@enumeratio/hypercomplex

Hypercomplex-number extensions for compute-engine: multicomplex, split/perplex, dual and Clifford unit families as ordinary subscripted symbols, wired into + - × ÷, integer powers, Norm and Conjugate with exact coefficients. Background and the family grid are in the guide; finite-quotient arithmetic (units mod n) is in its own page.

Declaring

import { ComputeEngine } from "@cortex-js/compute-engine";
import { declareHypercomplex } from "@enumeratio/hypercomplex";

const ce = new ComputeEngine();
declareHypercomplex(ce);

./src is also exported directly, for packages (like @enumeratio/geometric) that build on the multivector internals rather than just the declared heads.

A generator is two dials

Every unit is fixed by what it squares to and whether it commutes — the whole family table is a 3×2 grid, i_k / j_k / ε_k (commuting) against Clifford's anticommuting generators. The named algebras package up common corners of that grid: Quaternions ($\mathrm{Cl}(0,2)$), plus BicomplexNumbers, TricomplexNumbers, SplitComplexNumbers and DualNumbers.

Heads

• Signature and structure — AlgebraSignature, Quaternions, SplitAlgebra, DualAlgebra, MulticomplexAlgebra
• Arithmetic — Expand, Norm

src/modular.ts also exports the number-theoretic side of the units mod $n$ — imaginaryUnitsMod, splitUnitsMod, factorize — used by the finite guide.

Next

Read the guide for the multiplication-table construction and how canonicalisation interacts with anticommuting generators; @enumeratio/geometric is the grade-aware layer built on top.

Pages

• Hypercomplex Algebras
• Finite: ℤ/m and the places

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• Source: packages/symbols/algebras/hypercomplex
• Depends on: boxes, engine, structures
• In development, also: config, manifest