commutative_semigroup

Additive Semigroup

Mathematically an Additive Semigroup is a set S along with an associative binary operation add: S X S -> S.

Important

Contract: Group initializer parameters must have

  • add closed, commutative and associative on reps

class boring_math.abstract_algebra.algebras.commutative_semigroup.CommutativeSemigroup(add: ~collections.abc.Callable[[H, H], H], process: ~collections.abc.Callable[[H], H] = <function CommutativeSemigroup.<lambda>>)
__init__(add: ~collections.abc.Callable[[H, H], H], process: ~collections.abc.Callable[[H], H] = <function CommutativeSemigroup.<lambda>>) → None
__call__(rep: H) → CommutativeSemigroupElement

Add the unique element to the additive semigroup with a given rep.

Parameters:

rep – Representation to add if not already present.

Returns:

The unique element with that representation.

class boring_math.abstract_algebra.algebras.commutative_semigroup.CommutativeSemigroupElement(rep: H, algebra: CommutativeSemigroup[H])
__init__(rep: H, algebra: CommutativeSemigroup[H]) → None
__add__(other: int | Self) → Self

Add two elements of the same concrete additive semigroup together.

Parameters:

other – Another element within the same additive semigroup or an int.

Returns:

The sum self + other.

Raises:

  • ValueError – If self and other are same type but different concrete additive semigroups.

  • TypeError – If self and other are different types.

__radd__(other: object) → Self

When left side of addition does not know how to add right side.

Parameters:

other – Left side of the addition.

Returns:

Never returns, otherwise left.__add__(right) would have worked.

Raises:

TypeError – When left side does not know how to add the additive semigroup element.

__mul__(n: int | Self) → Self

Multiplying additive semigroup element by a positive int is the same as repeated addition.

Parameters:

n – Add additive semigroup element to itself n > 0 times.

Returns:

The sum of the semigroup element n times.

Raises:

  • ValueError – When n <= 0.

  • ValueError – If for some reason an add method was not defined on the semigroup.