FractionInterval

FractionInterval is a closed interval whose endpoints are representation-preserving Fraction values. It is useful when mediant subdivision must retain unreduced numerators and denominators.

Construction

import { Fraction, FractionInterval } from "@ratmath/core";

const interval = new FractionInterval(
  new Fraction(1, 3),
  new Fraction(2, 3),
);

interval.low.toString();  // "1/3"
interval.high.toString(); // "2/3"
interval.toString();      // "1/3:2/3"

Both endpoints must be Fraction instances. They are sorted mathematically; unlike RationalInterval, input orientation is not retained.

Mediant partitioning

Method	Result
mediantSplit()	Two intervals split at the endpoint mediant
partitionWithMediants(depth?)	Repeats every split depth times; returns 2^depth intervals
partitionWith(fn)	Adds callback-provided Fraction points, sorts/deduplicates, and returns adjacent intervals

const pieces = interval.mediantSplit();
pieces.map((piece) => piece.toString());
// ["1/3:3/6", "3/6:2/3"]

interval.partitionWithMediants(2).map((piece) => piece.toString());
// ["1/3:4/9", "4/9:3/6", "3/6:5/9", "5/9:2/3"]

interval.partitionWith((low, high) => [low.mediant(high)]);
// same two-way split

A custom partition function must return an array of Fraction values inside the interval. Depth must be nonnegative; depth zero returns [interval].

Conversion and utility methods

Method	Result
toRationalInterval()	Equivalent reduced RationalInterval
FractionInterval.fromRationalInterval(interval)	Uses each rational’s reduced components
toString()	low:high, preserving each fraction’s representation
equals(other)	Exact endpoint-representation equality
E(exponent)	Applies exact decimal scaling to both endpoint fractions

const scaled = new FractionInterval(
  new Fraction(1, 2),
  new Fraction(3, 4),
).E(2);

scaled.toString(); // "100/2:300/4"
scaled.toRationalInterval().toString(); // "50:75"

Conversion through RationalInterval reduces endpoint representations, so it is not a lossless round trip for values such as 2/4.