number-theory-toolkit

提供数论算法的实现方案与指导建议

SKILL.md

--- frontmatter

name: number-theory-toolkit
description: Provide number theory algorithm implementations and guidance
allowed-tools:
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Number Theory Toolkit Skill

Purpose

Provide implementations and guidance for number theory algorithms commonly used in competitive programming.

Capabilities

•Modular arithmetic operations
•Extended Euclidean algorithm
•Chinese Remainder Theorem
•Modular inverse and exponentiation
•FFT/NTT for polynomial multiplication
•Linear sieve implementations

Target Processes

•number-theory-algorithms
•prime-algorithms
•combinatorics-counting

Algorithm Catalog

Modular Arithmetic

•Modular exponentiation (binary exp)
•Modular inverse (Fermat/Extended GCD)
•Modular square root (Tonelli-Shanks)

GCD and Extensions

•Euclidean algorithm
•Extended Euclidean algorithm
•Linear Diophantine equations

Chinese Remainder Theorem

•CRT for coprime moduli
•General CRT

FFT/NTT

•Fast Fourier Transform
•Number Theoretic Transform
•Polynomial multiplication

Input Schema

json

{
  "type": "object",
  "properties": {
    "algorithm": { "type": "string" },
    "parameters": { "type": "object" },
    "language": {
      "type": "string",
      "enum": ["cpp", "python", "java"]
    },
    "modulo": { "type": "integer" }
  },
  "required": ["algorithm"]
}

Output Schema

json

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "code": { "type": "string" },
    "explanation": { "type": "string" },
    "complexity": { "type": "string" }
  },
  "required": ["success"]
}