https://github.com/cshaa/arithmetic-types

Interfaces for mathematical data-types to implement
https://github.com/cshaa/arithmetic-types

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Interfaces for mathematical data-types to implement

• Host: GitHub
• URL: https://github.com/cshaa/arithmetic-types
• Owner: cshaa
• License: cc0-1.0
• Created: 2021-05-12T12:09:58.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2021-06-08T01:38:11.000Z (over 3 years ago)
• Last Synced: 2024-10-13T19:38:15.535Z (3 months ago)
• Language: TypeScript
• Size: 44.9 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# 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`](https://github.com/m93a/arithmetic-types/blob/main/lib/scalar-arithmetic.ts) and [`tensor-arithmetic.ts`](https://github.com/m93a/arithmetic-types/blob/main/lib/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.

```typescript

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

const { Arithmetics } = symbols

type Numeric = InstanceOf< NormedDivisionRing >

function arithmeticMean(first: Numeric, ...args: Numeric[])

{

  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(first: Numeric, ...args: Numeric[])

{

  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)

}

```