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@kkitahara/quaternion-algebra

v1.0.4

Published

ECMAScript modules for exactly manipulating quaternions of which coefficients are numbers of the form (p / q)sqrt(b).

Downloads

1

Readme

JavaScript Style Guide license pipeline status coverage report version bundle size downloads per month downloads total

QuaternionAlgebra

ECMAScript modules for exactly manipulating quaternions of which coefficients are numbers of the form (p / q)sqrt(b), where p is an integer, q is a positive (non-zero) integer, and b is a positive, square-free integer.

Installation

npm install @kkitahara/quaternion-algebra @kkitahara/real-algebra

Examples

import { ExactRealAlgebra as RealAlgebra } from '@kkitahara/real-algebra'
import { QuaternionAlgebra } from '@kkitahara/quaternion-algebra'
let r = new RealAlgebra()
let h = new QuaternionAlgebra(r)
let q1, q2, q3

Generate a new quaternion

q1 = h.$(1, 2, 3, 4)
q1.toString() // '1 + i(2) + j(3) + k(4)'

q1 = h.$(0, 0, 0, r.$(1, 2, 5))
q1.toString() // 'k((1 / 2)sqrt(5))'

Real and imaginary parts

q1 = h.$(1, 2, 3, 4)
q1.re.toString() // '1'
q1.im instanceof Array // true
q1.im[0].toString() // '2'
q1.im[1].toString() // '3'
q1.im[2].toString() // '4'

Copy (create a new object)

q1 = h.$(1, 2, 3, 4)
q2 = h.copy(q1)
q2.toString() // '1 + i(2) + j(3) + k(4)'

Equality

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, -2, 3, 4)
h.eq(q1, q2) // false

q2 = h.$(1, 2, 3, 4)
h.eq(q1, q2) // true

Inequality

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, -2, 3, 4)
h.ne(q1, q2) // true

q2 = h.$(1, 2, 3, 4)
h.ne(q1, q2) // false

isZero

h.isZero(h.$(0, 0, 0, 0)) // true
h.isZero(h.$(1, 0, 0, 0)) // false
h.isZero(h.$(0, 1, 0, 0)) // false
h.isZero(h.$(0, 0, 1, 0)) // false
h.isZero(h.$(0, 0, 0, 1)) // false

isInteger

h.isInteger(h.$(1, 2, 3, 4)) // true
h.isInteger(h.$(1, r.$(2, 3), 3, 4)) // false
h.isInteger(h.$(1, r.$(4, 2), 3, 4)) // true

Addition

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 1, 2, 1)
// new object is generated
q3 = h.add(q1, q2)
q3.toString() // '2 + i(3) + j(5) + k(5)'

In-place addition

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 1, 2, 1)
// new object is not generated
q1 = h.iadd(q1, q2)
q1.toString() // '2 + i(3) + j(5) + k(5)'

Subtraction

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 1, 2, 1)
// new object is generated
q3 = h.sub(q1, q2)
q3.toString() // 'i(1) + j(1) + k(3)'

In-place subtraction

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 1, 2, 1)
// new object is not generated
q1 = h.isub(q1, q2)
q1.toString() // 'i(1) + j(1) + k(3)'

Maltiplication

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, -2, -3, -4)
// new object is generated
q3 = h.mul(q1, q2)
q3.toString() // '30'

// some fundametal products
h.mul(h.$(1, 0, 0, 0), h.$(0, 1, 0, 0)).toString() // 'i(1)'
h.mul(h.$(0, 1, 0, 0), h.$(1, 0, 0, 0)).toString() // 'i(1)'
h.mul(h.$(1, 0, 0, 0), h.$(0, 0, 1, 0)).toString() // 'j(1)'
h.mul(h.$(0, 0, 1, 0), h.$(1, 0, 0, 0)).toString() // 'j(1)'
h.mul(h.$(1, 0, 0, 0), h.$(0, 0, 0, 1)).toString() // 'k(1)'
h.mul(h.$(0, 0, 0, 1), h.$(1, 0, 0, 0)).toString() // 'k(1)'
h.mul(h.$(1, 0, 0, 0), h.$(1, 0, 0, 0)).toString() // '1'
h.mul(h.$(0, 1, 0, 0), h.$(0, 1, 0, 0)).toString() // '-1'
h.mul(h.$(0, 0, 1, 0), h.$(0, 0, 1, 0)).toString() // '-1'
h.mul(h.$(0, 0, 0, 1), h.$(0, 0, 0, 1)).toString() // '-1'
h.mul(h.$(0, 1, 0, 0), h.$(0, 0, 1, 0)).toString() // 'k(1)'
h.mul(h.$(0, 0, 1, 0), h.$(0, 1, 0, 0)).toString() // 'k(-1)'
h.mul(h.$(0, 0, 1, 0), h.$(0, 0, 0, 1)).toString() // 'i(1)'
h.mul(h.$(0, 0, 0, 1), h.$(0, 0, 1, 0)).toString() // 'i(-1)'
h.mul(h.$(0, 0, 0, 1), h.$(0, 1, 0, 0)).toString() // 'j(1)'
h.mul(h.$(0, 1, 0, 0), h.$(0, 0, 0, 1)).toString() // 'j(-1)'

In-place multiplication

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, -2, -3, -4)
// new object is not generated
q1 = h.imul(q1, q2)
q1.toString() // '30'

Division

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 2, 3, 4)
// new object is generated
q3 = h.div(q1, q2)
q3.toString() // '1'

In-place division

q1 = h.$(1, 2, 3, 4)
q2 = h.$(1, 2, 3, 4)
// new object is not generated
q1 = h.idiv(q1, q2)
q1.toString() // '1'

Multiplication by -1

q1 = h.$(1, 2, 3, 4)
// new object is generated
q2 = h.neg(q1)
q2.toString() // '-1 + i(-2) + j(-3) + k(-4)'

In-place multiplication by -1

q1 = h.$(1, 2, 3, 4)
// new object is not generated
q1 = h.ineg(q1)
q1.toString() // '-1 + i(-2) + j(-3) + k(-4)'

Conjugate

q1 = h.$(1, 2, 3, 4)
// new object is generated
q2 = h.cjg(q1)
q2.toString() // '1 + i(-2) + j(-3) + k(-4)'

In-place evaluation of the conjugate

q1 = h.$(1, 2, 3, 4)
// new object is not generated
q1 = h.icjg(q1)
q1.toString() // '1 + i(-2) + j(-3) + k(-4)'

Square of the absolute value

q1 = h.$(1, 2, 3, 4)
let a = h.abs2(q1)
a.toString() // '30'
// return value is not a quaternion (but a real number)
a.re // undefined
a.im // undefined

JSON (stringify and parse)

q1 = h.$(1, 2, 3, 4)
let str = JSON.stringify(q1)
q2 = JSON.parse(str, h.reviver)
h.eq(q1, q2) // true

ESDoc documents

For more examples, see ESDoc documents:

cd node_modules/@kkitahara/quaternion-algebra
npm install --only=dev
npm run doc

and open doc/index.html in your browser.

LICENSE

© 2019 Koichi Kitahara
Apache 2.0