@kkitahara/real-algebra

RealAlgebra

ECMAScript modules for exactly manipulating real 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/real-algebra

Examples

import { ExactRealAlgebra as RealAlgebra } from '@kkitahara/real-algebra'
let ralg = new RealAlgebra()
let a, b, c

Generate a new number

a = ralg.num(1, 2, 5)
a.toString() // '(1 / 2)sqrt(5)'

a = ralg.num(1, 2)
a.toString() // '1 / 2'

a = ralg.num(3)
a.toString() // '3'

Generate a new number (short form, since v1.2.0)

a = ralg.$(1, 2, 5)
a.toString() // '(1 / 2)sqrt(5)'

a = ralg.$(1, 2)
a.toString() // '1 / 2'

a = ralg.$(3)
a.toString() // '3'

:warning: num and $ methods do not check if the 3rd parameter is a square-free integer or not (must be square-free!).

Copy (create a new object)

a = ralg.num(1, 2, 5)
b = ralg.copy(a)
b.toString() // '(1 / 2)sqrt(5)'

Equality

a = ralg.num(1, 2, 5)
b = ralg.num(3, 2, 5)
ralg.eq(a, b) // false

b = ralg.num(1, 2, 5)
ralg.eq(a, b) // true

Inequality

a = ralg.num(1, 2, 5)
b = ralg.num(3, 2, 5)
ralg.ne(a, b) // true

b = ralg.num(1, 2, 5)
ralg.ne(a, b) // false

isZero

ralg.isZero(ralg.num(0)) // true
ralg.isZero(ralg.num(1, 2, 5)) // false
ralg.isZero(ralg.num(-1, 2, 5)) // false

isPositive

ralg.isPositive(ralg.num(0)) // false
ralg.isPositive(ralg.num(1, 2, 5)) // true
ralg.isPositive(ralg.num(-1, 2, 5)) // false

isNegative

ralg.isNegative(ralg.num(0)) // false
ralg.isNegative(ralg.num(1, 2, 5)) // false
ralg.isNegative(ralg.num(-1, 2, 5)) // true

isInteger (since v1.1.0)

ralg.isInteger(ralg.num(0)) // true
ralg.isInteger(ralg.num(6, 3)) // true
ralg.isInteger(ralg.num(1, 2)) // false
ralg.isInteger(ralg.num(2, 1, 3)) // false

Addition

a = ralg.num(1, 2, 5)
b = ralg.num(1, 2, 1)
// new object is generated
c = ralg.add(a, b)
c.toString() // '1 / 2 + (1 / 2)sqrt(5)'

In-place addition

a = ralg.num(1, 2, 5)
b = ralg.num(1, 2, 1)
// new object is not generated
a = ralg.iadd(a, b)
a.toString() // '1 / 2 + (1 / 2)sqrt(5)'

Subtraction

a = ralg.num(1, 2, 5)
b = ralg.num(1, 2, 1)
// new object is generated
c = ralg.sub(a, b)
c.toString() // '-1 / 2 + (1 / 2)sqrt(5)'

In-place subtraction

a = ralg.num(1, 2, 5)
b = ralg.num(1, 2, 1)
// new object is not generated
a = ralg.isub(a, b)
a.toString() // '-1 / 2 + (1 / 2)sqrt(5)'

Multiplication

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
b = ralg.iadd(ralg.num(-1, 2), ralg.num(1, 2, 5))
// new object is generated
c = ralg.mul(a, b)
c.toString() // '1'

In-place multiplication

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
b = ralg.iadd(ralg.num(-1, 2), ralg.num(1, 2, 5))
// new object is not generated
a = ralg.imul(a, b)
a.toString() // '1'

Division

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
b = ralg.iadd(ralg.num(-1, 2), ralg.num(1, 2, 5))
// new object is generated
c = ralg.div(a, b)
c.toString() // '3 / 2 + (1 / 2)sqrt(5)'

In-place division

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
b = ralg.iadd(ralg.num(-1, 2), ralg.num(1, 2, 5))
// new object is not generated
a = ralg.idiv(a, b)
a.toString() // '3 / 2 + (1 / 2)sqrt(5)'

Multiplication by -1

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
// new object is generated
b = ralg.neg(a)
b.toString() // '-1 / 2 - (1 / 2)sqrt(5)'

In-place multiplication by -1

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
// new object is not generated
a = ralg.ineg(a)
a.toString() // '-1 / 2 - (1 / 2)sqrt(5)'

Absolute value

a = ralg.iadd(ralg.num(1, 2), ralg.num(-1, 2, 5))
// new object is generated
b = ralg.abs(a)
b.toString() // '-1 / 2 + (1 / 2)sqrt(5)'

In-place evaluation of the absolute value

a = ralg.iadd(ralg.num(1, 2), ralg.num(-1, 2, 5))
// new object is not generated
a = ralg.iabs(a)
a.toString() // '-1 / 2 + (1 / 2)sqrt(5)'

JSON (stringify and parse)

a = ralg.iadd(ralg.num(1, 2), ralg.num(1, 2, 5))
let str = JSON.stringify(a)
b = JSON.parse(str, ralg.reviver)
ralg.eq(a, b) // true

Numerical algebra

The above codes work with built-in numbers if you use

import { RealAlgebra } from '@kkitahara/real-algebra'
let ralg = new RealAlgebra()

instead of ExactRealAlgebra.

In the numerical algebra, equality can be controlled by the constructor argument eps:

import { RealAlgebra } from '@kkitahara/real-algebra'
let ralg = new RealAlgebra()

let a = ralg.num(1, 2)
let b = ralg.num(1, 3)
ralg.eq(a, b) // false
ralg.isZero(ralg.num(1, 999999)) // false

import { RealAlgebra } from '@kkitahara/real-algebra'
let eps = 0.5
let ralg = new RealAlgebra(eps)

let a = ralg.num(1, 2)
let b = ralg.num(1, 3)
ralg.eq(a, b) // true
ralg.isZero(ralg.num(1, 2)) // true
ralg.isZero(ralg.num(2, 3)) // false

Two numbers are considered to be equal if the difference is smaller than or equal to eps.

ESDoc documents

For more examples, see ESDoc documents:

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

and open doc/index.html in your browser.

LICENSE

© 2019 Koichi Kitahara
Apache 2.0