
typedefs Typedef SymEngine::vec_uint Quick search Class Mul¶ Defined in File mul.h Inheritance Relationships¶ Base Type¶ `public SymEngine::Basic` (Class Basic) Class Documentation¶ class `SymEngine::Mul` : public SymEngine::Basic ¶ 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(-2I, {{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}}) Public Functions `Mul`(const* RCP<const Number> &coef, map_basic_basic &&dict)¶ the dictionary of the rest (e.g. `xy` in `2xy`) Constructs Mul from a dictionary by copying the contents of the dictionary: hash_t `__hash__`() const¶ Return* size of the hash bool `__eq__`(const Basic &o) const¶ Equality comparator Return whether the 2 objects are equal Parameters `o`: - Object to be compared with int `compare`(const Basic &o) const¶ 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. void `as_two_terms`(const Ptr<RCP<const Basic>> &a, const Ptr<RCP<const Basic>> &b) const¶ Rewrite as 2 terms. Example: if this=3x2y*2z2`, then`a=x2`and`b=3y2z*2` 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¶ Return true if both `coef` and `dict` are in canonical form vec_basic `get_args`() const¶ Returns the list of arguments. const RCP<const Number> &`get_coef`() const¶ const map_basic_basic &`get_dict`() const¶ Public Static Functions RCP<const Basic> `from_dict`(const RCP<const Number> &coef, map_basic_basic &&d)¶ Create a Mul from a dict. void `dict_add_term`(map_basic_basic &d, const RCP<const Basic> &exp, const RCP<const Basic> &t)¶ Add terms to dict. 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)¶ 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.

Class Mul¶

Defined in File mul.h

Inheritance Relationships¶

Base Type¶

public SymEngine::Basic (Class Basic)

Class Documentation¶

class SymEngine::Mul : public SymEngine::Basic ¶

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}})

Public Functions

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

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

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

hash_t __hash__() const¶

Return: size of the hash

bool __eq__(const Basic &o) const¶

Equality comparator

Return

whether the 2 objects are equal

Parameters

o: - Object to be compared with

int compare(const Basic &o) const¶: 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.

void 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`

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¶

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

vec_basic get_args() const¶: Returns the list of arguments.

const RCP<const Number> &get_coef() const¶

const map_basic_basic &get_dict() const¶

Public Static Functions

RCP<const Basic> from_dict(const RCP<const Number> &coef, map_basic_basic &&d)¶: Create a Mul from a dict.

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

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)¶

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.