Lattice Documentation (Indefinite-First)

Purpose

This docs set exists to provide practical, accurate references for free/open lattice software with a primary focus on indefinite lattices.

The goal is to support workflows such as:

• indefinite quadratic form classification,
• local/global/rational isometry checks,
• discriminant-form and genus computations,
• hyperbolic/reflection-lattice methods (e.g. Vinberg-style workflows),
• lattice-with-isometry constructions used in arithmetic/algebraic geometry contexts.

Priorities

1. Indefinite-lattice methods first.
2. Explicit method-level documentation (not vague package summaries).
3. Clear definiteness constraints and caveats.
4. Source-backed claims (official docs/source when possible).
5. Coverage across major free systems and packages.

Non-Goals

• Proprietary CAS workflows (e.g. Magma, Wolfram).
• Polytope-counting-first documentation unless directly relevant to indefinite lattice work.
• Credit-by-alias or hidden coverage shortcuts.

Practical Rule

When deciding what to add or refine, prefer content that improves indefinite workflows before expanding Euclidean-only reduction material.

Setup

1. Install Miniforge (conda)

curl -L -O "https://github.com/conda-forge/miniforge/releases/latest/download/Miniforge3-$(uname)-$(uname -m).sh"
bash "Miniforge3-$(uname)-$(uname -m).sh" -b -p ~/miniforge3
~/miniforge3/bin/conda init bash

Open a new shell (or source ~/.bashrc) so that conda is on your PATH.

2. Create the SageMath environment

conda create -n sage sage -y

This downloads and installs SageMath (~1 GB, takes several minutes).

3. Install project Python dependencies

conda run -n sage python -m pip install pytest juliacall juliapkg pydantic pyright black

4. Verify

conda run -n sage sage -c "print('Hello from SageMath', version())"

Shortcut

Steps 1–3 are wrapped in a single just recipe (run from the repo root):

just install-sage

Running tests

just test       # standard suite
just test-full  # includes in-progress wrapper-contract tests

Agents

Agents live under agents/, one directory per task. Each task has a shared task.log (the running record of all work done on that task, appended by every agent run) and per-agent debug subdirectories for individual run output.

agents/doc_coverage/ — documentation coverage

• prompt: agents/doc_coverage/prompt.md
• playbook: agents/doc_coverage/playbook.md
• runners:
  • run_codex_docs_agent.sh — OpenAI Codex
  • run_claude_docs_agent.sh — Claude (Sonnet, extended thinking)
  • run_amp_docs_agent.sh — Amp (smart mode)
  • run_ollama_docs_agent.sh — Ollama launching Claude integration (non-interactive)

agents/test_coverage/ — test coverage

• prompt: agents/test_coverage/prompt.md
• playbook: agents/test_coverage/playbook.md
• runners:
  • run_codex_test_coverage_agent.sh — OpenAI Codex
  • run_claude_test_coverage_agent.sh — Claude (Sonnet, extended thinking)
  • run_amp_test_coverage_agent.sh — Amp (smart mode)
  • run_ollama_test_coverage_agent.sh — Ollama launching Claude integration (non-interactive)

Runners can be invoked directly or scheduled via system cron.