Crate deep_causality_algebra 

Re-exports

pub use crate::iso::AlgebraIso;

pub use crate::iso::DivisionAlgebraIso;

pub use crate::iso::FieldIso;

pub use crate::iso::GroupIso;

pub use crate::iso::RingIso;

Modules

iso

Tier 1 structure-preserving isomorphism marker subtraits.

utils_tests

Structs

Conjunction

The boolean conjunction (∧) monoid: identity true, combine = &&. A bounded semilattice.

Count

The count monoid (ℕ, +, 0): identity 0, combine = +. Commutative, not idempotent.

Disjunction

The boolean disjunction (∨) monoid: identity false, combine = ||. A bounded semilattice.

Prob

A probability in [0, 1]. The Monoid is the product t-norm (identity 1), giving the AggregateLogic::All reducer ∏ pᵢ; commutative, not idempotent.

Traits

AbelianGroup

A marker trait for an Abelian Group (also known as a Commutative Group).

AddGroup

Represents an Additive Group.

AddMagma

An Additive Magma.

AddMonoid

Represents an Additive Monoid.

AddSemigroup

Represents an Additive Semigroup.

Algebra

Represents a Unital Algebra over a Ring.

Associative

Marker trait: Promises that (a * b) * c == a * (b * c). IMPLEMENT THIS for f64, f32, Float, Complex, Quaternion. DO NOT IMPLEMENT for Octonion.

AssociativeAlgebra

A marker trait for an Associative Algebra.

AssociativeDivisionAlgebra

A marker trait for an Associative Division Algebra.

AssociativeRing

A marker trait for an Associative Ring.

BoundedSemilattice

A bounded semilattice: a CommutativeMonoid that is also Idempotent — associative, commutative, idempotent, with an identity (the bound).

Commutative

Marker trait: Promises that a * b == b * a. IMPLEMENT THIS for f64, f32, Float, Complex. DO NOT IMPLEMENT for Quaternion, Octonion.

CommutativeMonoid

A commutative monoid: a Monoid whose operation additionally satisfies

CommutativeRing

A marker trait for a Commutative Ring.

ComplexField

Represents a Complex Field — a field extension of the reals with complex conjugation and component access.

ConjugateScalar

A scalar carrying a conjugation and a real modulus, spanning the three scalar families numerical linear algebra cares about: real fields, dual numbers (forward-mode AD), and complex.

Distributive

Marker trait: Promises that a * (b + c) == (a * b) + (a * c).

DivGroup

A marker trait for a Division Group.

DivisionAlgebra

Represents a Division Algebra over a Field.

Field

Represents a Field in abstract algebra.

Group

Represents a Group in abstract algebra.

Idempotent

An idempotent monoid operation:

InvMonoid

Represents a Multiplicative Monoid with the additional property that every element has a multiplicative inverse.

Module

Represents a Module over a Ring.

Monoid

A monoid: a set with an associative binary operation combine and an identity empty.

MulGroup

Represents a Multiplicative Group.

MulMagma

MulMonoid

Represents a Multiplicative Monoid.

MulSemigroup

Represents a Multiplicative Semigroup.

Normed

A value with a real modulus and real scaling: the bridge that lets generic code treat a real (f64) and a complex (Complex<f64>) uniformly for norm work.

NormedScalar

A normed scalar: a field element that also carries a real modulus — the bound for normed linear algebra (norms, orthogonalization, singular values) over either real or complex scalars.

Real

An analytic real scalar: commutative-ring arithmetic plus the elementary functions, constants, ordering, rounding, and exceptional-value predicates of the real numbers — without field invertibility.

RealField

An ordered Field that is also an analytic real scalar.

Ring

Represents a Ring in abstract algebra.

Rotation

A trait for types that can be rotated in 3D space (or the Bloch Sphere).

Scalar

Scalar sits in the real tower between Real and RealField: it adds division to Real but, unlike a field, does not require a total inverse. That is deliberate, so that Dual qualifies — its ε component is a zero divisor, so it has division yet is not a field. The deep_causality_calculus crate writes its differentiation and integration operators against Scalar, so a single model evaluates at f64 (the value) and at Dual (the derivative).

Verdict

A verdict: a bounded lattice with complement (a Boolean algebra for bool; an MV-algebra for the probability carrier, where complement(p) = 1 − p).