[ToricVarieties] Serialize cohomology classes

[HereAround]

This PR aims to serialize cohomology classes on toric varieties. This boils down to saving a polynomial, and ensuring that it resides in the cohomology ring of the toric variety (= a quotient ring)/the base ring of this quotient ring. Sadly I cannot get the code to work. The line:

poly = load_object(s, MPolyDecRingElem, base_ring(cohomology_ring(tv)), :polynomial)

raises the error:

ERROR: KeyError: key Symbol("1") not found

I am out of ideas how to fix this. Any ideas @antonydellavecchia? Help appreciated.

Here is a MWE, based on this PR:

p4 = projective_space(NormalToricVariety, 4)
cc = volume_form(p4)
save("/tmp/test.mrdi", cc)
load("/tmp/test.mrdi")

[HereAround]

Aside, I tried save_typed_object(s, polynomial(cc), :polynomial) first. Unless I am mistaken, serialization for MPolyQuoRingElem is not yet supported, correct?

[antonydellavecchia]

I think @HechtiDerLachs added support for this? Maybe it hasn't been merged?

[HereAround]

Ok. But do we really need this here?

The current version of the code tries to serialize a polynomial in the base ring (rather than the quotient ring). In theory, this is sufficient to serialize a (toric) cohomology class. But the loading of said polynomial does not work (yet) - reasons unclear/unknown to me.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 84.49%. Comparing base (4f19d60) to head (456e261).
Report is 9 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4266      +/-   ##
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+ Coverage   84.47%   84.49%   +0.02%     
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  Files         641      641              
  Lines       85394    85459      +65     
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+ Hits        72133    72210      +77     
+ Misses      13261    13249      -12     

Files with missing lines	Coverage Δ
src/Serialization/ToricGeometry.jl	98.41% <100.00%> (+0.37%)	⬆️

... and 4 files with indirect coverage changes