Cox-Zucker

The Cox-Zucker Machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines if a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface $E \to S$ where $S$ is isomorphic to the projective line.

The algorithm was first published in Intersection numbers of sections of elliptic surfaces (1979), by Cox and Zucker, and it was later named the "Cox–Zucker machine" by Charles F. Schwartz in A Mordell-Weil group of rank 8, and a subgroup of finite index (1984).

And I did check the paper by Charles Schwartz, and indeed:

We will find, for a specific equation of this form, $$y^2 = 4(x^3 - u^4x + 1),$$ 8 solutions that generate a subgroup of index 4 in the Mordell-Weil group of the fibration given by this equation. We do this using the Cox-Zucker Machine. We then use this result to draw certain conclusions concerning the general case, and to make certain conjectures. 

§ 1. The algorithm of Cox and Zucker (AKA, The Cox-Zucker Machine)...

6 tech problems that every lawyer should think about

I wrote an email to an acquaintance who is a lawyer, advising them on the most pressing issues that a lawyer should deal with in a world that's changing quickly by AI, cryptocurrency, and some other technologies. Here's the edited version of it.

Have you studied more about AI? Kai-fu Lee wrote a new book AI Superpowers, and it is worth a read. You could read and watch a presentation here, and an interview with Wharton here.

There will be a very strong market for lawyers proficient in legal issues around AI and other emerging technologies, and I think you can benefit from learning more. Here are some problems for you to think about:

1. Income inequality is increasing more and more in the world due to AI. Read a piece by Kai-fu Lee to see why. How should the laws be changed so that those who lose their jobs won't sink into poverty? Universal Basic Income? Free education? Unemployment benefits?
2. If a self-driving car kills someone, who are legally responsible?
3. If a self-driving car senses that the brakes failed and there is a group of people walking in front, should it crash into the crowd, killing 3, or crash into the side of the road, killing 1 in the car?
4. How would the laws treat bitcoins and other cryptocurrencies?
5. What are the legal tasks that AI can perform? What would the lawyers do instead? Watch this TED talk. There are already companies like Kira that do lawyer work with AI, and their capabilities would only grow and grow.
6. Algorithmic discrimination: what to do where the algorithms create discrimination? See this and this.