Preserve octonion structure under exact and intrinsic calculation

Make nonassociativity visible

Runnable RiXRun cell

.Plugin.Load("octonion"); e1 := .octonion.Basis(1); e2 := .octonion.Basis(2); e4 := .octonion.Basis(4); {: ((e1*e2)*e4).Components(),e1*(e2*e4), .octonion.VerifyIdentity(:alternativityLeft,e1+e2,e4), .octonion.VerifyIdentity(:moufang,e1,e2,e4), .octonion.VerifyIdentity(:nonassociative,e1,e2,e4) };

Refine certified components

Runnable RiXRun cell

.Plugin.Load("octonion"); .Plugin.Load("algebraic-real"); o := .octonion.Octonion(1,.ar.Sqrt2(),0,0,1/3,0,0,0); box := o.Refine({= absoluteWidth=1/1000,maxWork=500 }); {: o.Conjugate().Components(),o.NormSquared(),o.ZeroStatus(),box[:componentIntervals] };

Stay inside a one-generated associative slice

Runnable RiXRun cell

.Plugin.Load("octonion"); o := .octonion.Octonion(0,1,0,0,0,0,0,0); polynomial := o.Series([1,2,3]); family := .octonion.Octonion(-1).LogResult(); {: polynomial.Components(),polynomial.Record()[:evaluationOrder], polynomial.Record()[:sliceEvidence],o.Exp().Components(),family[:branchFamily] };

The series record fixes right-Horner evaluation and refuses to imply that independent octonion expressions can be reordered or reassociated.