Monomial class. More...

#include <piranha/monomial.hpp>

Inheritance diagram for piranha::monomial< T, S >:

Collaboration diagram for piranha::monomial< T, S >:

Public Types
using	container_type = small_vector< T, S >
	The internal container type.

using	value_type = typename container_type::value_type
	Value type.

using	iterator = typename container_type::iterator
	Iterator type.

using	const_iterator = typename container_type::const_iterator
	Const iterator type.

using	size_type = typename container_type::size_type
	Size type.

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

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

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

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

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

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

	~monomial ()
	Destructor.

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

monomial &	operator= (monomial &&other)=default
	Defaulted move assignment operator. 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 &args) const
	Check if the monomial is unitary. More...

template<typename U = T>
degree_type< U >	degree (const symbol_fset &args) const
	Degree. More...

template<typename U = T>
degree_type< U >	degree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial degree. More...

template<typename U = T>
degree_type< U >	ldegree (const symbol_fset &args) const
	Low degree (equivalent to the degree). More...

template<typename U = T>
degree_type< U >	ldegree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial low degree (equivalent to the partial degree). More...

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

template<typename U , pow_enabler< U > = 0>
monomial	pow (const U &x, const symbol_fset &args) const
	Monomial exponentiation. More...

template<typename U = T, partial_enabler< U > = 0>
std::pair< T, monomial >	partial (const symbol_idx &p, const symbol_fset &args) const
	Partial derivative. More...

template<typename U = T, integrate_enabler< U > = 0>
std::pair< T, monomial >	integrate (const std::string &s, const symbol_fset &args) const
	Integration. 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...

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 >, 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 >, monomial > >	ipow_subs (const symbol_idx &p, const integer &n, const U &x, const symbol_fset &args) const
	Substitution of integral power. More...

bool	operator< (const 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 = 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...

iterator	begin ()
	Begin iterator. More...

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

iterator	end ()
	End iterator. More...

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

size_type	size () const
	Size. More...

void	resize (const size_type &new_size)
	Resize the internal array container. More...

value_type &	operator[] (const size_type &i)
	Element access. More...

const value_type &	operator[] (const size_type &i) const
	Const element access. More...

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

void	push_back (value_type &&x)
	Move-add element at the end. More...

void	push_back (const value_type &x)
	Copy-add element at the end. More...

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

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

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

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

void	vector_add (array_key &retval, const array_key &other) const
	Vector add. More...

void	vector_sub (array_key &retval, const array_key &other) const
	Vector sub. More...

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

auto	size_begin_end () const -> decltype(m_container.size_begin_end())
	Get size, begin and end iterator (const version). More...

auto	size_begin_end () -> decltype(m_container.size_begin_end())
	Get size, begin and end iterator. More...

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

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

Protected Attributes
container_type	m_container
	Internal container.

Detailed Description

template<typename T, typename S = std::integral_constant<std::size_t, 0u>>
class piranha::monomial< T, S >

Monomial class.

This class extends piranha::array_key to define a series key type representing monomials, that is, objects of the form:

\[ x_0^{y_0} \cdot x_1^{y_1} \cdot \ldots \cdot x_n^{y_n}. \]

The type T represents the type of the exponents \( y_i \), which are stored in a flat array.

This class satisfies the piranha::is_key type trait.

Type requirements

T and S must be suitable for use as first and third template arguments in piranha::array_key. Additionally, T must be copy-assignable and it must satisfy the following type-traits:

Exception safety guarantee

Unless noted otherwise, this class provides the same exception safety guarantee as piranha::array_key.

Move semantics

Move semantics is equivalent to piranha::array_key's move semantics.

Definition at line 100 of file monomial.hpp.

Constructor & Destructor Documentation

◆ monomial() [1/3]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U , init_list_enabler = 0>

piranha::monomial< T, S >::monomial ( std::initializer_list list )

inlineexplicit

Constructor from initializer list.

Note: This constructor is enabled only if the corresponding constructor in piranha::array_key is enabled.

Parameters

list	initializer list.

See also: piranha::array_key's constructor from initializer list.

Definition at line 137 of file monomial.hpp.

◆ monomial() [2/3]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

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

piranha::monomial< T, S >::monomial	(	Iterator	begin,
		Iterator	end
	)

inlineexplicit

Constructor from range.

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

This constructor will copy the elements from the range defined by begin and end into this, using piranha::safe_cast() for any necessary type conversion.

Parameters

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

Exceptions

unspecified

any exception thrown by:

Definition at line 167 of file monomial.hpp.

◆ monomial() [3/3]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

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

piranha::monomial< T, S >::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 can be cast safely to T.

This constructor will copy the elements from the range defined by begin and end into this, using piranha::safe_cast() for any necessary type conversion. If the final size of this is different from the size of s, a runtime error will be produced. This constructor is used by piranha::polynomial::find_cf().

Parameters

begin	beginning of the range.
end	end of the range.
s	reference symbol set.

Exceptions

std::invalid_argument	if the final size of `this` and the size of `s` differ.
unspecified	any exception thrown by: piranha::safe_cast(), push_back().

Definition at line 194 of file monomial.hpp.

Member Function Documentation

◆ begin() [1/2]

iterator piranha::array_key< T, monomial< T, S > , S >::begin ( )

inlineinherited

Begin iterator.

Returns: iterator to the first element of the internal container.

Definition at line 222 of file array_key.hpp.

◆ begin() [2/2]

const_iterator piranha::array_key< T, monomial< T, S > , S >::begin ( ) const

inlineinherited

Begin const iterator.

Returns: const iterator to the first element of the internal container.

Definition at line 238 of file array_key.hpp.

◆ degree() [1/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T>

degree_type piranha::monomial< T, S >::degree ( const symbol_fset & args ) const

inline

Degree.

Note

This method is enabled only if:

T is addable, yielding a type degree_type,
degree_type is constructible from int,
monomial::value_type can be added in-place to degree_type,
degree_type satisfies piranha::is_returnable.

This method will return the degree of the monomial, computed via the summation of the exponents of the monomial. If T is a C++ integral type, the addition of the exponents will be checked for overflow.

Parameters

args	reference piranha::symbol_fset.

Returns: the degree of the monomial.

Exceptions

std::invalid_argument	if the sizes of `args` and `this` differ.
std::overflow_error	if the exponent type is a C++ integral type and the computation of the degree overflows.
unspecified	any exception thrown by the invoked constructor or arithmetic operators.

Definition at line 313 of file monomial.hpp.

◆ degree() [2/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T>

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

inline

Partial degree.

Note

This method is enabled only if:

T is addable, yielding a type degree_type,
degree_type is constructible from int,
monomial::value_type can be added in-place to degree_type,
degree_type satisfies piranha::is_returnable.

This method will return the partial degree of the monomial, computed via the summation of the exponents of the monomial. If T is a C++ integral type, the addition of the exponents will be checked for overflow.

The p argument is used to indicate the positions of the exponents to be taken into account when computing the partial degree. Exponents at positions not present in p will be discarded during the computation of the partial degree.

Parameters

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

Returns: the partial degree of the monomial.

Exceptions

std::invalid_argument	if the sizes of `args` and `this` differ, or if the largest value in `p` is not less than the size of the monomial.
std::overflow_error	if the exponent type is a C++ integral type and the computation of the degree overflows.
unspecified	any exception thrown by the invoked constructor or arithmetic operators.

Definition at line 357 of file monomial.hpp.

◆ end() [1/2]

iterator piranha::array_key< T, monomial< T, S > , S >::end ( )

inlineinherited

End iterator.

Returns: iterator one past the last element of the internal container.

Definition at line 230 of file array_key.hpp.

◆ end() [2/2]

const_iterator piranha::array_key< T, monomial< T, S > , S >::end ( ) const

inlineinherited

End const iterator.

Returns: const iterator one past the last element of the internal container.

Definition at line 246 of file array_key.hpp.

◆ evaluate()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U >

eval_type<U> piranha::monomial< T, S >::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, or if the sizes of `this` and `args` differ.
unspecified	any exception thrown by: the construction of the return type, math::pow() or the in-place multiplication operator of the return type.

Definition at line 846 of file monomial.hpp.

◆ hash()

std::size_t piranha::array_key< T, monomial< T, S > , S >::hash ( ) const

inlineinherited

Hash value.

Returns: hash value of the key, computed via piranha::small_vector::hash().

Exceptions

unspecified any exception thrown by piranha::small_vector::hash().

Definition at line 296 of file array_key.hpp.

◆ integrate()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T, integrate_enabler = 0>

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

inline

Integration.

Note: This method is enabled only if the exponent type supports the pre-increment operator.

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.

If the exponent type is an integral type, then the increment-by-one operation on the affected exponent is checked for negative overflow.

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 sizes of `args` and `this` differ, or if the exponent associated to `s` is -1.
std::overflow_error	if `T` is a C++ integral type and the integration leads to integer overflow.
unspecified	any exception thrown by: piranha::math::is_zero(), exponent construction, push_back(), the exponent type's pre-increment operator.

Definition at line 654 of file monomial.hpp.

◆ ipow_subs()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U >

std::vector<std::pair<ipow_subs_type<U>, monomial> > piranha::monomial< T, S >::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,
the exponent type can be safely cast to piranha::integer, and piranha::integer can be safely cast to the exponent type.

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, or if the sizes of `args` and `this` differ.
unspecified	any exception thrown by: the construction of the return value, piranha::safe_cast(), piranha::math::pow(), arithmetics on piranha::integer, the copy assignment operator of the exponent type, memory errors in standard containers.

Definition at line 1044 of file monomial.hpp.

◆ is_compatible()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

bool piranha::monomial< T, S >::is_compatible ( const symbol_fset & args ) const

inlinenoexcept

Compatibility check.

A monomial and a set of arguments are compatible if their sizes coincide.

Parameters

args	reference piranha::symbol_fset.

Returns: true if the size of this is equal to the size of args, false otherwise.

Definition at line 235 of file monomial.hpp.

◆ is_linear()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

std::pair<bool, symbol_idx> piranha::monomial< T, S >::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

std::invalid_argument	if the sizes of `this` and `args` differ.
unspecified	any exception thrown by piranha::math::is_zero() or piranha::math::is_unitary().

Definition at line 421 of file monomial.hpp.

◆ is_unitary()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

bool piranha::monomial< T, S >::is_unitary ( const symbol_fset & args ) const

inline

Check if the monomial is unitary.

A monomial is unitary if, for all its elements, piranha::math::is_zero() returns true.

Parameters

args	reference piranha::symbol_fset.

Returns: true if the monomial is unitary, false otherwise.

Exceptions

std::invalid_argument	if the sizes of `args` and `this` differ.
unspecified	any exception thrown by piranha::math::is_zero().

Definition at line 260 of file monomial.hpp.

◆ is_zero()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

bool piranha::monomial< T, S >::is_zero ( const symbol_fset & ) const

inlinenoexcept

Zero check.

A monomial is never zero.

Returns: false.

Definition at line 245 of file monomial.hpp.

◆ ldegree() [1/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T>

degree_type piranha::monomial< T, S >::ldegree ( const symbol_fset & args ) const

inline

Low degree (equivalent to the degree).

Parameters

args	reference piranha::symbol_fset.

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

Exceptions

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

Definition at line 389 of file monomial.hpp.

◆ ldegree() [2/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T>

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

inline

Partial low degree (equivalent to the partial degree).

Parameters

p	positions of the symbols to be considered.
args	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 403 of file monomial.hpp.

◆ merge_symbols()

monomial< T, S > piranha::array_key< T, monomial< T, S > , S >::merge_symbols	(	const symbol_idx_fmap< symbol_fset > &	ins_map,
		const symbol_fset &	args
	)		const

inlineinherited

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::array_key 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 Derived instance resulting from inserting into this zeroes at the positions specified by ins_map.

Exceptions

std::invalid_argument	in the following cases: the size 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 `this`.
unspecified	any exception thrown by: piranha::small_vector::push_back(), the construction of instances of type array_key::value_type from the integral constant 0.

Definition at line 508 of file array_key.hpp.

◆ msgpack_convert()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = monomial, msgpack_convert_enabler = 0>

void piranha::monomial< T, S >::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 the internal container type satisfies piranha::has_msgpack_convert.

This method will deserialize o into this using the format f. This method provides the basic exception safety guarantee.

Parameters

o	msgpack object that will be deserialized.
f	serialization format.
s	the 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 piranha::msgpack_convert().

Definition at line 1219 of file monomial.hpp.

◆ msgpack_pack()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

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

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

inline

Serialize 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 into packer using the format f.

Parameters

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

Exceptions

std::invalid_argument	if the sizes of `s` and `this` differ.
unspecified	any exception thrown by piranha::msgpack_pack().

Definition at line 1192 of file monomial.hpp.

◆ multiply()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

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

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

inlinestatic

Multiply terms with a monomial key.

Note

This method is enabled only if the following conditions hold:

T satisfies piranha::has_add3,
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 size of `t1` differs from the size of `args`.
unspecified	any exception thrown by piranha::array_key::vector_add(), or by piranha::math::mul3().

Definition at line 1116 of file monomial.hpp.

◆ operator!=()

bool piranha::array_key< T, monomial< T, S > , S >::operator!= ( const array_key< T, monomial< T, S >, S > & other ) const

inlineinherited

Inequality operator.

Parameters

other the comparison argument.

Returns: the negation of operator==().

Exceptions

unspecified any exception thrown by the equality operator.

Definition at line 344 of file array_key.hpp.

◆ operator<()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

bool piranha::monomial< T, S >::operator< ( const monomial< T, S > & other ) const

inline

Comparison operator.

The two monomials will be compared lexicographically.

Parameters

other comparison argument.

Returns: true if this is lexicographically less than other, false otherwise.

Exceptions

std::invalid_argument	if the sizes of `this` and `other` differ.
unspecified	any exception thrown by `std::lexicographical_compare()`.

Definition at line 1143 of file monomial.hpp.

◆ operator=() [1/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

monomial& piranha::monomial< T, S >::operator= ( const monomial< T, S > & 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 the base class.

◆ operator=() [2/2]

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

monomial& piranha::monomial< T, S >::operator= ( monomial< T, S > && other )

default

Defaulted move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator==()

bool piranha::array_key< T, monomial< T, S > , S >::operator== ( const array_key< T, monomial< T, S >, S > & other ) const

inlineinherited

Equality operator.

Parameters

other the comparison argument.

Returns: the result of piranha::small_vector::operator==().

Exceptions

unspecified any exception thrown by piranha::small_vector::operator==().

Definition at line 332 of file array_key.hpp.

◆ operator[]() [1/2]

value_type& piranha::array_key< T, monomial< T, S > , S >::operator[] ( const size_type & i )

inlineinherited

Element access.

Parameters

i	the index of the element to be accessed.

Returns: reference to the element of the container at index i.

Definition at line 276 of file array_key.hpp.

◆ operator[]() [2/2]

const value_type& piranha::array_key< T, monomial< T, S > , S >::operator[] ( const size_type & i ) const

inlineinherited

Const element access.

Parameters

i	the index of the element to be accessed.

Returns: const reference to the element of the container at index i.

Definition at line 286 of file array_key.hpp.

◆ partial()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U = T, partial_enabler = 0>

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

inline

Partial derivative.

Note: This method is enabled only if the exponent type supports the pre-decrement operator.

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,monomial{args}).

If the exponent type is an integral type, then the decrement-by-one operation on the affected exponent is checked for negative overflow.

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::invalid_argument	if the sizes of `args` and `this` differ.
std::overflow_error	if the decrement of the affected exponent results in overflow.
unspecified	any exception thrown by: the construction of the return value, the exponent type's pre-decrement operator, piranha::math::is_zero().

Definition at line 566 of file monomial.hpp.

◆ pow()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U , pow_enabler = 0>

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

inline

Monomial 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 T and U are C++ integral types, then the multiplication is checked for overflow; otherwise,
if T and U are the same type, and they support math::mul3(), then math::mul3() is used to compute the product; otherwise,
if the multiplication of T by U produces a result of type T, then the binary multiplication operator is used to compute the product; 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, 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::invalid_argument	if the sizes of `args` and `this` differ.
std::overflow_error	if both `T` and `U` are integral types and the exponentiation results in overflow.
unspecified	any exception thrown by: the construction of a piranha::monomial, math::mul3(), the multiplication of the monomial's exponents by `x`, piranha::safe_cast().

Definition at line 489 of file monomial.hpp.

◆ print()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

void piranha::monomial< T, S >::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

std::invalid_argument	if the sizes of `args` and `this` differ.
unspecified	any exception resulting from: printing exponents to stream and the public interface of `os`, piranha::math::is_zero(), piranha::math::is_unitary().

Definition at line 732 of file monomial.hpp.

◆ print_tex()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

void piranha::monomial< T, S >::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

std::invalid_argument	if the sizes of `args` and `this` differ.
unspecified	any exception resulting from: construction, comparison and assignment of exponents, printing exponents to stream and the public interface of `os`, piranha::math::negate(), piranha::math::is_zero(), piranha::math::is_unitary().

Definition at line 771 of file monomial.hpp.

◆ push_back() [1/2]

void piranha::array_key< T, monomial< T, S > , S >::push_back ( value_type && x )

inlineinherited

Move-add element at the end.

Move-add x at the end of the internal container.

Parameters

x	the element to be added to the internal container.

Exceptions

unspecified any exception thrown by piranha::small_vector::push_back().

Definition at line 308 of file array_key.hpp.

◆ push_back() [2/2]

void piranha::array_key< T, monomial< T, S > , S >::push_back ( const value_type & x )

inlineinherited

Copy-add element at the end.

Copy-add x at the end of the internal container.

Parameters

x	the element to be added to the internal container.

Exceptions

unspecified any exception thrown by piranha::small_vector::push_back().

Definition at line 320 of file array_key.hpp.

◆ resize()

void piranha::array_key< T, monomial< T, S > , S >::resize ( const size_type & new_size )

inlineinherited

Resize the internal array container.

Equivalent to piranha::small_vector::resize().

Parameters

new_size the desired new size for the internal container.

Exceptions

unspecified any exception thrown by piranha::small_vector::resize().

Definition at line 266 of file array_key.hpp.

◆ size()

size_type piranha::array_key< T, monomial< T, S > , S >::size ( ) const

inlineinherited

Size.

Returns: number of elements stored within the container.

Definition at line 254 of file array_key.hpp.

◆ size_begin_end() [1/2]

auto piranha::array_key< T, monomial< T, S > , S >::size_begin_end ( ) const-> decltype(m_container.size_begin_end())

inlineinherited

Get size, begin and end iterator (const version).

Returns: the output of the piranha::small_vector::size_begin_end() method called on the internal piranha::small_vector container.

Definition at line 525 of file array_key.hpp.

◆ size_begin_end() [2/2]

auto piranha::array_key< T, monomial< T, S > , S >::size_begin_end ( ) -> decltype(m_container.size_begin_end())

inlineinherited

Get size, begin and end iterator.

Returns: the output of the piranha::small_vector::size_begin_end() method called on the internal piranha::small_vector container.

Definition at line 534 of file array_key.hpp.

◆ subs()

template<typename T , typename S = std::integral_constant<std::size_t, 0u>>

template<typename U >

std::vector<std::pair<subs_type<U>, monomial> > piranha::monomial< T, S >::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 eval_type,
eval_type is constructible from int,
eval_type is multipliable in place,
eval_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 `this`, or if the sizes of `this` and `args` differ.
unspecified	any exception thrown by: the construction of the return value, the construction of an exponent from zero, the copy assignment of the exponent type, piranha::math::pow() or the in-place multiplication operator of the return type, memory errors in standard containers.

Definition at line 915 of file monomial.hpp.

◆ trim()

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

inlineinherited

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 elements will be removed.
args	the reference piranha::symbol_fset.

Returns: a trimmed copy of this.

Exceptions

std::invalid_argument	if the sizes of `this` or `trim_mask` differ from the size of `args`.
unspecified	any exception thrown by push_back().

Definition at line 409 of file array_key.hpp.

◆ trim_identify()

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

inlineinherited

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. 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 it 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 sizes of `this` or `trim_mask` differ from the size of `args`.
unspecified	any exception thrown by piranha::math::is_zero().

Definition at line 367 of file array_key.hpp.

◆ vector_add()

void piranha::array_key< T, monomial< T, S > , S >::vector_add	(	array_key< T, monomial< T, S >, S > &	retval,
		const array_key< T, monomial< T, S >, S > &	other
	)		const

inlineinherited

Vector add.

Note: This method is enabled only if the call to piranha::small_vector::add() is well-formed.

Equivalent to calling piranha::small_vector::add() on the internal containers of this and of the arguments.

Parameters

retval	the piranha::array_key that will hold the result of the addition.
other	the piranha::array_key that will be added to `this`.

Exceptions

unspecified any exception thrown by piranha::small_vector::add().

Definition at line 459 of file array_key.hpp.

◆ vector_sub()

void piranha::array_key< T, monomial< T, S > , S >::vector_sub	(	array_key< T, monomial< T, S >, S > &	retval,
		const array_key< T, monomial< T, S >, S > &	other
	)		const

inlineinherited

Vector sub.

Note: This method is enabled only if the call to piranha::small_vector::sub() is well-formed.

Equivalent to calling piranha::small_vector::sub() on the internal containers of this and of the arguments.

Parameters

retval	the piranha::array_key that will hold the result of the subtraction.
other	the piranha::array_key that will be subtracted from `this`.

Exceptions

unspecified any exception thrown by piranha::small_vector::sub().

Definition at line 478 of file array_key.hpp.

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

monomial.hpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

template<typename T, typename S = std::integral_constant<std::size_t, 0u>> class piranha::monomial< T, S >

Type requirements

Exception safety guarantee

Move semantics

Constructor & Destructor Documentation

◆ monomial() [1/3]

◆ monomial() [2/3]

◆ monomial() [3/3]

Member Function Documentation

◆ begin() [1/2]

◆ begin() [2/2]

◆ degree() [1/2]

◆ degree() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ evaluate()

◆ 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==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ partial()

◆ pow()

◆ print()

◆ print_tex()

◆ push_back() [1/2]

◆ push_back() [2/2]

◆ resize()

◆ size()

◆ size_begin_end() [1/2]

◆ size_begin_end() [2/2]

◆ subs()

◆ trim()

◆ trim_identify()

◆ vector_add()

◆ vector_sub()

template<typename T, typename S = std::integral_constant<std::size_t, 0u>>
class piranha::monomial< T, S >