enumeratio

@enumeratio/geometric ​

The geometric-algebra layer over @enumeratio/hypercomplex: grade projection, the outer and regressive products, the contractions, the involutions and the Poincaré dual. Where @enumeratio/hypercomplex gives a Clifford algebra its arithmetic, this package gives a multivector its structure — which blades it lives in, and the operations that only make sense once grade is in view.

Declaring ​

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

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

declareGeometric needs the units declared first — it operates on the multivectors @enumeratio/hypercomplex already knows how to add and multiply.

Heads ​

Usage ​

Wedge(e_1, e_2, e_1)     // 0 — a repeated generator kills the wedge
GeometricProduct(e_1, e_1)  // 1 — but the geometric product does not vanish

The wedge of two distinct generators is their blade and anticommutes: Wedge(e_1, e_2) = e_1e_2 = -Wedge(e_2, e_1); it is associative and linear in each argument, so it folds over any number of operands.

Next ​

Sandwich and Dual are the two operations most worth reading the source for (src/dual.ts, src/products.ts) — the dual's sign depends on the ambient AlgebraSignature, and the sandwich is how reflections and rotations are actually built from versors.