#include <mul.h>

Inheritance diagram for SymEngine::Mul:

Collaboration diagram for SymEngine::Mul:

Public Member Functions
void	accept (Visitor &v) const override

void	accept (EvalRealDoubleVisitorFinal &v) const override

	Mul (const RCP< const Number > &coef, map_basic_basic &&dict)

hash_t	__hash__ () const override

bool	__eq__ (const Basic &o) const override

int	compare (const Basic &o) const override

void	as_two_terms (const Ptr< RCP< const Basic >> &a, const Ptr< RCP< const Basic >> &b) const
	Rewrite as 2 terms. More...

void	power_num (const Ptr< RCP< const Number >> &coef, map_basic_basic &d, const RCP< const Number > &exp) const
	Power all terms with the exponent `exp`

bool	is_canonical (const RCP< const Number > &coef, const map_basic_basic &dict) const

vec_basic	get_args () const override
	Returns the list of arguments.

const RCP< const Number > &	get_coef () const

const map_basic_basic &	get_dict () const

Public Member Functions inherited from SymEngine::Basic
TypeID	get_type_code () const

	Basic ()
	Constructor.

	Basic (const Basic &)=delete
	Delete the copy constructor and assignment.

Basic &	operator= (const Basic &)=delete
	Assignment operator in continuation with above.

	Basic (Basic &&)=delete
	Delete the move constructor and assignment.

Basic &	operator= (Basic &&)=delete
	Assignment operator in continuation with above.

hash_t	hash () const

bool	__neq__ (const Basic &o) const
	true if `this` is not equal to `o`. More...

int	__cmp__ (const Basic &o) const
	Comparison operator.

std::string	__str__ () const

std::string	dumps () const
	Returns a string of the instance serialized.

RCP< const Basic >	subs (const map_basic_basic &subs_dict) const
	Substitutes 'subs_dict' into 'self'.

RCP< const Basic >	xreplace (const map_basic_basic &subs_dict) const

virtual RCP< const Basic >	expand_as_exp () const
	expands the special function in terms of exp function

RCP< const Basic >	diff (const RCP< const Symbol > &x, bool cache=true) const

Public Member Functions inherited from SymEngine::EnableRCPFromThis< Basic >
RCP< Basic >	rcp_from_this ()
	Get RCP<T> pointer to self (it will cast the pointer to T)

RCP< const Basic >	rcp_from_this () const
	Get RCP<const T> pointer to self (it will cast the pointer to const T)

RCP< const T2 >	rcp_from_this_cast () const
	Get RCP<T2> pointer to self (it will cast the pointer to T2)

unsigned int	use_count () const

Static Public Member Functions
static RCP< const Basic >	from_dict (const RCP< const Number > &coef, map_basic_basic &&d)
	Create a Mul from a dict.

static void	dict_add_term (map_basic_basic &d, const RCP< const Basic > &exp, const RCP< const Basic > &t)
	Add terms to dict.

static void	dict_add_term_new (const Ptr< RCP< const Number >> &coef, map_basic_basic &d, const RCP< const Basic > &exp, const RCP< const Basic > &t)

static void	as_base_exp (const RCP< const Basic > &self, const Ptr< RCP< const Basic >> &exp, const Ptr< RCP< const Basic >> &base)
	Convert to a base and exponent form.

Static Public Member Functions inherited from SymEngine::Basic
static RCP< const Basic >	loads (const std::string &)
	Creates an instance of a serialized string.

Static Public Attributes
static const TypeID	type_code_id = SYMENGINE_MUL
	the dictionary of the rest (e.g. `xy` in `2x*y`) More...

Private Attributes
RCP< const Number >	coef_

map_basic_basic	dict_
	The coefficient (e.g. `2` in `2xy`)

Additional Inherited Members
Data Fields inherited from SymEngine::Basic
TypeID	type_code_

Detailed Description

Mul class keeps a product of symbolic expressions. Internal representation of an Mul is a numeric coefficient coef_ and a dictionary dict_ of key-value pairs.

 Mul(coef_, {{key1, value1}, {key2, value2}, ... })

This represents the following expression,

 coef_ * key1^value1 * key2^value2 * ...

coef_ is an objecct of type Number, i.e. a numeric coefficient like Integer, RealDouble, Complex.

For example, the following are valid representations

 Mul(2, {{x, 2}, {y, 5}})
 Mul(3, {{x, 1}, {y, 4}, {z, 3}})

Following are invalid representations. (valid equivalent is shown next to them)

When key is a numeric and value is an integers,

Mul(2, {{3, 2}, {x, 2}}) -> Mul(18, {{x, 2}}) Mul(2, {{I, 3}, {x, 2}}) -> Mul(-2*I, {{x, 2}})

When key is an integer and value is a Rational not in the range (0, 1)

Mul(2, {{3, 3/2}, {x, 2}}) -> Mul(6, {{3, 1/2}, {x, 2}}) Mul(2, {{3, -1/2}, {x, 2}}) -> Mul(2/3, {{3, 1/2}, {x, 2}})

When the value is zero

Mul(3, {{x, 0}, {y, 2}}) -> Mul(3, {{y, 2}})

When key and value are numeric and one of them is inexact

Mul(2, {{3, 0.5}, {x, 2}}) -> Mul(3.464..., {x, 2}})

When coef_ is one and the dictionary is of size 1

Mul(1, {{x, 2}}) -> Pow(x, 2)

When coef_ is zero

Mul(0, {{x, 2}}) -> Integer(0) Mul(0.0, {{x, 2}}) -> RealDouble(0.0)

When key is 1

Mul(2, {{1, x}, {x, 2}}) -> Mul(2, {{x, 2}})

When value is zero

Mul(2, {{1, x}, {x, 2}}) -> Mul(2, {{x, 2}})

Definition at line 73 of file mul.h.

Constructor & Destructor Documentation

◆ Mul()

SymEngine::Mul::Mul	(	const RCP< const Number > &	coef,
		map_basic_basic &&	dict
	)

Constructs Mul from a dictionary by copying the contents of the dictionary:

Definition at line 10 of file mul.cpp.

     : coef_{coef}, dict_{std::move(dict)}
 {
     SYMENGINE_ASSIGN_TYPEID()
     SYMENGINE_ASSERT(is_canonical(coef, dict_))
 }

Member Function Documentation

◆ eq()

bool SymEngine::Mul::__eq__ ( const Basic & o ) const

overridevirtual

Equality comparator

Parameters

o	- Object to be compared with

Returns: whether the 2 objects are equal

Implements SymEngine::Basic.

Definition at line 89 of file mul.cpp.

 {
     if (is_a<Mul>(o) and eq(*coef_, *(down_cast<const Mul &>(o).coef_))
         and unified_eq(dict_, down_cast<const Mul &>(o).dict_))
         return true;
  
     return false;
 }

◆ hash()

hash_t SymEngine::Mul::__hash__ ( ) const

overridevirtual

Returns: size of the hash

Implements SymEngine::Basic.

Definition at line 78 of file mul.cpp.

 {
     hash_t seed = SYMENGINE_MUL;
     hash_combine<Basic>(seed, *coef_);
     for (const auto &p : dict_) {
         hash_combine<Basic>(seed, *(p.first));
         hash_combine<Basic>(seed, *(p.second));
     }
     return seed;
 }

◆ as_two_terms()

void SymEngine::Mul::as_two_terms	(	const Ptr< RCP< const Basic >> &	a,
		const Ptr< RCP< const Basic >> &	b
	)		const

Rewrite as 2 terms.

Example: if this=3*x**2*y**2*z**2, thena=x**2andb=3*y**2*z**2`

Definition at line 309 of file mul.cpp.

 {
     // Example: if this=3*x**2*y**2*z**2, then a=x**2 and b=3*y**2*z**2
     auto p = dict_.begin();
     *a = pow(p->first, p->second);
     map_basic_basic d = dict_;
     d.erase(p->first);
     *b = Mul::from_dict(coef_, std::move(d));
 }

◆ compare()

int SymEngine::Mul::compare ( const Basic & o ) const

overridevirtual

Returns -1, 0, 1 for this < o, this == o, this > o. This method is used when you want to sort things like x+y+z into canonical order. This function assumes that o is the same type as this. Use __cmp__ if you want general comparison.

Implements SymEngine::Basic.

Definition at line 98 of file mul.cpp.

 {
     SYMENGINE_ASSERT(is_a<Mul>(o))
     const Mul &s = down_cast<const Mul &>(o);
     // # of elements
     if (dict_.size() != s.dict_.size())
         return (dict_.size() < s.dict_.size()) ? -1 : 1;
  
     // coef
     int cmp = coef_->__cmp__(*s.coef_);
     if (cmp != 0)
         return cmp;
  
     // Compare dictionaries:
     return unified_compare(dict_, s.dict_);
 }

◆ is_canonical()

bool SymEngine::Mul::is_canonical	(	const RCP< const Number > &	coef,
		const map_basic_basic &	dict
	)		const

Returns: true if both coef and dict are in canonical form

Definition at line 17 of file mul.cpp.

 {
     if (coef == null)
         return false;
     // e.g. 0*x*y
     if (coef->is_zero())
         return false;
     if (dict.size() == 0)
         return false;
     if (dict.size() == 1) {
         // e.g. 1*x, 1*x**2
         if (coef->is_one())
             return false;
     }
     // Check that each term in 'dict' is in canonical form
     for (const auto &p : dict) {
         if (p.first == null)
             return false;
         if (p.second == null)
             return false;
         // e.g. 2**3, (2/3)**4
         // However for Complex no simplification is done
         if ((is_a<Integer>(*p.first) or is_a<Rational>(*p.first))
             and is_a<Integer>(*p.second))
             return false;
         // e.g. 0**x
         if (is_a<Integer>(*p.first)
             and down_cast<const Integer &>(*p.first).is_zero())
             return false;
         // e.g. 1**x
         if (is_a<Integer>(*p.first)
             and down_cast<const Integer &>(*p.first).is_one())
             return false;
         // e.g. x**0
         if (is_a_Number(*p.second)
             and down_cast<const Number &>(*p.second).is_zero())
             return false;
         // e.g. (x*y)**2 (={xy:2}), which should be represented as x**2*y**2
         //     (={x:2, y:2})
         if (is_a<Mul>(*p.first)) {
             if (is_a<Integer>(*p.second))
                 return false;
             if (is_a_Number(*p.second)
                 and neq(*down_cast<const Mul &>(*p.first).coef_, *one)
                 and neq(*down_cast<const Mul &>(*p.first).coef_, *minus_one))
                 return false;
         }
         // e.g. x**2**y (={x**2:y}), which should be represented as x**(2y)
         //     (={x:2y})
         if (is_a<Pow>(*p.first) && is_a<Integer>(*p.second))
             return false;
         // e.g. 0.5^2.0 should be represented as 0.25
         if (is_a_Number(*p.first) and is_a_Number(*p.second)
             and (not down_cast<const Number &>(*p.first).is_exact()
                  or not down_cast<const Number &>(*p.second).is_exact()))
             return false;
     }
     return true;
 }

Field Documentation

◆ type_code_id

const TypeID SymEngine::Mul::type_code_id = SYMENGINE_MUL

static

the dictionary of the rest (e.g. x*y in 2*x*y)

Type_code_id shared by all instances

Definition at line 81 of file mul.h.

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

/home/runner/work/symengine/symengine/symengine/mul.h
/home/runner/work/symengine/symengine/symengine/mul.cpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Mul()

Member Function Documentation

◆ __eq__()

◆ __hash__()

◆ as_two_terms()

◆ compare()

◆ is_canonical()

Field Documentation

◆ type_code_id

◆ eq()

◆ hash()