https://github.com/alex-mashin/complex.lua
A small Lua ligrary implementing complex numbers
https://github.com/alex-mashin/complex.lua
complex-numbers lua lua-li
Last synced: about 1 year ago
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A small Lua ligrary implementing complex numbers
- Host: GitHub
- URL: https://github.com/alex-mashin/complex.lua
- Owner: alex-mashin
- Created: 2024-02-14T14:44:54.000Z (over 2 years ago)
- Default Branch: master
- Last Pushed: 2024-02-16T02:06:57.000Z (over 2 years ago)
- Last Synced: 2025-02-17T21:46:12.151Z (over 1 year ago)
- Topics: complex-numbers, lua, lua-li
- Language: Lua
- Homepage:
- Size: 3.91 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# complex.lua
*Version 0.1*
*complex.lua* is a small Lua ligrary that implements complex numbers. It started as an [answer on Code Review Stack Exchange](https://codereview.stackexchange.com/a/253022/230923).
## Usage:
- `complex = require 'complex'` — require the library,
- `complex.IMAGINARY_CHAR = 'j'` — use electrical notation for serialisation,
- `complex.PREFIX = true` — use *i*/*j* as a prefix for serialisation,
- `complex.PARENTHESES = true` — serialise complex numbers in parentheses,
- `local i = complex.i` — set *i*,
- `complex (re, im)` will return the complex number with real part `re` and imaginary part `im`,
- `z = complex (re, im); z1 = complex (z)` will copy `z` to `z1`,
- `z.r` and `z.i` are real and imaginary parts of `z`, respectively,
- `z.conjugate ()` — complex conjugation,
- `+`, `-`, `*` and `/` operators work as expected; both Lua (real) numbers and complex numbers can be left or right operands: `local z = 1 + complex.i`, `local z = complex.i + 1`, `local z = complex (1, 0) + complex.i` will set `z` to the same value,
- unary `-` will work as expected,
- `==` will work as expected,
- `<` will give a correct result when both operands are real. In addition, it will return true only if the real parts of operands are equal and the imaginary part of the first one is less than that of the secon one, which can facilitate sorting,
- `complex:abs ()` — the absolute value,
- `complex:abs2 ()` — the absolute value squared,
- `complex:arg ()` — the argument,
- `complex.polar (abs, arg)` — return a complex number with the absolute value of `abs` and argument of `arg`,
- `complex:exp ()` — exponent of a complex number,
- `x ^ y` will return a complex number, if either Euler's or de Moivre's formula is applicable, i.e., if either the first operand is positive number, or the second argument is real integer,
- `complex:roots (n)` will return all `n` `n`th roots of a complex number,
- `tostring (x)` will serialise the complex number rather prettily (e.g., `5 - 5i`, `-5i` or `5`) subject to `complex.IMAGINARY_CHAR`, `complex.PREFIX` and `complex.PARENTHESES`.
## Requirements
- Lua 5.1, 5.2, 5.3, 5.4 or LuaJIT.
# Credits
*complex.lua* is written by Alexander Mashin in 2020 and 2024, originally as a rework of the [code](https://codereview.stackexchange.com/q/252982/230923) written by [Nick](https://codereview.stackexchange.com/users/77934/nick). *Lua* is created by Roberto Ierusalimschy.