Build Cayley–Dickson algebras over certified scalars

Levels, bases, and multiplication order

Runnable RiXRun cell

.Plugin.Load("cayley"); quaternions := .cayley.Level(2); i := quaternions.BasisValue(1); j := quaternions.BasisValue(2); {: quaternions.Basis(), (i*j).Components(), (j*i).Components(), (i*j).Parenthesization(), .cayley.VerifyMultiplication(i,j) };

Certified component boxes

Runnable RiXRun cell

.Plugin.Load("cayley"); .Plugin.Load("algebraic-real"); q := .cayley.Value(2,[1,.ar.Sqrt2(),0,1/3]); box := q.Refine({= absoluteWidth=1/1000,maxWork=400 }); {: q.Conjugate().Components(),q.NormSquared(),q.ZeroStatus(), box[:componentIntervals],box[:certified] };

Every exact component is returned as a zero-width interval. Certified singleton components are refined through Numerics, so the box always contains the known true value even if bounded work leaves it wider than requested.

Adapters and gated division

Runnable RiXRun cell

.Plugin.Load("cayley"); z := .complex.FromParts(2,3); old := .exactAlgebras.Quaternion(1,2,3,4); {: .cayley.FromComplex(z).Components(), .cayley.FromExactAlgebra(old).Components(), .cayley.Level(4).Capabilities()[:division] };