Explore unreduced fractions

Load .fraction directly or through .fracfun/.symbolic. Its .frac and .f aliases refer to the same plugin.

Runnable RiXRun cell

.Plugin.Load("fraction"); a := .frac(6,8); b := .f`6/8`; c := `6/8`; {: a, b, c, a.Numerator(), a.Denominator() };

Rational values versus written pairs

Ordinary / constructs a reduced Rational before .F() can run. Structural backticks or the two-component constructor preserve the pair.

Runnable RiXRun cell

.Plugin.Load("fraction"); canonicalPair := (6/8).F(); writtenPair := (`6/8`).F(); {: canonicalPair, writtenPair, canonicalPair.Rational(), writtenPair.Rational() };

Unreduced arithmetic

Usual arithmetic uses the represented components and does no cancellation.

Runnable RiXRun cell

.Plugin.Load("fraction"); a := `1/2`; b := `1/3`; c := `2/4`; d := `3/6`; {: a+b, a-b, c*d, c/d, c^2, -c };

Classroom denominator policies

General + uses cross-products. Two explicit methods model the common classroom steps of retaining like denominators or first finding the LCM.

Runnable RiXRun cell

.Plugin.Load("fraction"); a := `1/4`; b := `2/4`; c := `1/6`; {: a+b, a.AddLikeDenominator(b), a+c, a.AddLCMDenominator(c) };

Representation-sensitive mediants

Pair equality and mathematical equivalence answer different questions, and a mediant deliberately uses the represented components.

Runnable RiXRun cell

.Plugin.Load("fraction"); written := `6/8`; canonical := (6/8).F(); other := `1/2`; {: written == canonical, written.Equivalent(canonical), written.Mediant(other), canonical.Mediant(other) };

Subdivide a fraction interval

Fraction intervals keep the written endpoint pairs. Their mediants therefore make each classroom subdivision step inspectable.

Runnable RiXRun cell

.Plugin.Load("fraction"); interval := .fraction.Interval(.frac(1,3), .frac(2,3)); {= interval=interval, mediant=interval.Mediant(), split=interval.MediantSplit(), depthTwo=interval.PartitionWithMediants(2), canonical=interval.RationalInterval() };

The four depth-two intervals retain unreduced mediants such as 4/6 where the represented construction step matters.

Use infinity only as an explicit boundary

The signed Stern–Brocot tree uses -1/0 and 1/0 as boundary markers. They do not silently become ordinary numbers.

Runnable RiXRun cell

.Plugin.Load("fraction"); whole := .fraction.Interval( .fraction.Infinity(-1), .fraction.Infinity(1) ); {= root=whole.Mediant(), halves=whole.MediantSplit() };

Calling whole.RationalInterval() is intentionally an error because core RationalInterval has only finite Rational endpoints. 0/0 is never admitted.

Round-trip through a finite continued fraction

The adapter keeps the original written pair even though continued-fraction coefficients describe its reduced value:

Runnable RiXRun cell

.Plugin.Load("fraction"); written := .frac(42,56); adapter := written.ContinuedFraction(); restored := .fraction.FromContinuedFraction(adapter); {: adapter[:coefficients],adapter[:componentProvenance],restored[:fraction] };

It also consumes the finite protocol owned by .continuedFraction:

Runnable RiXRun cell

.Plugin.Load("continued-fraction"); .Plugin.Load("fraction"); external := .continuedFraction.FromRational(7/11); .fraction.FromContinuedFraction(external);

The other direction is direct as well:

Runnable RiXRun cell

asContinuedFraction := .continuedFraction(adapter); {: asContinuedFraction.Value(),asContinuedFraction.Record()[:evidence] };

Bound a Farey search

Runnable RiXRun cell

.Plugin.Load("fraction"); found := .fraction.FareySearch(.frac(42,56), {= maxSteps=20,maxDenominator=20 }); partial := .fraction.FareySearch(.frac(355,113), {= maxSteps=3,maxDenominator=1000 }); {: found[:status],found[:path],found[:componentProvenance], partial[:status],partial[:result],partial[:bounds] };

The partial result remains usable and its trace records every represented mediant considered before the explicit work limit.