algebraical module

Subclass of the built-in function type for representing algebraic operators (that are typically associated with algebraic structures and algebraic circuits) as immutable, hashable, sortable, and callable objects.

Instances of the class exported by this library can be used as gate operations within circuits as they are implemented within the circuit library. This library is intended to complement the logical library for logical operations.

class algebraical.algebraical.algebraical(function: operator, name: str)[source]

Class for representing algebraic operators. This class is derived from the type of the built-in functions found in the operator library. Thus, it is possible to invoke these operators on values of numeric types and on objects that define the special methods associated with these built-in operators.

>>> algebraical.add_(1, 2)
3

The name and arity of an instance can be retrieved.

>>> algebraical.mul_.name()
'mul'
>>> algebraical.mul_.arity()
2

Instances can be compared according to their precedence.

>>> pow_ > mul_
True
>>> pow_ < add_
False
>>> sorted([pow_, mul_, add_]) # From lowest to highest precedence.
[add_, mul_, pow_]

Instances are also hashable and can be used as members of set instances and as keys within dict instances.

>>> from algebraical import *
>>> {add_, add_, add_}
{add_}
>>> sorted({add_: 0, mul_: 1}.items())
[(add_, 0), (mul_, 1)]

names: dict = {pos_: 'pos', neg_: 'neg', add_: 'add', sub_: 'sub', mul_: 'mul', matmul_: 'matmul', truediv_: 'truediv', floordiv_: 'floordiv', mod_: 'mod', pow_: 'pow', abs_: 'abs'}: Typical concise names for operators.

arities: dict = {pos_: 1, neg_: 1, add_: 2, sub_: 2, mul_: 2, matmul_: 2, truediv_: 2, floordiv_: 2, mod_: 2, pow_: 2, abs_: 1}: Arities of operators.

__call__(*arguments: Tuple[Any, ...]) → Any[source]

Apply the function represented by this instance to zero or more arguments.

>>> algebraical.add_(1, 2)
3

name() → str[source]

Return the canonical concise name for this operator.

>>> algebraical.mul_.name()
'mul'

arity() → int[source]

Return the arity of this operator.

>>> algebraical.mul_.arity()
2
>>> algebraical.neg_.arity()
1

__repr__() → str[source]

String representation of this instance.

>>> algebraical.mul_
mul_

__str__() → str[source]

String representation of this instance.

>>> str(algebraical.mul_)
'mul_'

__lt__(other: algebraical.algebraical.algebraical) → bool[source]

Compare two operators according to their precedence, where an operator with lower precedence is less than an operator with higher precedence.

>>> add_ < mul_
True
>>> add_ < pow_
True
>>> pow_ < mul_
False
>>> add_ > abs_
False

Operators that have the same precedence are not less than one another.

>>> mul_ < mul_
False
>>> sub_ > add_
False

__le__(other: algebraical.algebraical.algebraical) → bool[source]

Compare two operators according to their precedence, where an operator with lower precedence is less than or equal to an operator with higher precedence.

>>> add_ <= mul_
True
>>> add_ <= pow_
True
>>> mul_ >= pow_
False
>>> mul_ >= mul_
True

pos_: algebraical.algebraical.algebraical = pos_

Identity operator.

>>> pos_(2)
2

neg_: algebraical.algebraical.algebraical = neg_

Negation operator.

>>> neg_(2)
-2

abs_: algebraical.algebraical.algebraical = abs_

Absolute value operator.

>>> abs(-2)
2

add_: algebraical.algebraical.algebraical = add_

Addition operator.

>>> add_(1, 2)
3

sub_: algebraical.algebraical.algebraical = sub_

Subtraction operator.

>>> sub_(3, 2)
1

mul_: algebraical.algebraical.algebraical = mul_

Multiplication operator.

>>> mul_(2, 3)
6

matmul_: algebraical.algebraical.algebraical = matmul_

Alternative multiplication operator.

>>> class free(tuple):
...     def __matmul(self, other):
...         return free((self, other))
>>> isinstance(matmul_(free(), free()), free)
True

truediv_: algebraical.algebraical.algebraical = truediv_

Division operator.

>>> truediv_(4, 2)
2

floordiv_: algebraical.algebraical.algebraical = floordiv_

Integer division operator.

>>> floordiv_(3, 2)
1

mod_: algebraical.algebraical.algebraical = mod_

Modulus operator.

>>> mod_(7, 4)
3

pow_: algebraical.algebraical.algebraical = pow_

Exponentiation operator.

>>> pow_(2, 3)
8