commutative_ring

Commutative Ring

Mathematically a Commutative Ring is a Ring whose multiplication is commutative.

Important

Contract: Ring initializer parameters must have

  • add closed, commutative and associative on reps

  • mult closed, commutative and associative on reps

  • one an identity on reps, rep*one == rep == one*rep

  • zero an identity on reps, rep+zero == rep == zero+rep

  • negate maps rep -> -rep, rep + negate(rep) == zero

  • zero != one

class boring_math.abstract_algebra.algebras.commutative_ring.CommutativeRing(add: ~collections.abc.Callable[[H, H], H], mult: ~collections.abc.Callable[[H, H], H], one: H, zero: H, negate: ~collections.abc.Callable[[H], H], process: ~collections.abc.Callable[[H], H] = <function CommutativeRing.<lambda>>)
Parameters:

  • add – Closed commutative and associative function reps.

  • mult – Closed associative function reps.

  • one – Representation for multiplicative identity.

  • zero – Representation for additive identity.

  • negate – Function mapping element representation to the representation of corresponding negated element.

__init__(add: ~collections.abc.Callable[[H, H], H], mult: ~collections.abc.Callable[[H, H], H], one: H, zero: H, negate: ~collections.abc.Callable[[H], H], process: ~collections.abc.Callable[[H], H] = <function CommutativeRing.<lambda>>)
Parameters:

  • add – Closed commutative and associative function reps.

  • mult – Closed associative function reps.

  • one – Representation for multiplicative identity.

  • zero – Representation for additive identity.

  • negate – Function mapping element representation to the representation of corresponding negated element.

__call__(rep: H) → CommutativeRingElement

Add the unique element to the ring 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_ring.CommutativeRingElement(rep: H, algebra: CommutativeRing[H])
__init__(rep: H, algebra: CommutativeRing[H]) → None
__str__() → str

Return str(self).