AI4Math · Computational Mathematics

Computational workflows for numerical evidence, symbolic structure, finite element reasoning, and mathematical invariant computation.

中文说明 · Contributors · Skill packages · Installation · Quick start · Security model

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What This Repository Is

This repository is the AI4Math home for computational mathematics skills. It collects packages for turning mathematical objects, equations, data, or paper excerpts into reviewed computational representations and reproducible evidence.

Use the root page as the public map, then open the package that matches your task.

Skill Packages

Package	Use it for	Start here
finite-element-analysis	Work through finite element modeling prompts, weak forms, element choices, and classroom-scale examples.	README · SKILL1 · SKILL2 · SKILL3
invariant-computation	Route and validate algebraic, topological, geometric, TDA, and certified numerical invariant computations.	README · SKILL
least-squares	Fit linear, polynomial, nonlinear, regularized, constrained, and Bayesian least-squares models.	README · SKILL
scientific-computing-reproduction	Reproduce, diagnose, tune, visualize, and report computational mathematics research code with human approval checkpoints.	README · SKILL

Installation

The recommended path is AI-assisted installation: ask your coding agent to clone or update this repository, read the Skill instructions, install the entrypoints, and verify discovery.

Please install these AI4Math Skills for me.

Repository: https://github.com/VeryMath/AI4Math-Computational-Mathematics.git
Branch: main
Skill paths:
- skills/finite-element-analysis
- skills/invariant-computation
- skills/least-squares
- skills/scientific-computing-reproduction

Steps:
1. Clone or update the repository locally.
2. Read README.md, SKILL.md, AGENTS.md if present, and each target Skill entrypoint.
3. If this environment supports local Skill discovery, link each directory that contains SKILL.md into the local skills directory.
4. Keep shared sibling support directories in place when a Skill depends on them.
5. Verify that the installed Skills are discoverable.
6. Tell me the installed paths, whether a restart is needed, and give me one test prompt.

Manual fallback for Codex-style local discovery:

git clone https://github.com/VeryMath/AI4Math-Computational-Mathematics.git
cd AI4Math-Computational-Mathematics
mkdir -p ~/.codex/skills
ln -s "$PWD/skills/finite-element-analysis" ~/.codex/skills/finite-element-analysis
ln -s "$PWD/skills/invariant-computation" ~/.codex/skills/invariant-computation
ln -s "$PWD/skills/least-squares" ~/.codex/skills/least-squares
ln -s "$PWD/skills/scientific-computing-reproduction" ~/.codex/skills/scientific-computing-reproduction

If your agent uses a different local Skill directory, replace ~/.codex/skills with that configured path.

Quick Start

Clone the repository and choose a package:

git clone https://github.com/VeryMath/AI4Math-Computational-Mathematics.git
cd AI4Math-Computational-Mathematics

For invariant workflows, start with:

skills/invariant-computation/SKILL.md

For finite element analysis, start with:

skills/finite-element-analysis/README.md

For least-squares modeling, start with:

skills/least-squares/SKILL.md

For scientific-computing reproduction and tuning, start with:

skills/scientific-computing-reproduction/SKILL.md

Repository Layout

AI4Math-Computational-Mathematics/
├── README.md
├── README.zh-CN.md
├── SKILL.md
└── skills/
    ├── finite-element-analysis/
    ├── invariant-computation/
    ├── least-squares/
    └── scientific-computing-reproduction/

Package-local examples are illustrative fixtures. Computation outputs, environment caches, and large generated artifacts should stay outside git unless they are intentionally curated examples.

Validation

There is no root build step. Validate changed standard skill packages with the local skill validator. For the finite-element package, review README.md and the numbered SKILL*.md files directly because it predates the standard single-SKILL.md layout.

Security and Scope

Do not commit private datasets, unpublished paper excerpts, solver credentials, API keys, .env files, generated caches, or large local outputs. Public examples should be source-attributed and safe to redistribute.