Talk:Pólya enumeration theorem

In the formulas enumerating colourings of objects with respect to their edge length/size k, the exponents in each term (for each action) are polynomial functions of k, and can be split into fractions, such that each one with denominator d has as its numerator the number of cycles with length d (where d is a proper divisor of the action's period). My program outputs them in this form, I had initially kept all of the polynomials for different cycle lengths in separate fractions and conserved their denominators, so they conserved this information, however my reduction to the octahedron one I inlined some ternary operators into modulos and sacrificed this. Shall it be changed for all equations, with the mention of the program moved to the bottom and explained to be able to provide this? DroneBetter (talk) 16:11, 5 January 2023 (UTC)

Probably it is not necessary to keep, I will group everything together in a single fraction in each exponent for the others, to avoid incurring floating point precision errors (that doesn't seem to occur for hypercubes). DroneBetter (talk) 17:52, 5 January 2023 (UTC)

Update: In creating A361870, I realised they could all be expressed more simply in single cases, with the branching over parities done by floor divisions, then was informed that it seemed I was adding one less than the denominator to the numerator in all cases, and that this constant offset could be removed by replacing them with ceiling divisions, which I have used here (in my rewrite). DroneBetter (talk) 14:23, 6 August 2023 (UTC)

Cleanup suggestions

Suggested changes:
- use juxtaposition or '·' for multiplication, instead of '*'.
- use '°' for angles measured in degrees, instead of 'º'.
- surround '=', '+', '−', '·', '/' with single spaces.
- add single spaces after ',' in integer sequences.
- in "Example derivation", reduce width of the diagram. (Currently the diagram doesn't fit on the wider of my screens. If I zoom the page in the browser then the text becomes too small to read.)
- for expressions with multiple subcases, use multi-line case notation, instead of single-line nested if-then-else. Confocal (talk) 08:50, 6 August 2023 (UTC)

- I spoke with Darren Li, who recommended that the beginning be rewritten to forgo the initial trivial conditions and instead state the theorem directly, maybe I will also add a proof.
-We are somewhat constrained by the lack of anything like the MediaWiki math library here. Apple Bottom added LaTeX images to frequency class and apgcode, but it seems quite inelegant to resort to embedding them and as though it would be hasslesome to edit, and this way they have wrapping.
- Though I'm not sure about your first or third suggestions, the current degrees symbols aren't chosen out of any personal preference, only because they're the default ones from pressing option-0 on macOS, I've been told that it renders underlined for others (like the Pólya enumeration theorem ), I'll change it in the next edit.
- Regarding decreasing width, I have a 13-inch MacBook, currently, with a 2560*1600 display, minimal text size and the "Looks like 1680*1050" option enabled (which may not seem much, but the default option is 1440*900), all embeds here seem to fit if I view them in my (below average) monitor's default setting. I've noticed you complained of a few LifeViewer galleries not fitting on your screen either when splitting them into multiple columns, they do for me (and I think also galoomba), perhaps check your own settings. DroneBetter (talk) 14:23, 6 August 2023 (UTC)

Even without something like MediaWiki math library, it is possible to split a long nested expression into parts, with e.g. each individual line of the form "f(n) = ... if P(n)". When an expression is wrapped through multiple lines, I think that's a signal that the expression is probably too long.
Re: screen width -- it's not about my screen width. I don't have major problems with viewing other viewers in the current version. But that "diagram of actions" is too wide, not only for me, but also for potential and actual readers. Confocal (talk) 14:55, 6 August 2023 (UTC)