ECMAScript modules for exactly manipulating complex numbers of which real and imaginary parts are numbers of the form (p / q)sqrt(b).
ECMAScript modules for exactly manipulating complex numbers
of which real and imaginary parts 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.
npm install @kkitahara/complex-algebra @kkitahara/real-algebra
Examples
javascript
import { ExactRealAlgebra as RealAlgebra } from '@kkitahara/real-algebra'
import { ComplexAlgebra } from '@kkitahara/complex-algebra'
let ralg = new RealAlgebra()
let calg = new ComplexAlgebra(ralg)
let z, w, v
`
Generate a new real number
javascript
z = calg.num(1, 2, 5)
z.toString() // '(1 / 2)sqrt(5)'z = calg.num(1, 2)
z.toString() // '1 / 2'
z = calg.num(3)
z.toString() // '3'
`
Generate a new imaginary number
javascript
z = calg.inum(1, 2, 5)
z.toString() // 'i((1 / 2)sqrt(5))'z = calg.inum(1, 2)
z.toString() // 'i(1 / 2)'
z = calg.inum(3)
z.toString() // 'i(3)'
`
:warning: and inum methods do not check if
(the absolute value of) the 3rd parameter is a square-free integer or not
(must be square-free!).Real and imaginary parts
`javascript
z = calg.num(1, 2, 5)
z.re.toString() // '(1 / 2)sqrt(5)'
z.im.toString() // '0'z = calg.inum(1, 2, 5)
z.re.toString() // '0'
z.im.toString() // '(1 / 2)sqrt(5)'
`
Generate from two real numbers (since v1.2.0)
javascript
let a = ralg.$(1, 2, 3)
let b = ralg.$(1, 2, 5)
z = calg.$(a, b)
z.toString() // '(1 / 2)sqrt(3) + i((1 / 2)sqrt(5))'
`
Copy (create a new object)
javascript
z = calg.inum(1, 2, 5)
w = calg.copy(z)
w.toString() // 'i((1 / 2)sqrt(5))'
`
Equality
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2, 5)
calg.eq(z, w) // falsew = calg.num(1, 2, 5)
calg.eq(z, w) // true
`
Inequality
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2, 5)
calg.ne(z, w) // truew = calg.num(1, 2, 5)
calg.ne(z, w) // false
`
isZero
javascript
calg.isZero(calg.num(0)) // true
calg.isZero(calg.inum(0)) // true
calg.isZero(calg.num(1, 2, 5)) // false
calg.isZero(calg.inum(1, 2, 5)) // false
calg.isZero(calg.num(-1, 2, 5)) // false
calg.isZero(calg.inum(-1, 2, 5)) // false
`
isInteger (since v1.1.0)
javascript
calg.isInteger(calg.num(0)) // true
calg.isInteger(calg.inum(0)) // true
calg.isInteger(calg.num(1, 2)) // false
calg.isInteger(calg.inum(1, 2)) // false
calg.isInteger(calg.num(6, 3)) // true
calg.isInteger(calg.inum(6, 3)) // true
calg.isInteger(calg.num(6, 3, 2)) // false
calg.isInteger(calg.inum(6, 3, 2)) // false
`
Addition
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2)
// new object is generated
v = calg.add(z, w)
v.toString() // '(1 / 2)sqrt(5) + i(1 / 2)'
`
In-place addition
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2)
// new object is not generated
z = calg.iadd(z, w)
z.toString() // '(1 / 2)sqrt(5) + i(1 / 2)'
`
Subtraction
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2)
// new object is generated
v = calg.sub(z, w)
v.toString() // '(1 / 2)sqrt(5) + i(-1 / 2)'
`
In-place subtraction
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2)
// new object is not generated
z = calg.isub(z, w)
z.toString() // '(1 / 2)sqrt(5) + i(-1 / 2)'
`
Multiplication
javascript
z = calg.inum(1, 2, 5)
w = calg.inum(1, 2)
// new object is generated
v = calg.mul(z, w)
v.toString() // '-(1 / 4)sqrt(5)'
`
In-place multiplication
javascript
z = calg.inum(1, 2, 5)
w = calg.inum(1, 2)
// new object is not generated
z = calg.imul(z, w)
z.toString() // '-(1 / 4)sqrt(5)'
`
Division
javascript
z = calg.inum(1, 2, 5)
w = calg.inum(1, 2)
// new object is generated
v = calg.div(z, w)
v.toString() // 'sqrt(5)'
`
In-place division
javascript
z = calg.inum(1, 2, 5)
w = calg.inum(1, 2)
// new object is not generated
z = calg.idiv(z, w)
z.toString() // 'sqrt(5)'
`
Multiplication by -1
javascript
z = calg.inum(1, 2, 5)
// new object is generated
w = calg.neg(z)
w.toString() // 'i(-(1 / 2)sqrt(5))'
`
In-place multiplication by -1
javascript
z = calg.inum(1, 2, 5)
// new object is not generated
z = calg.ineg(z)
z.toString() // 'i(-(1 / 2)sqrt(5))'
`
Complex conjugate
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2, 5)
// new object is generated
v = calg.cjg(z)
v.toString() // '(1 / 2)sqrt(5)'
v = calg.cjg(w)
v.toString() // 'i(-(1 / 2)sqrt(5))'
`
In-place evaluation of the complex conjugate
javascript
z = calg.num(1, 2, 5)
w = calg.inum(1, 2, 5)
// new object is not generated
z = calg.icjg(z)
z.toString() // '(1 / 2)sqrt(5)'
w = calg.icjg(w)
w.toString() // 'i(-(1 / 2)sqrt(5))'
`
Square of the absolute value
javascript
z = calg.iadd(calg.num(3), calg.inum(4))
let a = calg.abs2(z)
a.toString() // '25'
// return value is not a complex number (but a real number)
a.re // undefined
a.im // undefined
`
JSON (stringify and parse)
javascript
z = calg.iadd(calg.num(1, 2, 5), calg.inum(-1, 2, 7))
let str = JSON.stringify(z)
w = JSON.parse(str, calg.reviver)
calg.eq(z, w) // true
`$3
The above codes work with built-in numbers if you use
javascript
import { RealAlgebra } from '@kkitahara/real-algebra'
import { ComplexAlgebra } from '@kkitahara/complex-algebra'
let ralg = new RealAlgebra()
let calg = new ComplexAlgebra(ralg)
`
instead of ExactRealAlgebra.
See the documents of @kkitahara/real-algebra for more details.$3
For more examples, see ESDoc documents:
cd node_modules/@kkitahara/complex-algebra
npm install --only=dev
npm run doc
and open