Kronecker monomial class. More...

#include <piranha/kronecker_monomial.hpp>

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

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

using	v_type = static_vector< T, 255u >
	Vector type used for temporary packing/unpacking.

Public Member Functions
	kronecker_monomial ()
	Default constructor. More...

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

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

template<typename U , container_ctor_enabler< U > = 0>
	kronecker_monomial (const U &c)
	Constructor from container. More...

template<typename U , init_list_ctor_enabler< U > = 0>
	kronecker_monomial (std::initializer_list< U > list)
	Constructor from initializer list. More...

template<typename Iterator , it_ctor_enabler< Iterator > = 0>
	kronecker_monomial (Iterator begin, Iterator end)
	Constructor from range. More...

template<typename Iterator , it_ctor_enabler< Iterator > = 0>
	kronecker_monomial (Iterator begin, Iterator end, const symbol_fset &s)
	Constructor from range and symbol set. More...

	kronecker_monomial (const symbol_fset &)
	Constructor from set of symbols. More...

	kronecker_monomial (const kronecker_monomial &other, const symbol_fset &)
	Converting constructor. More...

	kronecker_monomial (const T &n)
	Constructor from `T`. More...

	~kronecker_monomial ()
	Destructor.

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

kronecker_monomial &	operator= (kronecker_monomial &&other)=default
	Defaulted move assignment operator. More...

void	set_int (const T &n)
	Set the internal integer instance. More...

T	get_int () const
	Get internal instance. More...

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

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

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

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

degree_type	degree (const symbol_fset &args) const
	Degree. More...

degree_type	ldegree (const symbol_fset &args) const
	Low degree (equivalent to the degree). More...

degree_type	degree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial degree. More...

degree_type	ldegree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial low degree (equivalent to the partial degree). More...

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

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

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

std::pair< bool, symbol_idx >	is_linear (const symbol_fset &args) const
	Detect linear monomial. More...

template<typename U , pow_enabler< U > = 0>
kronecker_monomial	pow (const U &x, const symbol_fset &args) const
	Exponentiation. More...

v_type	unpack (const symbol_fset &args) const
	Unpack internal integer instance. More...

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

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

std::pair< T, kronecker_monomial >	partial (const symbol_idx &p, const symbol_fset &args) const
	Partial derivative. More...

std::pair< T, kronecker_monomial >	integrate (const std::string &s, const symbol_fset &args) const
	Integration. More...

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

template<typename U >
std::vector< std::pair< subs_type< U >, kronecker_monomial > >	subs (const symbol_idx_fmap< U > &smap, const symbol_fset &args) const
	Substitution. More...

template<typename U >
std::vector< std::pair< ipow_subs_type< U >, kronecker_monomial > >	ipow_subs (const symbol_idx &p, const integer &n, const U &x, const symbol_fset &args) const
	Substitution of integral power. More...

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

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

bool	operator< (const kronecker_monomial &other) const
	Comparison operator. More...

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

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

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

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

Detailed Description

template<typename T = std::make_signed<std::size_t>::type>
class piranha::kronecker_monomial< T >

Kronecker monomial class.

This class represents a multivariate monomial with integral exponents. The values of the exponents are packed in a signed integer using Kronecker substitution, using the facilities provided by piranha::kronecker_array.

This class satisfies the piranha::is_key, piranha::key_has_degree, piranha::key_has_ldegree and piranha::key_is_differentiable type traits.

Type requirements

T must be suitable for use in piranha::kronecker_array. The default type for T is the signed counterpart of std::size_t.

Exception safety guarantee

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

Move semantics

The move semantics of this class are equivalent to the move semantics of C++ signed integral types.

Definition at line 119 of file kronecker_monomial.hpp.

Member Typedef Documentation

◆ size_type

template<typename T = std::make_signed<std::size_t>::type>

using piranha::kronecker_monomial< T >::size_type = typename ka::size_type

Size type.

Used to represent the number of variables in the monomial. Equivalent to the size type of piranha::kronecker_array.

Definition at line 134 of file kronecker_monomial.hpp.

Constructor & Destructor Documentation

◆ kronecker_monomial() [1/8]

template<typename T = std::make_signed<std::size_t>::type>

piranha::kronecker_monomial< T >::kronecker_monomial ( )

inline

Default constructor.

After construction all exponents in the monomial will be zero.

Definition at line 147 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [2/8]

template<typename T = std::make_signed<std::size_t>::type>

template<typename U , container_ctor_enabler = 0>

piranha::kronecker_monomial< T >::kronecker_monomial ( const U & c )

inlineexplicit

Constructor from container.

Note: This constructor is enabled only if U satisfies piranha::has_input_begin_end, and the value type of the iterator type of U can be safely cast to T.

This constructor will build internally a vector of values from the input container c, encode it and assign the result to the internal integer instance. The value type of the container is converted to T using piranha::safe_cast().

Parameters

c	the input container.

Exceptions

unspecified any exception thrown by kronecker_monomial::kronecker_monomial(Iterator, Iterator).

Definition at line 188 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [3/8]

template<typename T = std::make_signed<std::size_t>::type>

template<typename U , init_list_ctor_enabler = 0>

piranha::kronecker_monomial< T >::kronecker_monomial ( std::initializer_list list )

inlineexplicit

Constructor from initializer list.

Note: This constructor is enabled only if U can be safely cast to T.

Parameters

list	the input initializer list.

Exceptions

unspecified any exception thrown by kronecker_monomial::kronecker_monomial(Iterator, Iterator).

Definition at line 207 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [4/8]

template<typename T = std::make_signed<std::size_t>::type>

template<typename Iterator , it_ctor_enabler< Iterator > = 0>

piranha::kronecker_monomial< T >::kronecker_monomial	(	Iterator	begin,
		Iterator	end
	)

inlineexplicit

Constructor from range.

Note: This constructor is enabled only if Iterator is an input iterator whose value type is safely convertible to T.

This constructor will build internally a vector of values from the input iterators, encode it and assign the result to the internal integer instance. The value type of the iterator is converted to T using piranha::safe_cast().

Parameters

begin	the beginning of the range.
end	the end of the range.

Exceptions

unspecified

any exception thrown by:

piranha::kronecker_array::encode(),
piranha::safe_cast(),
piranha::static_vector::push_back(),
increment and dereference of the input iterators.

Definition at line 239 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [5/8]

template<typename T = std::make_signed<std::size_t>::type>

template<typename Iterator , it_ctor_enabler< Iterator > = 0>

piranha::kronecker_monomial< T >::kronecker_monomial	(	Iterator	begin,
		Iterator	end,
		const symbol_fset &	s
	)

inlineexplicit

Constructor from range and symbol set.

Note: This constructor is enabled only if Iterator is an input iterator whose value type is safely convertible to T.

This constructor is identical to the constructor from range. In addition, after construction it will also check that the distance between begin and end is equal to the size of s.

Parameters

begin	the beginning of the range.
end	the end of the range.
s	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the distance between `begin` and `end` is different from the size of `s`.
unspecified	any exception thrown by kronecker_monomial::kronecker_monomial(Iterator, Iterator)

Definition at line 261 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [6/8]

template<typename T = std::make_signed<std::size_t>::type>

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

inlineexplicit

Constructor from set of symbols.

After construction all exponents in the monomial will be zero.

Definition at line 276 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [7/8]

template<typename T = std::make_signed<std::size_t>::type>

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

inlineexplicit

Converting constructor.

This constructor is for use when converting from one term type to another in piranha::series. It will set the internal integer instance to the same value of other.

Parameters

other the construction argument.

Definition at line 284 of file kronecker_monomial.hpp.

◆ kronecker_monomial() [8/8]

template<typename T = std::make_signed<std::size_t>::type>

piranha::kronecker_monomial< T >::kronecker_monomial ( const T & n )

inlineexplicit

Constructor from T.

This constructor will initialise the internal integer instance to n.

Parameters

n	the value that will be used to construct the internal integer instance.

Definition at line 292 of file kronecker_monomial.hpp.

Member Function Documentation

◆ degree() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::kronecker_monomial< T >::degree ( const symbol_fset & args ) const

inline

Degree.

The type returned by this method is the type resulting from the addition of two instances of T.

Parameters

args	the reference piranha::symbol_fset.

Returns: the degree of the monomial.

Exceptions

std::overflow_error	if the computation of the degree overflows.
unspecified	any exception thrown by unpack().

Definition at line 432 of file kronecker_monomial.hpp.

◆ degree() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::kronecker_monomial< T >::degree	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial degree.

Partial degree of the monomial: only the symbols at the positions specified by p are considered. The type returned by this method is the type resulting from the addition of two instances of T.

Parameters

p	the positions of the symbols to be considered in the calculation of the degree.
args	the reference piranha::symbol_fset.

Returns: the summation of the exponents of the monomial at the positions specified by p.

Exceptions

std::invalid_argument	if the last element of `p`, if existing, is not less than the size of `args`.
std::overflow_error	if the computation of the degree overflows.
unspecified	any exception thrown by unpack().

Definition at line 473 of file kronecker_monomial.hpp.

◆ evaluate()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

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

inline

Evaluation.

Note

This method is available only if U satisfies the following requirements:

it can be used in piranha::math::pow() with the monomial exponents as powers, yielding a type eval_type,
eval_type is constructible from int,
eval_type is multipliable in place,
eval_type satisfies piranha::is_returnable.

The return value will be built by iteratively applying piranha::math::pow() using the values provided by values as bases and the values in the monomial as exponents. If the size of the monomial is zero, 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 the sizes of `values` and `args` differ.
unspecified	any exception thrown by: unpack(), the construction of the return type, piranha::math::pow() or the in-place multiplication operator of the return type.

Definition at line 858 of file kronecker_monomial.hpp.

◆ get_int()

template<typename T = std::make_signed<std::size_t>::type>

T piranha::kronecker_monomial< T >::get_int ( ) const

inline

Get internal instance.

Returns: value of the internal integer instance.

Definition at line 327 of file kronecker_monomial.hpp.

◆ hash()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Hash value.

Returns: the internal integer instance, cast to std::size_t.

Definition at line 543 of file kronecker_monomial.hpp.

◆ integrate()

template<typename T = std::make_signed<std::size_t>::type>

std::pair<T, kronecker_monomial> piranha::kronecker_monomial< T >::integrate	(	const std::string &	s,
		const symbol_fset &	args
	)		const

inline

Integration.

This method will return the antiderivative of this with respect to the symbol s. The result is a pair consisting of the exponent associated to s increased by one and the monomial itself after integration. If s is not in args, the returned monomial will have an extra exponent set to 1 in the same position s would have if it were added to args. If the exponent corresponding to s is -1, an error will be produced.

Parameters

s	the symbol with respect to which the integration will be calculated.
args	the reference piranha::symbol_fset.

Returns: the result of the integration.

Exceptions

std::invalid_argument	if the exponent associated to `s` is -1.
std::overflow_error	if the integration leads to integer overflow.
unspecified	any exception thrown by: unpack(), piranha::static_vector::push_back(), piranha::kronecker_array::encode().

Definition at line 780 of file kronecker_monomial.hpp.

◆ ipow_subs()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

std::vector<std::pair<ipow_subs_type<U>, kronecker_monomial> > piranha::kronecker_monomial< T >::ipow_subs	(	const symbol_idx &	p,
		const integer &	n,
		const U &	x,
		const symbol_fset &	args
	)		const

inline

Substitution of integral power.

Note

This method is enabled only if:

U can be raised to a piranha::integer power, yielding a type subs_type,
subs_type is constructible from int,
subs_type satisfies piranha::is_returnable.

This method will substitute the n-th power of the symbol at the position p with the quantity x. The return value is a vector containing a single pair in which the first element is the result of the substitution, and the second element the monomial after the substitution has been performed. If p is not less than the size of args, the return value will be (1,this) (i.e., the monomial is unchanged and the substitution yields 1).

The method will substitute also powers higher than n in absolute value. For instance, the substitution of y**2 with a in the monomial y**7 will produce a**3 * y, and the substitution of y**-2 with a in the monomial y**-7 will produce a**3 * y**-1.

Parameters

p	the position of the symbol that will be substituted.
n	the integral power that will be substituted.
x	the quantity that will be substituted.
args	the reference piranha::symbol_fset.

Returns: the result of substituting x for the n-th power of the symbol at the position p.

Exceptions

std::invalid_argument	is `n` is zero.
unspecified	any exception thrown by: unpack(), the construction of the return value, piranha::math::pow(), arithmetics on piranha::integer, piranha::kronecker_array::encode().

Definition at line 1003 of file kronecker_monomial.hpp.

◆ is_compatible()

template<typename T = std::make_signed<std::size_t>::type>

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

inlinenoexcept

Compatibility check.

A monomial is considered incompatible with a piranha::symbol_fset if any of these conditions holds:

the size of args is zero and the internal integer is not zero,
the size of args is equal to or larger than the size of the output of piranha::kronecker_array::get_limits(),
the internal integer is not within the limits reported by piranha::kronecker_array::get_limits().

Otherwise, the monomial is considered to be incompatible.

Parameters

args	the reference piranha::symbol_fset.

Returns: compatibility flag for the monomial.

Definition at line 346 of file kronecker_monomial.hpp.

◆ is_linear()

template<typename T = std::make_signed<std::size_t>::type>

std::pair<bool, symbol_idx> piranha::kronecker_monomial< T >::is_linear ( const symbol_fset & args ) const

inline

Detect linear monomial.

If the monomial is linear in a variable (i.e., all exponents are zero apart from a single unitary exponent), then this method will return a pair formed by the true value and the position, in args, of the linear variable. Otherwise, the returned value will be a pair formed by the false value and an unspecified position value.

Parameters

args	the reference piranha::symbol_fset.

Returns: a pair indicating if the monomial is linear.

Exceptions

unspecified any exception thrown by unpack().

Definition at line 581 of file kronecker_monomial.hpp.

◆ is_unitary()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Check if monomial is unitary.

Returns: true if all the exponents are zero, false otherwise.

Definition at line 409 of file kronecker_monomial.hpp.

◆ is_zero()

template<typename T = std::make_signed<std::size_t>::type>

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

inlinenoexcept

Zero check.

A monomial is never zero.

Returns: false.

Definition at line 371 of file kronecker_monomial.hpp.

◆ ldegree() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::kronecker_monomial< T >::ldegree ( const symbol_fset & args ) const

inline

Low degree (equivalent to the degree).

Parameters

args	the reference piranha::symbol_fset.

Returns: the output of degree(const symbol_fset &) const.

Exceptions

unspecified any exception thrown by degree(const symbol_fset &) const.

Definition at line 453 of file kronecker_monomial.hpp.

◆ ldegree() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::kronecker_monomial< T >::ldegree	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial low degree (equivalent to the partial degree).

Parameters

p	the positions of the symbols to be considered in the calculation of the degree.
args	the reference piranha::symbol_fset.

Returns: the output of degree(const symbol_idx_fset &, const symbol_fset &) const.

Exceptions

unspecified any exception thrown by degree(const symbol_idx_fset &, const symbol_fset &) const.

Definition at line 499 of file kronecker_monomial.hpp.

◆ merge_symbols()

template<typename T = std::make_signed<std::size_t>::type>

kronecker_monomial piranha::kronecker_monomial< 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 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.

For instance, given a piranha::kronecker_monomial containing the values [1,2,3,4], a symbol set args containing ["c","e","g","h"] and an insertion map ins_map containing the pairs [(0,["a","b"]),(1,["d"]),(2,["f"]),(4,["i"])], the output of this method will be [0,0,1,0,2,0,3,4,0]. That is, the symbols appearing in ins_map are merged into this with a value of zero at the specified positions.

Parameters

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

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

Exceptions

std::invalid_argument	in the following cases: the size of `ins_map` is zero, the last index in `ins_map` is greater than the size of `args`.
unspecified	any exception thrown by: unpack(), piranha::static_vector::push_back(), piranha::kronecker_array::encode().

Definition at line 401 of file kronecker_monomial.hpp.

◆ msgpack_convert()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U = kronecker_monomial, msgpack_convert_enabler = 0>

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

inline

Deserialize from msgpack object.

Note: This method is activated only if both T and piranha::kronecker_monomial::v_type satisfy piranha::has_msgpack_convert.

This method will deserialize o into this. In binary mode, no check is performed on the content of o, and calling this method will result in undefined behaviour if o does not contain a monomial serialized via msgpack_pack().

Parameters

o	msgpack object that will be deserialized.
f	serialization format.
s	reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the size of the deserialized array differs from the size of `s`.
unspecified	any exception thrown by: the constructor of piranha::kronecker_monomial from a container, piranha::msgpack_convert().

Definition at line 1151 of file kronecker_monomial.hpp.

◆ msgpack_pack()

template<typename T = std::make_signed<std::size_t>::type>

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

void piranha::kronecker_monomial< T >::msgpack_pack	(	msgpack::packer< Stream > &	packer,
		msgpack_format	f,
		const symbol_fset &	s
	)		const

inline

Serialize in msgpack format.

Note: This method is activated only if Stream satisfies piranha::is_msgpack_stream and both T and piranha::kronecker_monomial::v_type satisfy piranha::has_msgpack_pack.

This method will pack this into packer. The packed object is the internal integral instance in binary format, an array of exponents in portable format.

Parameters

packer	the target packer.
f	the serialization format.
s	reference piranha::symbol_fset.

Exceptions

unspecified any exception thrown by unpack() or piranha::msgpack_pack().

Definition at line 1122 of file kronecker_monomial.hpp.

◆ multiply()

template<typename T = std::make_signed<std::size_t>::type>

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

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

inlinestatic

Multiply terms with a Kronecker monomial 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. This method offers the basic exception safety guarantee. If Cf is an instance of piranha::mp_rational, then only the numerators of the coefficients will be multiplied.

Note that the key of the return value is generated directly from the addition of the values of the input keys. No check is performed for overflow of either the limits of the integral type or the limits of the Kronecker codification.

Parameters

res	the return value.
t1	the first argument.
t2	the second argument.

Exceptions

unspecified any exception thrown by piranha::math::mul3().

Definition at line 530 of file kronecker_monomial.hpp.

◆ operator!=()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Inequality operator.

Parameters

other the comparison argument.

Returns: the opposite of operator==().

Definition at line 564 of file kronecker_monomial.hpp.

◆ operator<()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Comparison operator.

Parameters

other comparison argument.

Returns: true if the internal integral value of this is less than the internal integral value of other, false otherwise.

Definition at line 1089 of file kronecker_monomial.hpp.

◆ operator=() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

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

default

Copy assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator=() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

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

default

Defaulted move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator==()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Equality operator.

Parameters

other the comparison argument.

Returns: true if the internal integral instance of this is equal to the integral instance of other, false otherwise.

Definition at line 554 of file kronecker_monomial.hpp.

◆ partial()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Partial derivative.

This method will return the partial derivative of this with respect to the symbol at the position indicated by p. The result is a pair consisting of the exponent associated to p before differentiation and the monomial itself after differentiation. If p is not smaller than the size of args or if its corresponding exponent is zero, the returned pair will be (0,kronecker_monomial{args}).

Parameters

p	the position of the symbol with respect to which the differentiation will be calculated.
args	the reference piranha::symbol_fset.

Returns: the result of the differentiation.

Exceptions

std::overflow_error	if the computation of the derivative causes a negative overflow.
unspecified	any exception thrown by: unpack(), piranha::kronecker_array::encode().

Definition at line 740 of file kronecker_monomial.hpp.

◆ pow()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U , pow_enabler = 0>

kronecker_monomial piranha::kronecker_monomial< T >::pow	(	const U &	x,
		const symbol_fset &	args
	)		const

inline

Exponentiation.

This method will return a monomial corresponding to this raised to the x-th power. The exponentiation is computed via the multiplication of the exponents by x. The multiplication is performed in different ways, depending on the type U:

if U is a C++ integral type, then the multiplication is checked for overflow; otherwise,
if the multiplication of T by U results in another type T2, then the multiplication is performed via the binary multiplication operator and the result is cast back to T via piranha::safe_cast().

If the type U cannot be used as indicated above (e.g., because the multiplication of T by U is not available, or T2 does not support piranha::safe_cast()), then the method will be disabled.

Parameters

x	the exponent.
args	the reference piranha::symbol_fset.

Returns: this to the power of x.

Exceptions

std::overflow_error	if `U` is an integral type and the exponentiation causes overflow.
unspecified	any exception thrown by: unpack(), the multiplication of the monomial's exponents by `x`, piranha::safe_cast(), piranha::kronecker_array::encode().

Definition at line 635 of file kronecker_monomial.hpp.

◆ print()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Print.

This method will print to stream a human-readable representation of the monomial.

Parameters

os	the target stream.
args	the reference piranha::symbol_fset.

Exceptions

unspecified any exception thrown by unpack() or by streaming instances of T.

Definition at line 669 of file kronecker_monomial.hpp.

◆ print_tex()

template<typename T = std::make_signed<std::size_t>::type>

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

inline

Print in TeX mode.

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

Parameters

os	the target stream.
args	the reference piranha::symbol_fset.

Exceptions

unspecified any exception thrown by unpack() or by streaming instances of T.

Definition at line 697 of file kronecker_monomial.hpp.

◆ set_int()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::kronecker_monomial< T >::set_int ( const T & n )

inline

Set the internal integer instance.

Parameters

n	the value to which the internal integer instance will be set.

Definition at line 319 of file kronecker_monomial.hpp.

◆ subs()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

std::vector<std::pair<subs_type<U>, kronecker_monomial> > piranha::kronecker_monomial< T >::subs	(	const symbol_idx_fmap< U > &	smap,
		const symbol_fset &	args
	)		const

inline

Substitution.

Note

This method is available only if U satisfies the following requirements:

it can be used in piranha::math::pow() with the monomial exponents as powers, yielding a type subs_type,
subs_type is constructible from int,
subs_type is multipliable in place,
subs_type satisfies piranha::is_returnable.

This method will substitute the symbols at the positions specified in the keys of smap with the mapped values. The return value is a vector containing one pair in which the first element is the result of the substitution (i.e., the product of the values of smap raised to the corresponding exponents in the monomial), and the second element is the monomial after the substitution has been performed (i.e., with the exponents at the positions specified by the keys of smap set to zero). If smap is empty, the return value will be (1,this) (i.e., the monomial is unchanged and the substitution yields 1).

For instance, given the monomial [2,3,4], the reference piranha::symbol_fset ["x","y","z"] and the substitution map [(0,1),(2,-3)], then the return value will be a vector containing the single pair (81,[0,3,0]).

Parameters

smap	the map relating the positions of the symbols to be substituted to the values they will be substituted with.
args	the reference piranha::symbol_fset.

Returns: the result of the substitution.

Exceptions

std::invalid_argument	if the last element of the substitution map is not smaller than the size of `args`.
unspecified	any exception thrown by: unpack(), the construction of the return value, piranha::math::pow() or the in-place multiplication operator of the return type, piranha::kronecker_array::encode().

Definition at line 923 of file kronecker_monomial.hpp.

◆ trim()

template<typename T = std::make_signed<std::size_t>::type>

kronecker_monomial piranha::kronecker_monomial< 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) elements of this to be removed. The method will return a copy of this in which the specified elements have been removed.

For instance, if this contains the values [0,5,3,0,4] and trim_mask contains the values [false,false,false,true,false], then the output of this method will be the array of values [0,5,3,4] (that is, the fourth element has been removed as indicated by a true value in trim_mask's fourth element).

Parameters

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

Returns: a trimmed copy of this.

Exceptions

std::invalid_argument	if the size of `trim_mask` differs from the size of `args`.
unspecified	any exception thrown by unpack() or piranha::static_vector::push_back().

Definition at line 1078 of file kronecker_monomial.hpp.

◆ trim_identify()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::kronecker_monomial< 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 (i.e., a zero value means that the symbol at the corresponding position in args is not a candidate for trimming, while a nonzero value means that the symbol is a candidate for trimming). This method will set to zero those values in trim_mask for which the corresponding element in this is nonzero.

For instance, if this contains the values [0,5,3,0,4] and trim_mask originally contains the values [1,1,0,1,0], after a call to this method trim_mask will contain [1,0,0,1,0] (that is, the second element was set from 1 to 0 as the corresponding element in this has a value of 5 and thus must not be trimmed).

Parameters

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

Exceptions

std::invalid_argument	if the size of `trim_mask` differs from the size of `args`.
unspecified	any exception thrown by unpack().

Definition at line 1054 of file kronecker_monomial.hpp.

◆ unpack()

template<typename T = std::make_signed<std::size_t>::type>

v_type piranha::kronecker_monomial< T >::unpack ( const symbol_fset & args ) const

inline

Unpack internal integer instance.

This method will decode the internal integral instance into a piranha::static_vector of size equal to the size of args.

Parameters

args	the reference piranha::symbol_fset.

Returns: piranha::static_vector containing the result of decoding the internal integral instance via piranha::kronecker_array.

Exceptions

std::invalid_argument	if the size of `args` is larger than the maximum size of piranha::static_vector.
unspecified	any exception thrown by piranha::kronecker_array::decode().

Definition at line 656 of file kronecker_monomial.hpp.

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

kronecker_monomial.hpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename T = std::make_signed<std::size_t>::type> class piranha::kronecker_monomial< T >

Type requirements

Exception safety guarantee

Move semantics

Member Typedef Documentation

◆ size_type

Constructor & Destructor Documentation

◆ kronecker_monomial() [1/8]

◆ kronecker_monomial() [2/8]

◆ kronecker_monomial() [3/8]

◆ kronecker_monomial() [4/8]

◆ kronecker_monomial() [5/8]

◆ kronecker_monomial() [6/8]

◆ kronecker_monomial() [7/8]

◆ kronecker_monomial() [8/8]

Member Function Documentation

◆ degree() [1/2]

◆ degree() [2/2]

◆ evaluate()

◆ get_int()

◆ hash()

◆ integrate()

◆ ipow_subs()

◆ is_compatible()

◆ is_linear()

◆ is_unitary()

◆ is_zero()

◆ ldegree() [1/2]

◆ ldegree() [2/2]

◆ merge_symbols()

◆ msgpack_convert()

◆ msgpack_pack()

◆ multiply()

◆ operator!=()

◆ operator<()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ partial()

◆ pow()

◆ print()

◆ print_tex()

◆ set_int()

◆ subs()

◆ trim()

◆ trim_identify()

◆ unpack()

template<typename T = std::make_signed<std::size_t>::type>
class piranha::kronecker_monomial< T >