algebra Directory Reference

Directory dependency graph for algebra:

Files
	algebra.cppm
	Groups ⊂ Rings ⊂ Modules ⊂ Polynomials.
	boolean.cppm
	Boolean Starter Package: the algebra on the carrier bool and the canonical embedding 𝔹 ↪ 𝕂3.
	division.cppm
	The Euclidean Engine (Division Rings and Domains).
	field.cppm
	The Rules of Harmony (Groups, Rings, and Fields).
	free.cppm
	Free-algebra constructions — the textbook companion to HSP.
	galois.cppm
	Galois fields (finite fields).
	group.cppm
	The Symmetry of Numbers (ℤ, ℚ*).
	halfspace_transport.cppm
	Transport of halfspaces along the additive group: the ordered-group slice of the point-free relational DSL (image / inverse / argmax and the entireness inference).
	initial_ring.cppm
	ℤ as a Form — Initial Ring and Grothendieck group of ℕ.
	kleene.cppm
	Kleene starter: the three-valued truth surface 𝕂3 as an algebra on a set (the downstream sibling of the Boolean 𝔹).
	magma.cppm
	The Magma: base rung of the algebra tower (an algebraic set).
	modules.cppm
	The Linear Synthesis (Modules and Vector Spaces).
	monoid.cppm
	The Additive and Multiplicative Monoids (ℕ).
	ordered_algebra.cppm
	Ordered-algebra markers and concepts: carriers whose order is compatible with their group / ring / field structure (#664, #895).
	polynomial.cppm
	The monoid algebra R[M]: polynomials as finitely supported nets over the monomials, and the normal form of a rig's, ring's or field's terms.
	quotient.cppm
	HSP structure-preserving operations on algebras — H (quotient, with a relational congruence reading) + P (direct product) + S (subalgebra) carrier-side concepts; their laws and totality are read off the construction in category:total.
	registration.cppm
	Registration helpers for field-shaped carriers.
	ring.cppm
	The Rules of Harmony (The Semiring Synthesis).
	tropical.cppm
	The tropical semiring Tropical<T> = T ∪ {∞}, a dioid.
	universal.cppm
	The universal-algebra (A, F) meta-pattern: carrier + finitary operations.
	vectorspace.cppm
	vector-space concepts + concrete witnesses.