https://github.com/powergee/four-square-sum-wasm
WebAssembly package to solve Lagrange's four-square problems efficiently
https://github.com/powergee/four-square-sum-wasm
Last synced: 8 months ago
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WebAssembly package to solve Lagrange's four-square problems efficiently
- Host: GitHub
- URL: https://github.com/powergee/four-square-sum-wasm
- Owner: powergee
- License: apache-2.0
- Created: 2022-03-26T16:20:52.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2024-05-20T19:41:48.000Z (about 2 years ago)
- Last Synced: 2025-02-15T03:15:18.474Z (over 1 year ago)
- Language: Rust
- Size: 22.5 KB
- Stars: 1
- Watchers: 1
- Forks: 1
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE_APACHE
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README
# Lagrange's four-square calculator (Rust, WASM)
**This package is used for [four-square-sum](https://github.com/powergee/four-square-sum) project.**
**Lagrange's four-square theorem**, also known as **Bachet's conjecture**, states that *every natural number can be represented as the sum of four integer squares.* ([ref](https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem))
This algorithm can calculate one of the below:
* **an arbitrary solution** of any non-negative integer *N* by **randomized polynomial time.**
* **an optimal solution**, which use the fewest numbers, of any non-negative integer *N* by the time complexity proportional to the fourth square root of *N*.
The randomized polynomial algorithm is [based on MICHAEL 0. RABIN et al.](https://onlinelibrary.wiley.com/doi/10.1002/cpa.3160390713)
## Usage
```rust
#[wasm_bindgen(js_name = findSolution)]
pub fn find_solution_str(n: String, find_optimal: bool) -> String {}
```
Import the function above into your applications.
```js
import init, { findSolution } from "four-square-sum-wasm";
init().then(() => {
findSolution("1000", false); // ["6", "30", "8", "0"]
findSolution("1000", true); // ["10", "30", "0", "0"]
});
```
## Build
```bash
wasm-pack build --target web
```
## Test
```bash
wasm-pack test --chrome --headless
```
## Demostration and explanation
You can run the algorithm on [GitHub-Pages](https://powergee.github.io/four-square-sum/), which is implemented by React and Rust(Wasm). **There is also a short explanation about the background.**
## References
* [1] Rabin, M.O. and Shallit, J.O. (1986), Randomized algorithms in number theory. Comm. Pure Appl. Math., 39: S239-S256. [https://doi.org/10.1002/cpa.3160390713](https://doi.org/10.1002/cpa.3160390713)
* [2] Rabin, M. O., Efficient Algorithms, Lecture Notes MIT, 1977, transcribed by M. Lui.
* [3] Lagrange's four-square theorem, [https://en.wikipedia.org/w/index.php?title=Lagrange%27s_four-square_theorem&oldid=1070361127](https://en.wikipedia.org/w/index.php?title=Lagrange%27s_four-square_theorem&oldid=1070361127) (last visited Feb. 24, 2022).
* [4] Legendre's three-square theorem, [https://en.wikipedia.org/w/index.php?title=Legendre%27s_three-square_theorem&oldid=1030003352](https://en.wikipedia.org/w/index.php?title=Legendre%27s_three-square_theorem&oldid=1030003352) (last visited Feb. 24, 2022).
* [5] Fermat's theorem on sums of two squares, [https://en.wikipedia.org/w/index.php?title=Fermat%27s_theorem_on_sums_of_two_squares&oldid=1064865677](https://en.wikipedia.org/w/index.php?title=Fermat%27s_theorem_on_sums_of_two_squares&oldid=1064865677) (last visited Feb. 24, 2022).
* [6] Pollard's rho algorithm, [https://en.wikipedia.org/w/index.php?title=Pollard%27s_rho_algorithm&oldid=1044484908](https://en.wikipedia.org/w/index.php?title=Pollard%27s_rho_algorithm&oldid=1044484908) (last visited Feb. 24, 2022).
* [7] Brahmagupta–Fibonacci identity, [https://en.wikipedia.org/w/index.php?title=Brahmagupta%E2%80%93Fibonacci_identity&oldid=1072168983](https://en.wikipedia.org/w/index.php?title=Brahmagupta%E2%80%93Fibonacci_identity&oldid=1072168983) (last visited Feb. 24, 2022).