Add the (x*y)**a == ... formula

[certik]

Two issues to be resolved:

• [x] Precise definition of Arg(z)
• [x] How is the hash obtained? Randomly? This needs to be changed

Note: this formula is only correct if Arg is defined precisely as arg(z) = atan2(Im z, Re z), however, the Arg in Fungrim does not seem to be well defined (yet):

http://fungrim.org/entry/b7d740.html

so this needs to be settled first. Because if arg(z) is defined using some other branch cut, then the formula in this PR changes accordingly.

[fredrik-johansson]

python3 fungrim.py ids gives you a bunch of random ids. Just pick one.

You have the right definition of Arg. See http://fungrim.org/topic/Complex_parts.html and in particular entry b2a880.

A small bug: pi should be ConstPi. All the latin and greek letter variable names just represent variables right now in the Python code; perhaps pi should be overridden to alias ConstPi instead (or renamed to pi_) to prevent this bug.

Without having really checked the formula, I think the assumptions for x/y and a are swapped? Both x = 0 and y = 0 should be excluded since you want to rule out 0^-1. Conversely, a = 0 is ok as that just gives 1 on both sides.

Finally, the formula should be in a good subsection of the "Powers" topic page. Perhaps "Expansion", "Functional equations", or something like that. The structure can be improved when there are more formulas.

By the way, I haven't thought about how to record authorship for entries (if at all). If you want credit, you could perhaps just put your name in a comment next to the entry, until something concrete is implemented.

[certik]

Thanks for the feedback, I think I fixed everything. Regarding attribution, what git already does is enough for me.

[fredrik-johansson]

Very good, thanks!