Exact arithmetic and intrinsic quaternion functions

Exact, ordered arithmetic

Runnable RiXRun cell

.Plugin.Load("quaternion"); i := .quaternion.Basis(1); j := .quaternion.Basis(2); q := .quaternion.Quaternion(1,2,3,4); {: (i*j).Components(),(j*i).Components(),q.Conjugate().Components(), q.NormSquared(),q.Inverse().Components() };

Certified-real components

Runnable RiXRun cell

.Plugin.Load("quaternion"); .Plugin.Load("algebraic-real"); q := .quaternion.Quaternion(.ar.Sqrt2(),1/3,0,0); {: q.ZeroStatus(),q.Refine({= absoluteWidth=1/1000,maxWork=300 })[:componentIntervals] };

Slice functions and branches

Runnable RiXRun cell

.Plugin.Load("quaternion"); q := .quaternion.Quaternion(1,2,0,0); negative := .quaternion.Quaternion(-1); family := negative.LogResult(); chosen := negative.Log({= branchDirection=[0,1,0] }); {: q.Exp().Components(),q.Sin().Components(),family[:status], family[:branchFamily],chosen.Components() };

The Float elementary kernel is intentionally labeled approximate. The branch record, slice evidence, and chosen direction are retained even when the numeric components are approximate.