Changing visibility of ekore and Splitting constants.rs

[AkshatRai07]

This PR fixes #539, and is a pre-requisite to #537.

• Changed visibility of functions and modules in ekore crate. pub was converted to pub(super), and if that resulted in error it was converted to pub(crate).
• Split constants.rs to 3 files:
  • math_constants.rs with all the Zeta function values.
  • qcd_constants.rs with all QCD constants.
  • pid.rs with the rest of the constants, with PID_* and MAX_ORDER_* being the only public constants (are/will be exposed publicly in the future).

[Copilot]

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[AkshatRai07]

I was a bit confused in placing of MAX_ORDER_* constants, they aren't mathematical nor confined to QCD, so added them in pid.rs because other public constants are present in that.

Second, there was a warning in cargo build --workspace:

   Compiling ekore v0.0.1 (/home/akshatrai/Documents/GSoC/eko/crates/ekore)
warning: variants `Sm2o`, `Sm3o`, and `Sm21o` are never constructed
  --> crates/ekore/src/harmonics/cache.rs:41:5
   |
 9 | pub(crate) enum K {
   |                 - variants in this enum
...
41 |     Sm2o,
   |     ^^^^
...
45 |     Sm3o,
   |     ^^^^
...
49 |     Sm21o,
   |     ^^^^^
   |
   = note: `K` has a derived impl for the trait `Debug`, but this is intentionally ignored during dead code analysis
   = note: `#[warn(dead_code)]` (part of `#[warn(unused)]`) on by default

warning: `ekore` (lib) generated 1 warning
   Compiling eko v0.0.1 (/home/akshatrai/Documents/GSoC/eko/crates/eko)
    Finished `dev` profile [unoptimized + debuginfo] target(s) in 0.56s

This is not a pre-commit issue, just a warning that these three things, Sm2o, Sm3o, and Sm21o are used nowhere in the ekore crate except at their declarations and K.

[felixhekhorn]

• Please add a Changelog entry
• I'm not sure yet what to do with the unused functions ... let's discuss tomorrow; most likely we will just drop them

[AkshatRai07]

So Sm1o was also unused but compiler was not giving warning about that until I removed the other 3 functions.

[felixhekhorn]

I change my mind again: let's keep the functions! sorry 😇 can you please just revert 0bece9e ? We need them when we port

eko/src/ekore/anomalous_dimensions/polarized/space_like/as3.py

Line 331 in 9603243

def gamma_nss(N, nf, cache):

to Rust.

Here comes a math statement: at a given order in the coupling (e.g. $a_s^3$ -> as3.py), we explore a given set of special functions, in particular a given set of harmonic sums. In this case: $a_s^3$ explores harmonic sum up to weight 3. Specifically, here we need $S_3, S_{-3},S_{-2,1}$, etc. (i.e. the indices sum in absolute value to 3) and "up to" implies we also need lower order ones, e.g. $S_{-2}$. The polarized and unpolarized anomalous dimensions explore two different spaces (some of which is related by "odd" <-> "even"). Here we see an explicit example thereof.

[AkshatRai07]

All 4 functions are back now