Module number_theory 

Number theory module for Proof Engine.

Provides prime number distributions, zeta functions, modular arithmetic, continued fractions, p-adic numbers, Gaussian integers, elliptic curves, Galois fields, and classic conjectures (Collatz, Goldbach) — all with rendering primitives that map to the engine’s glyph system.

Re-exports

pub use primes::sieve_of_eratosthenes;

pub use primes::is_prime;

pub use primes::nth_prime;

pub use primes::prime_counting;

pub use primes::prime_gaps;

pub use primes::twin_primes;

pub use primes::prime_factorization;

pub use primes::UlamSpiral;

pub use primes::SacksSpiral;

pub use primes::PrimeDistributionRenderer;

pub use zeta::Complex;

pub use zeta::zeta;

pub use zeta::zeta_on_critical_line;

pub use zeta::z_function;

pub use zeta::find_zeros;

pub use modular::mod_pow;

pub use modular::mod_inverse;

pub use modular::chinese_remainder_theorem;

pub use modular::primitive_roots;

pub use modular::discrete_log;

pub use continued_fractions::ContinuedFraction;

pub use padic::PAdic;

pub use padic::padic_norm;

pub use padic::padic_distance;

pub use gaussian::GaussianInt;

pub use elliptic::EllipticCurve;

pub use elliptic::CurvePoint;

pub use galois::GaloisField;

pub use galois::GfElement;

pub use collatz::collatz_sequence;

pub use collatz::collatz_stopping_time;

pub use collatz::CollatzTree;

pub use goldbach::goldbach_partition;

pub use goldbach::goldbach_count;

pub use goldbach::goldbach_comet;

pub use totient::totient;

pub use totient::totient_sieve;

pub use totient::totient_sum;

pub use totient::sigma;

pub use totient::tau;

pub use totient::mobius;

Modules

collatz

Collatz conjecture: sequences, stopping times, and tree visualization.

continued_fractions

Continued fractions: representation, convergents, and visualization.

elliptic

Elliptic curves over the reals: point arithmetic, rendering, and group law.

galois

Galois fields GF(p^n): arithmetic, generators, and multiplication tables.

gaussian

Gaussian integers Z[i]: arithmetic, primes, factorization, and lattice rendering.

goldbach

Goldbach’s conjecture: partitions, counts, and comet visualization.

modular

Modular arithmetic, CRT, discrete logarithm, and visualization.

padic

p-adic numbers: representations, norms, arithmetic, and fractal rendering.

primes

Prime number distribution, sieves, and rendering utilities.

totient

Euler’s totient function, divisor functions, and heatmap rendering.

zeta

Riemann zeta function, critical strip rendering, and zero detection.