Cache harmonics sums for the as2 anomalous dimensions

[niclaurenti]

Dear @felixhekhorn @alecandido @giacomomagni I'm opening this PR since in the anomalous dimensions at order as2 there are some harmonics sums that are used also in the QED sector. Then, as @felixhekhorn was suggesting we can use the ones that were cached in the computation of the QED anomalous dimensions. I didn't want to include these changes in the QED PR since it is already big enough.

[codecov-commenter]

Codecov Report

Merging #179 (63d800a) into feature/qed-solution (c825451) will decrease coverage by 0.00%.
The diff coverage is 100.00%.

Additional details and impacted files

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##           feature/qed-solution     #179      +/-   ##
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- Coverage                 99.96%   99.96%   -0.01%     
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  Files                       100      100              
  Lines                      5224     5194      -30     
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- Hits                       5222     5192      -30     
  Misses                        2        2              

Flag	Coverage Δ
isobench	?
unittests	99.96% <100.00%> (-0.01%)	⬇️

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Impacted Files	Coverage Δ
src/eko/anomalous_dimensions/__init__.py	100.00% <100.00%> (ø)
src/eko/anomalous_dimensions/aem2.py	100.00% <100.00%> (ø)
src/eko/anomalous_dimensions/as1aem1.py	100.00% <100.00%> (ø)
src/eko/anomalous_dimensions/as2.py	100.00% <100.00%> (ø)
src/eko/harmonics/__init__.py	100.00% <100.00%> (ø)
src/eko/runcards.py	100.00% <0.00%> (ø)
src/eko/constants.py	100.00% <0.00%> (ø)
src/eko/output/struct.py	100.00% <0.00%> (ø)
src/eko/basis_rotation.py	100.00% <0.00%> (ø)
src/eko/harmonics/constants.py	100.00% <0.00%> (ø)

[felixhekhorn]

why not upgrade the existing compute_cache? it computes already a list of e.g. weight 3 sums? and as said we want to have the minimal number possible ...

[giacomomagni]

why not upgrade the existing compute_cache? it computes already a list of e.g. weight 3 sums? and as said we want to have the minimal number possible ...

To use that you would need to rotate some harmonics, for instance get rid of S[m, (n-1)/2] in favor or S[-m,n], but I'd definitely do that. Note that also g3 only enters in the anomalous dimensions through S[-2,1,n] and using the series definition you can simplify g3(n+2)

[felixhekhorn]

maybe better for order,mode0,mode1,bla,bla in params?

[niclaurenti]

@felixhekhorn @alecandido @giacomomagni Should I close this PR given that this will be implemented in #202 ?

[felixhekhorn]

You can close it now if you're not actively using this branch or later when #202 is fully in place ...

[niclaurenti]

You can close it now if you're not actively using this branch or later when #202 is fully in place ...

Ok let's close it when #202 is completed

[alecandido]

Since some time passed, even if #202 is not yet done at this point we know nothing else will happen here. Thus, I'm closing this.