القائمة
Number theory — prime sieving, primality tests, modular arithmetic
التثبيت باستخدام Codex أو Claude انسخ هذا Prompt والصقه في Codex أو Claude أو مساعد آخر ليراجع صفحة Skill ويثبّتها لك.
استنادا إلى تصنيف SOC المهني
| name | ix-number-theory |
| description | Number theory — prime sieving, primality tests, modular arithmetic |
| disable-model-invocation | true |
Prime number operations and modular arithmetic utilities.
When the user needs prime numbers, primality testing, modular exponentiation, GCD/LCM, or modular inverses.
base^exp mod m via squaringa^{-1} mod m when it existsuse ix_number_theory::sieve::sieve_of_eratosthenes;
use ix_number_theory::primality::{is_prime_trial, is_prime_miller_rabin};
use ix_number_theory::modular::{mod_pow, gcd, lcm, mod_inverse};
Tool name: ix_number_theory
Operations: sieve, is_prime, mod_pow, gcd, lcm, mod_inverse, prime_gaps
Test model robustness with adversarial attacks and defenses
Multi-armed bandit simulation — epsilon-greedy, UCB1, Thompson sampling
Benchmark and compare ix algorithm performance
Embedded Redis-like cache with TTL, LRU, pub/sub, and RESP protocol
Category theory primitives — monad laws verification, free-forgetful adjunction
Chaos theory analysis — Lyapunov exponents, bifurcation, attractors, fractals