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
{
"type": "object",
"properties": {
"algorithm": { "type": "string" },
"parameters": { "type": "object" },
"language": {
"type": "string",
"enum": ["cpp", "python", "java"]
},
"modulo": { "type": "integer" }
},
"required": ["algorithm"]
}Output Schema
{
"type": "object",
"properties": {
"success": { "type": "boolean" },
"code": { "type": "string" },
"explanation": { "type": "string" },
"complexity": { "type": "string" }
},
"required": ["success"]
}