mathlib
jupyter
mathlib | jupyter | |
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36 | 13 | |
1,639 | 14,731 | |
1.2% | 0.2% | |
8.8 | 7.2 | |
12 days ago | 6 days ago | |
Lean | Python | |
Apache License 2.0 | BSD 3-clause "New" or "Revised" License |
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mathlib
- An Easy-Sounding Problem Yields Numbers Too Big for Our Universe
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Towards a new SymPy: part 2 – Polynomials
It's been on my mind lately as well. I was trying out `symbolics.jl` (a CAS written in Julia), and it turned out that it didn't support symbolic integration beyond simple linear functions or polynomials (at least back then, things have changed now it seems). Implementing a generic algorithm for finding integrals is hard, but I was expecting more from that CAS since this seems to be implemented in most other CASs. The thing is that every single CAS that covers general maths knowledge will have to implement the same algorithm, while it's hard to do it even once!
I feel like at least a large part of the functionality of a general purpose CAS can be written down once, and every CAS out there could benefit from it, similar to what the Language Server Protocol did for programming tools. They also had to rewrite the same tool for some language multiple times because there are lots of editors out there, and the LSP cut the time investment down a lot. They did have to invest a large amount of time to get LSP up and running, and it'll have to be maintained, but I think it's orders of magnitudes more efficient than having every tool developed and maintained for every single (programming language, editor) pair out there.
Main problem is like you said how to write down mathematical knowledge in a way that all CASs can understand it. I've been learning about Mathlib lately [0], which seems like a great starting point for this. It is as far as I know one of the first machine readable libraries of mathematical knowledge; it has a large community which has been pushing it continuously forward for years into research-level mathematics and covering the entire undergraduate maths curriculum and it's still accelerating. If some kind of protocol can be designed to read from libraries like this and turn it into CAS code, that would be a major step towards making the CAS ecosystem more sustainable I think.
It's not exactly what you were talking about, as in, this would allow multiple CASs to co-exist and benefit from each other, but I think that's better than having one massive CAS that has a monopoly. No software is perfect, but having a diverse set of choices that are open source would be more than enough to satisfy everyone.
(I have posted about this before on the Lean Zulip forum, it's open to everyone to read without an account [1])
[0] https://leanprover-community.github.io/
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Lean 4.0.0, first official lean4 release
Kinda agree but Mathlib and its documentation makes for a big corpus to learn by example from. Not ideal but it helps.
https://github.com/leanprover-community/mathlib
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It's not mathematics that you need to contribute to (2010)
https://github.com/leanprover-community/mathlib
https://1lab.dev/
You can watch the next generation, or participate, right now.
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If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.
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Will Computers Redefine the Roots of Math?
For the math that you mention, I would suggest looking at mathlib (https://github.com/leanprover-community/mathlib). I agree that the foundations of Coq are somewhat distanced from the foundations most mathematicians are trained in. Lean/mathlib might be a bit more familiar, not sure. That said, I don't see any obstacles to developing classical real analysis or linear algebra in Coq, once you've gotten used to writing proofs in it.
- Did studying proof based math topics e.g. analysis make you a better programmer?
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Which proof assistant is the best to formalize real analysis/probability/statistics?
At this point I would go with Lean because of mathlib. Mathlib's goal is to formalize modern mathematics, so many of the theorems you would need for analysis should already be there for you.
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[R] Large Language Models trained on code reason better, even on benchmarks that have nothing to do with code
I think about that every day. Lean's mathlib is a gigantic (with respect to this kind of project) code base and each function, each definition has a precise and rigorous natural language counterpart (in a maths book, somewhere).
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Is there a paid service where someone can explain a paper to me like I am 15?
It's been around since 2013, although there are LLM that interact with Lean to do automated theorem proving. Anyway, you can learn more about Lean here. I enjoyed their natural numbers game (which reminds, me I should finish the last two levels)
jupyter
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Mastering Data Science: Top 10 GitHub Repos You Need to Know
6. Jupyter Jupyter is a collection of tools and applications designed for interactive computing and data visualization. At the heart of the Jupyter ecosystem is the Jupyter Notebook, an interactive web-based platform that allows you to create and share documents containing live code, equations, visualizations, and narrative text. It’s an excellent tool for exploratory data analysis, model prototyping, and creating reproducible data science workflows.
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You can run Rust code in a Jupyter notebook
How cool. This motivated a quick search - this could be fun:
How to write your own kernel
https://jupyter-client.readthedocs.io/en/stable/kernels.html
All the language kernels (a lot of abandoned ones - the mariaDB one ('binder') will take a while to load but SQL in Jupyter!)
https://github.com/jupyter/jupyter/wiki/Jupyter-kernels
- Resource for interesting data science project notebooks
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Mathics: A free, open-source alternative to Mathematica
There are Jupyter kernels for Python, Mathics, Wolfram, R, Octave, Matlab, xeus-cling, allthekernels (the polyglot kernel). https://github.com/jupyter/jupyter/wiki/Jupyter-kernels
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How does 3[a] gives the element at index 3 in an array?
Not only there is. But it is only a simple Google search away... But to make it simpler... There are 3 😁 https://github.com/jupyter/jupyter/wiki/Jupyter-kernels
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How to use Jupyter notebooks in a conda environment?
As it seems, this is not quite straight forward and manyusers have similar troubles.
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Semi-Weekly Discussion Thread - February 21, 2022
Community maintained kernels : https://github.com/jupyter/jupyter/wiki/Jupyter-kernels
- Node.js Notebooks
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Python Tutorials using Jupyter Notebook
Derek Banas on YouTube is doing a "Python for Finance" course at ghe moment using Jupyter, and is making the files available. I believe he's done others too.Failing that, there's this Git repo: A gallery of interesting jupyter notebooks
- Github Discussion: What is your favorite Data Science Repo?
What are some alternatives?
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
nteract - 📘 The interactive computing suite for you! ✨
Coq-Equations - A function definition package for Coq
cookiecutter-data-science - A logical, reasonably standardized, but flexible project structure for doing and sharing data science work.
mathquill - Easily type math in your webapp
pyodide - Pyodide is a Python distribution for the browser and Node.js based on WebAssembly
fricas - Official repository of the FriCAS computer algebra system
vscode-python - Python extension for Visual Studio Code
polynomial-algebra - polynomial-algebra Haskell library
quokka - Repository for Quokka.js questions and issues
lean-liquid - 💧 Liquid Tensor Experiment
Kedro - Kedro is a toolbox for production-ready data science. It uses software engineering best practices to help you create data engineering and data science pipelines that are reproducible, maintainable, and modular.