Inspect an exact repeating expansion

Load the plugin and inspect the familiar repeating decimal for one seventh:

Runnable RiXRun cell

.Plugin.Load("radix"); expansion := (1/7).Expansion(10, {= maxDigits=20 }); {: expansion.Get("nonRepeatingDigits"), expansion.Get("repeatingDigits"), (1/7).PeriodLength(10), (1/7).RadixString(10) };

The same operation remains safe for a denominator with a large period. A small budget returns an explicit partial result:

Runnable RiXRun cell

.Plugin.Load("radix"); (1/982451653).Expansion(10, {= maxDigits=40 });

Formatting can use any collision-free single-glyph alphabet. This base-62 policy keeps exact digit generation separate from its display glyphs:

Runnable RiXRun cell

.Plugin.Load("radix"); alphabet := "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"; {: 61.RadixString(62, {= alphabet=alphabet }), (1/3).RadixString(62, {= alphabet=alphabet }) };

Grouping works from the radix point outward. The shorthand groupSize applies to both sides; either side can be overridden independently:

Runnable RiXRun cell

.Plugin.Load("radix"); {: 1234567.RadixString(10, {= groupSize=3 }), (1/7).RadixString(10, {= fractionGroupSize=2, groupSeparator=" " }) };

Both bounded analyses expose portable work diagnostics:

Runnable RiXRun cell

.Plugin.Load("radix"); bounded := (1/97).PeriodInfo(10, {= maxWork=3 }); {: bounded[:status], bounded[:work], bounded[:diagnostics] };

Pull exact digits lazily

DigitStream uses RiX's restartable cached lazy-sequence protocol. With no count, a rational's fractional expansion is unbounded: a repeat continues to repeat, while a terminating expansion continues with exact zeros.

Runnable RiXRun cell

.Plugin.Load("radix"); digits := (1/7).DigitStream(10); terminating := (1/8).DigitStream(10); {: [digits[1], digits[6], digits[7], digits[8]], [terminating[1], terminating[3], terminating[5]], [digits.schema, digits.clonePolicy] };

Use a finite window when materialization is intended. start is one-based and count bounds the number of lazily produced digits.

Runnable RiXRun cell

.Plugin.Load("radix"); window := (1/7).DigitStream(10, {= start=3, count=5 }); window.Materialize();

A fresh copy keeps the current exact remainder and cached prefix but advances independently. A deep copy restarts the declared stream.

Runnable RiXRun cell

.Plugin.Load("radix"); digits := (1/7).DigitStream(10); digits[3]; copy := digits; copy[8]; restart ::= digits; {: [digits[7], copy[8], restart[2]], [digits.schema, copy.schema, restart.schema] };