Quartic formula, no obvious bugs

[Mathnerd314]

This should work. Tell me if I did anything wrong.

[fryguybob]

It would be nice to look into some numerical methods works and see if there is a comparison between using an explicit quartic formula and some other iterative algorithm. I suspect that the quartic formula will have cases with significant inaccuracy. I'm not saying not to include this, but it would also be nice to have appropriate iterative root finding methods and have a handle on when to use which. Also I agree with @jeffreyrosenbluth about style. Finally, the toler tolerance should be an explicit argument with a default argument baked into another function. I could be hardcoded if you had a proof that it is the best possible tolerance for the particular Floating instance.

[bergey]

First of all, I think we're all being more nitpicky than usual for a commit this size. @Mathnerd314, it's because we're looking forward to lots more code from you that we want to talk about these style points immediately. (I'm very glad that folks are reading and commenting.)

I really like the comment density. I always find this kind of numeric code hard to follow, but I think the comments make it about as coherent as possible. If you can take out a layer or two of nesting, as @jeffreyrosenbluth suggests, or assign names to some of the intermediate results, that will help even more.

Otherwise, I agree with what others' have said. quartForm' and cubForm' for the versions taking an extra tolerance argument would be consistent with other names in Diagrams.

[bergey]

Oh, and I think someone should open a new ticket about some numerical root-finding method. It's probably not a high priority since we don't yet have any code that uses polynomials above cubic.

[Mathnerd314]

I filed #188.

[bergey]

I think you should export cubForm' and quartForm' also. Otherwise, looks good to me.

[byorgey]

Looks good to me.