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AGENTS.md

Commands

python3 -m venv .venv && source .venv/bin/activate  # Setup venv
pip install numpy scipy sympy pytest                 # Dependencies
pytest tests/ -v                                     # Run test suite
python benchmark.py --quick                          # Quick benchmark
python -m factorization 1234567                      # CLI usage
python -m factorization --info                       # Show available algorithms

Architecture

Modular package in factorization/:

  • utils.py - GCD, primality, Tonelli-Shanks, factor base utilities
  • trial.py - Trial division O(√n)
  • fermat.py - Fermat's difference of squares (good for p≈q)
  • pollard_rho.py - Brent's cycle detection O(n^1/4)
  • squfof.py - Shanks' Square Forms O(n^1/4)
  • pollard_pm1.py - Two-stage p-1 for smooth (p-1)
  • williams_pp1.py - p+1 method using Lucas sequences
  • ecm.py - Montgomery curves, Lenstra's ECM
  • qs.py - Quadratic Sieve with log sieving
  • mpqs.py - Self-Initializing QS (SIQS)
  • gnfs.py - General Number Field Sieve (experimental)
  • linear_algebra.py - GF(2) Gaussian elimination
  • simd.py - Numba JIT-compiled hot loops
  • parallel.py - Multiprocessing support
  • __main__.py - CLI interface

Auto-selection in __init__.py: trial → Pollard Rho → ECM → MPQS based on size.

Code Style

  • Type hints everywhere (List, Tuple, Optional, etc.)
  • Docstrings explain the math, not just the API
  • gmpy2 optional for 10-100x speedup on big integers
  • Each algorithm self-contained with clear theory references