[FTheoryTools] Compute all well-quantized and vertical G4-fluxes

[HereAround]

Sadly still WIP.

cc @apturner @emikelsons

[HereAround]

Ok - this master piece (hopefully?) is finally getting ready. "What is in this PR?" is hear you ask:

• It implements the methods necessary to compute all well-quantized G4-fluxes. In particular, it adds specialized intersection theory, so we can handle the big model in a timely-fashion.
• I have serialized most of the computed data, so that we can save those fluxes in the .mrdi file of the big model. As such, once this big-model file is loaded, the data will be available almost instantly. Downside is that said .mrdi file is now almost 1GB in size.

I am waiting for the tests to pass now/will make adjustments so that they do.

Beyond this, there are the following improvements that are possible:

1. We could of course profile more to see if we get more performance. I have done some effort in this regard already, so this may not be the most pressing concern.
2. I wish to add a new type FamilyOfG4Fluxes which we can use to wrap the return value of the new method well_quantized_g4_fluxes. Currently, it returns a tuple of two matrices and I added documentation to explain what this means. But then, this is not super cool for the end user. So it would be good to improve on this.

@apturner @emikelsons maybe we can discuss more shortly. If you find the time, take a (brief) look and let me know your thoughts.

[HereAround]

This is ready for your reviews @apturner and @emikelsons .

[codecov]

Codecov Report

Attention: Patch coverage is 55.14334% with 266 lines in your changes missing coverage. Please review.

Project coverage is 84.31%. Comparing base (3e670f7) to head (7f7fd50).
Report is 4 commits behind head on master.

Files with missing lines	Patch %	Lines
...yTools/src/G4Fluxes/special-intersection-theory.jl	0.00%	143 Missing ⚠️
...al/FTheoryTools/src/G4Fluxes/special_attributes.jl	77.65%	42 Missing ⚠️
...eoryTools/src/Serialization/hypersurface_models.jl	37.50%	25 Missing ⚠️
...ntal/FTheoryTools/src/Serialization/tate_models.jl	37.50%	25 Missing ⚠️
...heoryTools/src/Serialization/weierstrass_models.jl	37.50%	25 Missing ⚠️
...xperimental/FTheoryTools/src/G4Fluxes/auxiliary.jl	95.68%	6 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4286      +/-   ##
==========================================
- Coverage   84.52%   84.31%   -0.21%     
==========================================
  Files         645      649       +4     
  Lines       85706    86369     +663     
==========================================
+ Hits        72440    72823     +383     
- Misses      13266    13546     +280     

Files with missing lines	Coverage Δ
experimental/FTheoryTools/test/g4s.jl	100.00% <100.00%> (ø)
...xperimental/FTheoryTools/src/G4Fluxes/auxiliary.jl	95.68% <95.68%> (ø)
...eoryTools/src/Serialization/hypersurface_models.jl	62.63% <37.50%> (-20.06%)	⬇️
...ntal/FTheoryTools/src/Serialization/tate_models.jl	71.42% <37.50%> (-26.65%)	⬇️
...heoryTools/src/Serialization/weierstrass_models.jl	61.53% <37.50%> (-19.24%)	⬇️
...al/FTheoryTools/src/G4Fluxes/special_attributes.jl	80.99% <77.65%> (-15.27%)	⬇️
...yTools/src/G4Fluxes/special-intersection-theory.jl	0.00% <0.00%> (ø)

... and 10 files with indirect coverage changes

[HereAround]

@emikelsons and I found a bug in this PR yesterday, which we fixed yesterday. I have squashed all of those changes into one (hopefully) working commit. To verify that indeed things are working as intended, the tests have been extended accordingly. Also, I have extended on the documentation.

[HereAround]

I am confident that the tests pass once #4341 is resolved. @apturner and @emikelsons , could you please review this PR and tell me if it is good to go as is?

Certainly, this PR/change is not perfect. Among others, we could look for better performance. Add an attribute like base_divisors, base_divisor_positions, zero_section_index etc. Or we could have a check to tell if c2 is even for a given FTheory models. Or we could also compute all G4-fluxes that do not break non-Abelian gauge groups. Or the names of these functions might change (I am very happy for suggestions).

Still - I have postponed these improvements to a point in the future.

[HereAround]

Maybe we could add these points to our to-do list in #2699. And of course, we should gauge at some point, which of these tasks have been completed/need attention (and if so how urgent) etc...

[emikelsons]

Looks good and this has been extensively tested.