Dedekind 0.0.0
A structuralist C++23 Module Library
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Class List
Here are the classes, structs, unions and interfaces with brief descriptions:
[detail level 12345]
 Ndedekind
 Nalgebra
 Ncategory
 Nsets
 Norder
 Nanalysis
 Ngeometry
 Nieee
 Nlinear_algebra
 Nmorphologies
 Nnumbers
 Nsequences
 Noptimization
 Nrelational
 Njlt
 CFactorA factor of a count, \(b^e\): a base raised to an exponent
 CFreeMonoidThe free monoid on a filtered alphabet, truncated below a length: \(\Sigma^{<L} = \coprod_{n < L} \Sigma^n\), the coproduct of the tensor powers, concatenation of words its operation
 CLetterMapAn arrow on the bytes given by a table, each letter of from to the letter at the same place of to, every other byte fixed: letter_map("ACGT", "TGCA") is the complement of a base, an involution
 CLettersA subobject of the bytes given by its letters, \(\chi : \Sigma \to \Omega\) as a packed word of 256 bits: the predicate a filtered alphabet is built from, letters("ACGT")
 CPowerThe tensor power \(\Sigma^n\): the words of length n over the letters of a chain that a predicate keeps, a box of n legs, each the filtered alphabet, never built
 CPowerMapAn arrow on the letters applied to every letter of a word, of any length: the list functor's action on arrows, \(\tau^{\times n}\) at each length \(n\) at once, beside power on the alphabet, Listing 4's power one level up. It commutes with every permutation of the positions, which is naturality read on words
 CReflectedReverse~rev: the reversal, then the reflection of the alphabet on every letter, the reverse complement. ~f is :posetal's: f then the reflection of its codomain's chain, which on the ranks of ACGT is \(x \mapsto 3 - x\), bitwise NOT on two bits. A word carries no alphabet, so ~rev is a family indexed by the alphabet, with a component at each, power(refl(Σ)) >> rev at Σ, taken where fixed_by(~rev) meets a power over Σ, as the exhibit's oligos & len(6) & fixed_by(~rev). Each component is an involution, two commuting involutions (commutes and is_involutive above). (#1141: an alphabet over another carrier has its component from its rank, as refl does.)
 CReflection
 CReverseAn involution on a carrier that is not a number: reversing a word twice is the identity, on any word a value holds, a std::string or a std::vector of letters; not a view, whose copy would alias the caller's letters. A pure function object, value in and value out, so that it is an arrow in the sense of the Jlt paper's Rule 1, and a family of them, one per word type, as std::logical_not is one per truth type; endo<W>(rev) names the domain
 CRotationThe rotation of the positions of a word by shift, \(i \mapsto i + d \bmod n\), the symmetry of a power \(u^j\): on a word, the letter at i moves to i + d, as std::rotl moves a bit. A family of arrows, one per word type, as Reverse is
 CAutomatonA matcher's plan: the transitions on each letter, and the states where a word of the set has just been read
 CCommutativeRingRegistrationA ring whose multiplication is also commutative
 CFieldRegistrationA commutative ring in which every non-zero multiplicative element is also invertible
 CGaloisFieldRegistrationExtends FieldRegistration with the Galois-specific opt-ins: the carrier is declared a finite field of a given order
 CRigRegistrationBase class for SpeciesTraits<T> of carriers forming a \emph{rig} (semiring) under (Add, Mult) with identities Zero (additive) and One (multiplicative)
 CRingRegistrationA rig whose additive monoid is an abelian group (i.e. has additive inverses). Mult is not required to commute here; see CommutativeRingRegistration for that