Release v1.0.0

Official implementation of numerical computations supporting the paper "Bad reduction of genus two curves with complex multiplication".

Features

• SageMath notebooks for intersection number computation on principal / non-principal orders
• Polarization matrix reduction following Algorithms 3.6 & 3.9 from GHR
• Magma script for genus-two curve generation and Rosenhain invariant computation
• LLL-based minimal polynomial reconstruction for Rosenhain lambda invariants

Methodological Improvements

• Replaces precision-sensitive BestApproximation recovery with LLL exact reconstruction
• Stable computation of invariants over general algebraic number fields
• Robust to numerical precision errors compared with previous GHR implementation

Usage

Manual bounds for $|c_1|,|c_2|$ and polarization class identification are required for "bad_reduction_intersection_number-nonprincipal.ipynb". Magma module requires manual matrix input for online calculator execution.