P-adic numbers

A collection of tools for p-adic numbers in Rust.

This includes a p-adic type and a rational type.

Status

This library is currently in development. It is not yet ready for use.

Usage

Add this to your Cargo.toml:

toml [dependencies] padic = "0.1.1"

rust use padic::Ratio; let r = Ratio::new(2, 5); let p = r.to_padic(3, 10); assert_eq!(p.valuation, 0); assert_eq!(p.expansion, vec![1, 1, 2, 1, 0, 1, 2, 1, 0, 1]);

```

From rational number to p-adic number

• Reduce ratio to lowest terms
• Convert ratio into a list of tuples of prime factors and their exponents
• Retrieve p-adic norm
• Retrieve p-adic absolute value
• Compute p-adic expansion

Helpers functions

• Prime factors with multiplicity (a: i64 / b: i64) -> Vec<(prime: u64, exp: u64)>
• Greatest common divisor (Stein's algorithm)
• Modular multiplicative inverse

TODOs

• [x] Extract sign information to transform ratio into a tuple of unsigned integer variables
• [x] Reduce ratio to lowest terms using GCD (Stein's algorithm)
• [x] Prime decomposition returning vector of (prime, exponent) tuples.
• [x] P-adic valuation of rational number
• [x] P-adic norm of rational number
• [ ] P-adic expansion of rational number
• [ ] Convert p-adic expansion into rational number
• [ ] Basic operations for p-adic numbers

License

MIT