Arithmetic Types

Standardized interfaces for mathematical data types, such as Complex, Fraction and Matrix. This repository is a draft, the standard has not been adopted anywhere yet.

Overview

• Every implementation of an Arithmetic Types interface must provide an Arithmetics object with static methods such as add(x, y) which accept arguments of a single data type and perform arithmetic operations on it.
• The available interfaces are in scalar-arithmetic.ts and tensor-arithmetic.ts.
• The methods of Arithmetics must treat the arguments as immutable and return a new instance where applicable.
• Every instance of the data type must provide a x.clone() method and a reference to the Arithmetics object using x[Symbol.for('arithmetics')].

Example usage

Static methods

This is how one can implement an arithmetic and geometric mean for fractions, decimals, complex numbers and quaternions etc., regardless of their implementation.

import { NormedDivisionRing, InstanceOf, symbols } from 'arithmetic-types'

const { Arithmetics } = symbols
type Numeric<T, F> = InstanceOf< NormedDivisionRing<T, F> >


function arithmeticMean<T, F>(first: Numeric<T, F>, ...args: Numeric<T, F>[])
{
  const arithmetics = first[Arithmetics]

  const sum = args.reduce( (a, b) => arithmetics.add(a, b), first )
  const count = args.length + 1

  return arithmetics.scale(sum, 1/count)
}


function geometricMean<T, F>(first: Numeric<T, F>, ...args: Numeric<T, F>[])
{
  const arithmetics = first[Arithmetics]
  if (!arithmetics.isCommutative) throw new TypeError('Geometric mean of non-commutative numbers is not supported.')

  const product = args.reduce( (a, b) => arithmetics.mul(a, b), first )
  const count = args.length + 1

  return arithmetics.pow(product, 1/count)
}