Explore the exact Stern–Brocot tree

The pure-RiX Stern–Brocot plugin builds portable records over the exact, representation-sensitive values supplied by .fraction. Loading it also loads that dependency.

Describe one rational node

Start with 3/5. The description retains its tree path, Farey boundaries, parent, children, continued fraction, and convergents as exact values.

Runnable RiXRun cell

.Plugin.Load("stern-brocot"); node := .sternBrocot.Describe(.frac(3, 5)); {= current=node["current"], parent=node["parent"], children=node["children"], path=node["path"], boundaries=node["boundaries"], convergents=node["convergents"] };

For 3/5, the exact path from the signed-tree root is R, L, R, L. The two Farey boundaries are 1/2 and 2/3.

Build a bounded portable tree

VisibleTree returns exact node and edge records rather than choosing a screen layout. A browser, notebook, or renderer can therefore decide how to present the same mathematical view.

Runnable RiXRun cell

.Plugin.Load("stern-brocot"); tree := .sternBrocot.VisibleTree(.frac(1, 2), 2); {= schema=tree["schema"], current=tree["current"], descendantDepth=tree["descendantdepth"], nodes=tree["nodes"], edges=tree["edges"] };

The second argument is a finite descendant depth. Keeping that bound explicit makes the result deterministic and safe to render.

Follow the exact path as classroom work

Path includes the root and every step to the target. Each step retains its direction and exact Farey boundaries. Grid turns those records into portable structured output.

Runnable RiXRun cell

.Plugin.Load("stern-brocot"); path := .sternBrocot.Path(.frac(3, 5)); {= directions=path["directions"], steps=path["steps"], grid=.sternBrocot.Grid(path["target"]) };

For 3/5, the successive nodes are 0, 1, 1/2, 2/3, and 3/5.

Generate a complete Farey sequence

The order is a required positive Integer and is bounded at 10,000. The result is exact and complete rather than a sampled display.

Runnable RiXRun cell

.Plugin.Load("stern-brocot"); farey := .sternBrocot.Farey(5); {= order=farey["order"], values=farey["values"], neighborEvidence=farey["adjacency"], grid=.sternBrocot.FareyView(5) };

Every adjacent determinant is exactly 1. The direct .fareySequence(5) and .fareyGrid(5) exports provide the same operations outside the namespace.

Evaluate a RiX function exactly

Evaluate accepts a RiX callable, not source text. The selected Fraction is converted to its exact Rational value before the function runs.

Runnable RiXRun cell

.Plugin.Load("stern-brocot"); value := .sternBrocot.Evaluate( (x) -> x^2 - 1/2, .frac(3, 5) ); value;

The result is exactly -7/50. A host that accepts formula text should parse it in a restricted RiX scope first, then pass the resulting callable to this API.