in each term is positive,
the \( a_{i,j} \) in each term have no non-unitary common divisor.

Type requirements

T must be either a C++ signed integral type or an instance of piranha::mp_integer.

Exception safety guarantee

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

Move semantics

Move semantics is equivalent to the move semantics of piranha::hash_set.

Definition at line 182 of file divisor.hpp.

Member Typedef Documentation

◆ size_type

template<typename T >

using piranha::divisor< T >::size_type = typename container_type::size_type

Size type.

It corresponds to the size type of the internal container.

Definition at line 334 of file divisor.hpp.

Constructor & Destructor Documentation

◆ divisor() [1/3]

template<typename T >

piranha::divisor< T >::divisor ( )

default

Defaulted default constructor.

This constructor will initialise an empty divisor.

◆ divisor() [2/3]

template<typename T >

piranha::divisor< T >::divisor	(	const divisor< T > &	other,
		const symbol_fset &	args
	)

inlineexplicit

Converting constructor.

This constructor is used in the generic constructor of piranha::series. It is equivalent to a copy constructor with extra checking.

Parameters

other	the construction argument.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if `other` is not compatible with `args`.
unspecified	any exception thrown by the copy constructor.

Definition at line 355 of file divisor.hpp.

◆ divisor() [3/3]

template<typename T >

piranha::divisor< T >::divisor ( const symbol_fset & )

inlineexplicit

Constructor from piranha::symbol_fset.

Equivalent to the default constructor.

Definition at line 366 of file divisor.hpp.

Member Function Documentation

◆ _container() [1/2]

template<typename T >

const container_type& piranha::divisor< T >::_container ( ) const

inline

Const access to the internal container.

Returns: a const reference to the internal container.

Definition at line 455 of file divisor.hpp.

◆ _container() [2/2]

template<typename T >

container_type& piranha::divisor< T >::_container ( )

inline

Mutable access to the internal container.

Returns: a reference to the internal container.

Definition at line 463 of file divisor.hpp.

◆ clear()

template<typename T >

void piranha::divisor< T >::clear ( )

inline

Clear.

This method will remove all terms from the divisor.

Definition at line 471 of file divisor.hpp.

◆ evaluate()

template<typename T >

template<typename U >

eval_type<U> piranha::divisor< T >::evaluate	(	const std::vector< U > &	values,
		const symbol_fset &	args
	)		const

inline

Evaluation.

Note: This method is available only if U supports the arithmetic operations necessary to construct the return type.

The return value will be built via multiplications of the \( a_{i,j} \) by the input values, additions, divisions and exponentiations via piranha::math::pow(). If the divisor has no terms, 1 will be returned.

Parameters

values	the values will be used for the evaluation.
args	the reference piranha::symbol_fset.

Returns: the result of evaluating this with the values provided in values.

Exceptions

std::invalid_argument	if there exist an incompatibility between `this`, `args` or `pmap`.
unspecified	any exception thrown by the construction of the return type.

Definition at line 761 of file divisor.hpp.

◆ hash()

template<typename T >

std::size_t piranha::divisor< T >::hash ( ) const

inline

Hash value.

The hash value is computed by combining the hash values of all terms. An empty divisor has a hash value of 0. Two equal divisors have the same hash value.

Returns: a hash value for the divisor.

Definition at line 517 of file divisor.hpp.

◆ insert()

template<typename T >

template<typename It , typename Exponent , insert_enabler< It, Exponent > = 0>

void piranha::divisor< T >::insert	(	It	begin,
		It	end,
		const Exponent &	e
	)

inline

Create and insert a term from range and exponent.

Note

This method is enabled only if:

It is an input iterator,
the value type of It can be safely cast to piranha::divisor::value_type,
Exponent can be safely cast to piranha::divisor::value_type.

This method will construct and insert a term into the divisor. The elements in the range [begin,end) will be used to construct the \( a_{i,j} \) of the term, while e will be used to construct the exponent (after a call to piranha::safe_cast()). If no term with the same set of \( a_{i,j} \) exists, then a new term will be inserted; otherwise, e will be added to the exponent of the existing term.

This method provides the basic exception safety guarantee.

Parameters

begin	start of the range of \( a_{i,j} \).
end	end of the range of \( a_{i,j} \).
e	exponent.

Exceptions

std::invalid_argument	if the term to be inserted is not in canonical form, or if the insertion leads to an overflow in the value of an exponent.
std::overflow_error	if the insertion results in the container to be resized over an implementation-defined limit.
unspecified	any exception thrown by: piranha::safe_cast(), manipulations of piranha::small_vector, the public interface of piranha::hash_set, arithmetic operations on the exponent.

Definition at line 420 of file divisor.hpp.

◆ is_compatible()

template<typename T >

bool piranha::divisor< T >::is_compatible ( const symbol_fset & args ) const

inlinenoexcept

Compatibility check.

An empty divisor is considered compatible with any set of symbols. Otherwise, a non-empty divisor is compatible if the number of variables in the terms is the same as the number of symbols in args.

Parameters

args	the reference piranha::symbol_fset.

Returns: true if this is compatible with args, false otherwise.

Definition at line 546 of file divisor.hpp.

◆ is_unitary()

template<typename T >

bool piranha::divisor< T >::is_unitary ( const symbol_fset & ) const

inline

Check if divisor is unitary.

Only an empty divisor is considered unitary.

Returns: true if this is empty, false otherwise.

Definition at line 566 of file divisor.hpp.

◆ is_zero()

template<typename T >

bool piranha::divisor< T >::is_zero ( const symbol_fset & ) const

inlinenoexcept

Zero check.

A divisor can never be zero.

Returns: false.

Definition at line 556 of file divisor.hpp.

◆ merge_symbols()

template<typename T >

divisor piranha::divisor< T >::merge_symbols	(	const symbol_idx_fmap< symbol_fset > &	ins_map,
		const symbol_fset &	args
	)		const

inline

Merge symbols.

This method will return a copy of this in which, for every factor of the divisor, the value 0 has been inserted at the positions specified by ins_map. Specifically, before each index appearing in ins_map a number of zeroes equal to the size of the mapped piranha::symbol_fset will be inserted.

Parameters

ins_map	the insertion map.
args	the reference symbol set for `this`.

Returns: a piranha::divisor resulting from inserting into this zeroes at the positions specified by ins_map.

Exceptions

std::invalid_argument	in the following cases: the size of the factors of `this` is different from the size of `args`, the size of `ins_map` is zero, the last index in `ins_map` is greater than the size of the factors of `this`.
unspecified	any exception thrown by: piranha::small_vector::push_back(), the construction of instances of type piranha::divisor::value_type from the integral constant 0, the copy assignment of piranha::divisor::value_type, piranha::hash_set::insert().

Definition at line 592 of file divisor.hpp.

◆ msgpack_convert()

template<typename T >

template<typename U = divisor, msgpack_convert_enabler< U > = 0>

void piranha::divisor< T >::msgpack_convert	(	const msgpack::object &	o,
		msgpack_format	f,
		const symbol_fset &	args
	)

inline

Convert from msgpack object.

Note: This method is enabled only if the internal container type satisfies piranha::has_msgpack_convert.

This method will convert the input msgpack object o into this, using the format f. The method provides the basic exception safety guarantee.

Parameters

o	the input `msgpack::object`.
f	the desired piranha::msgpack_format.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the deserialized divisor fails internal consistency checks, or if it is not compatible with `args`.
unspecified	any exception thrown by piranha::msgpack_convert().

Definition at line 1025 of file divisor.hpp.

◆ msgpack_pack()

template<typename T >

template<typename Stream , msgpack_pack_enabler< Stream > = 0>

void piranha::divisor< T >::msgpack_pack	(	msgpack::packer< Stream > &	p,
		msgpack_format	f,
		const symbol_fset &	args
	)		const

inline

Pack in msgpack format.

Note: This method is enabled only if Stream satisfies piranha::is_msgpack_stream and the internal container type satisfies piranha::has_msgpack_pack.

This method will pack this in to p using the format f.

Parameters

p	the target `msgpack::packer`.
f	the desired piranha::msgpack_format.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if `args` is not compatible with `this`.
unspecified	any exception thrown by piranha::msgpack_pack().

Definition at line 1000 of file divisor.hpp.

◆ multiply()

template<typename T >

template<typename Cf , multiply_enabler< Cf > = 0>

static void piranha::divisor< T >::multiply	(	std::array< term< Cf, divisor< T > >, multiply_arity > &	res,
		const term< Cf, divisor< T > > &	t1,
		const term< Cf, divisor< T > > &	t2,
		const symbol_fset &	args
	)

inlinestatic

Multiply terms with a divisor key.

Note: This method is enabled only if Cf satisfies piranha::has_mul3.

Multiply t1 by t2, storing the result in the only element of res. If Cf is an instance of piranha::mp_rational, then only the numerators of the coefficients will be multiplied.

This method offers the basic exception safety guarantee.

Parameters

res	the return value.
t1	the first argument.
t2	the second argument.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the key of `t1` and/or the key of `t2` are incompatible with `args`, or if the multiplication of the keys results in an exponent exceeding the allowed range.
std::overflow_error	if the multiplication of the keys results in the container of the result key to be resized over an implementation-defined limit.
unspecified	any exception thrown by: piranha::math::mul3(), the public interface of piranha::hash_set, arithmetic operations on the exponent.

Definition at line 826 of file divisor.hpp.

◆ operator!=()

template<typename T >

bool piranha::divisor< T >::operator!= ( const divisor< T > & other ) const

inline

Inequality operator.

Parameters

other comparison argument.

Returns: the opposite of operator==().

Definition at line 506 of file divisor.hpp.

◆ operator=() [1/2]

template<typename T >

divisor& piranha::divisor< T >::operator= ( const divisor< T > & other )

default

Copy assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

Exceptions

unspecified any exception thrown by the assignment operator of piranha::hash_set.

◆ operator=() [2/2]

template<typename T >

divisor& piranha::divisor< T >::operator= ( divisor< T > && other )

default

Move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator==()

template<typename T >

bool piranha::divisor< T >::operator== ( const divisor< T > & other ) const

inline

Equality operator.

Two divisors are considered equal if:

they have the same number of terms, and
for each term in the first divisor there exist an identical term in the second divisor.

Parameters

other comparison argument.

Returns: true if this is equal to other, false otherwise.

Definition at line 486 of file divisor.hpp.

◆ print()

template<typename T >

void piranha::divisor< T >::print	(	std::ostream &	os,
		const symbol_fset &	args
	)		const

inline

Print to stream.

This method will print to the stream os a text representation of this.

Parameters

os	the target stream.
args	the reference symbol set for `this`.

Exceptions

std::invalid_argument	if the number of variables in the terms of `this` is different from the size of `args`.
unspecified	any exception thrown by printing to `os` piranha::divisor::value_type, strings or characters.

Definition at line 619 of file divisor.hpp.

◆ print_tex()

template<typename T >

void piranha::divisor< T >::print_tex	(	std::ostream &	os,
		const symbol_fset &	args
	)		const

inline

Print to stream in TeX mode.

This method will print to the stream os a TeX representation of this.

Parameters

os	the target stream.
args	the reference symbol set for `this`.

Exceptions

std::invalid_argument	if the number of variables in the terms of `this` is different from the size of `args`.
unspecified	any exception thrown by printing to `os` piranha::divisor::value_type, strings or characters.

Definition at line 681 of file divisor.hpp.

◆ size()

template<typename T >

size_type piranha::divisor< T >::size ( ) const

inline

Size.

Returns: the size of the internal container - that is, the number of terms in the product.

Definition at line 447 of file divisor.hpp.

◆ split()

template<typename T >

std::pair<divisor, divisor> piranha::divisor< T >::split	(	const symbol_idx &	p,
		const symbol_fset &	args
	)		const

inline

Split divisor.

This method will split this into two parts: the first one will contain the terms of the divisor whose \( a_{i,j} \) values at the position p are not zero, the second one the remaining terms.

Parameters

p	the position of the splitting symbol.
args	the reference piranha::symbol_fset.

Returns: the original divisor split into two parts.

Exceptions

std::invalid_argument	if `args` is not compatible with `this` or `p`, or `p` is not less than the size of `args`.
unspecified	any exception thrown by: piranha::math::is_zero(), piranha::hash_set::insert().

Definition at line 940 of file divisor.hpp.

◆ trim()

template<typename T >

divisor piranha::divisor< T >::trim	(	const std::vector< char > &	trim_mask,
		const symbol_fset &	args
	)		const

inline

Trim.

This method is used in piranha::series::trim(). The input mask trim_mask is a vector of boolean flags signalling (with nonzero values) symbols to be removed. The method will return a copy of this in which the specified elements have been removed from each term of the divisor.

Parameters

trim_mask	a mask indicating which elements will be removed.
args	the reference piranha::symbol_fset.

Returns: a trimmed copy of this.

Exceptions

std::invalid_argument	if `this` is not compatible with `args` or if the sizes of `args` and `trim_mask` differ.
unspecified	any exception thrown by piranha::small_vector::push_back() or piranha::divisor::insert().

Definition at line 900 of file divisor.hpp.

◆ trim_identify()

template<typename T >

void piranha::divisor< T >::trim_identify	(	std::vector< char > &	trim_mask,
		const symbol_fset &	args
	)		const

inline

Identify symbols that can be trimmed.

This method is used in piranha::series::trim(). The input parameter trim_mask is a vector of boolean flags (i.e., a mask) which signals which elements in args are candidates for trimming: a nonzero value means that the symbol at the corresponding position is a candidate for trimming, while a zero value means that the symbol is not a candidate for trimming. The method will set to zero in trim_mask those symbols whose \( a_{i,j} \) in this are not all zeroes.

Parameters

trim_mask	a mask signalling candidate elements for trimming.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if `this` is not compatible with `args`, or if the sizes of `trim_mask` and `args` differ.
unspecified	any exception thrown by piranha::math::is_zero().

Definition at line 863 of file divisor.hpp.

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

divisor.hpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename T> class piranha::divisor< T >

Type requirements

Exception safety guarantee

Move semantics

Member Typedef Documentation

◆ size_type

Constructor & Destructor Documentation

◆ divisor() [1/3]

◆ divisor() [2/3]

◆ divisor() [3/3]

Member Function Documentation

◆ _container() [1/2]

◆ _container() [2/2]

◆ clear()

◆ evaluate()

◆ hash()

◆ insert()

◆ is_compatible()

◆ is_unitary()

◆ is_zero()

◆ merge_symbols()

◆ msgpack_convert()

◆ msgpack_pack()

◆ multiply()

◆ operator!=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ print()

◆ print_tex()

◆ size()

◆ split()

◆ trim()

◆ trim_identify()

template<typename T>
class piranha::divisor< T >