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https://github.com/programmerjake/algebraics
algebraic numbers implemented in rust; mirror of https://salsa.debian.org/Kazan-team/algebraics
https://github.com/programmerjake/algebraics
algebraic-numbers quadratic-equations quadratic-numbers real-number rust
Last synced: about 1 month ago
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algebraic numbers implemented in rust; mirror of https://salsa.debian.org/Kazan-team/algebraics
- Host: GitHub
- URL: https://github.com/programmerjake/algebraics
- Owner: programmerjake
- License: lgpl-2.1
- Created: 2019-07-16T09:39:30.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2023-11-28T23:33:26.000Z (10 months ago)
- Last Synced: 2024-04-04T18:32:50.395Z (6 months ago)
- Topics: algebraic-numbers, quadratic-equations, quadratic-numbers, real-number, rust
- Language: Rust
- Homepage:
- Size: 698 KB
- Stars: 25
- Watchers: 4
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE.md
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README
## [Algebraic Numbers](https://en.wikipedia.org/wiki/Algebraic_number) Library
Use when you need exact arithmetic, speed is not critical, and rational numbers aren't good enough.
## Example:
```rust
use algebraics::prelude::*;
use algebraics::RealAlgebraicNumber as Number;
let two = Number::from(2);
// 2 is a rational number
assert!(two.is_rational());
// 1/2 is the reciprocal of 2
let one_half = two.recip();
// 1/2 is also a rational number
assert!(one_half.is_rational());
// 2^(1/4)
let root = (&two).pow((1, 4));
// we can use all the standard comparison operators
assert!(root != Number::from(3));
assert!(root < Number::from(2));
assert!(root > Number::from(1));
// we can use all of add, subtract, multiply, divide, and remainder
let sum = &root + &root;
let difference = &root - Number::from(47);
let product = &root * &one_half;
let quotient = &one_half / &root;
let remainder = &root % &one_half;
// root is not a rational number
assert!(!root.is_rational());
// the calculations are always exact
assert_eq!((&root).pow(4), two);
// lets compute 30 decimal places of root
let scale = Number::from(10).pow(30);
let scaled = &root * scale;
let digits = scaled.into_integer_trunc();
assert_eq!(
digits.to_string(),
1_18920_71150_02721_06671_74999_70560u128.to_string()
);
// get the minimal polynomial
let other_number = root + two.pow((1, 2));
assert_eq!(
&other_number.minimal_polynomial().to_string(),
"2 + -8*X + -4*X^2 + 0*X^3 + 1*X^4"
);
// works with really big numbers
let really_big = Number::from(1_00000_00000i64).pow(20) + Number::from(23);
assert_eq!(
&really_big.to_integer_floor().to_string(),
"100000000000000000000000000000000000000000000\
000000000000000000000000000000000000000000000\
000000000000000000000000000000000000000000000\
000000000000000000000000000000000000000000000\
000000000000000000023"
)
```
## Python support
Using algebraics from Python:
```bash
python3 -m pip install algebraics
```
```python
from algebraics import RealAlgebraicNumber
sqrt_2 = 2 ** (RealAlgebraicNumber(1) / 2)
assert sqrt_2 * sqrt_2 == 2
```
Using algebraics in your own Rust project:
```toml
[dependencies.algebraics]
version = "0.3"
```
Developing algebraics:
```bash
cargo install maturin
maturin develop --cargo-extra-args="--features python-extension"
```