Hi folks, please can anyone help: mathematica.stackexchange.com/questions/87503/…

Now I know the inspiration for Mathematica Dataset... R data.table

The R recycling strategy for data.table is very interesting.

@Guesswhoitis. Since you have more experience in such things: Why is it so hard to construct a parametrisation for the implicit surface of this nice question? I did not had enough time to look at this carefully, but lets say we have given one point on the surface that we know. Additionally, as you pointed out we could use e.g. the Hopf parametrisation to stay on S^3.

Wouldn't there be any possibility to create parametrisation of the surface that somehow follows the surface by using our initial point and keeps track of the surface through the gradient?

@halirutan, I tried that this morning, actually. I wound up with rather intractable algebraic equations that don't admit nice solutions. Attempting to plot them resulted in a mess.

I had even thought that restricting the parameters would be a way to implicitly enforce the positive real part constraint, but Reduce[] did not produce anything useful. :(

In short: I'm out of ideas for that one.

@Guesswhoitis. I got lost too but to my defense, it was pretty late here and as I said, I read the first time about Hopf parametrisation.

Usually, it works nicely. I was able to do the Hopf fibration of the flat torus with that, so I had naïvely assumed it should also work here. Oh well…

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@halirutan IIRC, you were doing an automated window blind project at some point. If so, this might be of interest to you.