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:

[dependencies]

padic = "0.1.4"

use padic::Ratio;
let ratio = Ratio::new(1, 3);
let padic = r.to_padic(5, 6);
assert_eq!(padic.valuation, 0);
assert_eq!(padic.expansion, vec![3, 1, 3, 1, 3, 2]);
assert_eq!(padic.to_string(), "...3 1 3 1 3 2");

Helpers functions

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

Resources

• https://en.wikipedia.org/wiki/P-adic_number
• https://www.cut-the-knot.org/blue/p-adicExpansion.shtml

TODOs

Ratio

• Extract sign information to transform ratio into a tuple of unsigned integer variables
• Reduce ratio to lowest terms using GCD (Stein's algorithm)
• Basic arithmetic operations for rational numbers

P-adic

• Prime decomposition returning vector of (prime, exponent) tuples.
• P-adic valuation of rational number
• P-adic norm of rational number
• P-adic expansion of rational number with given precision
• P-adic string representation with given precision and given valuation
• Cyclic detection in p-adic expansion
• Convert p-adic expansion into rational number
• Basic operations for p-adic numbers

Bugs

• 5-adic expansion of 25/3 is not correct
• 5-adic expansion of 1/75 is not correct

License

MIT