Speed up arithmetic in simplicial cohomology rings

[HechtiDerLachs]

A first take on #6066.

I cut out some uses of the OFPModule functionality over the integers, cached the result of is_zero checks, and cached the output of faces on SimplicialComplexes. This brings down the timing from the example in #6066 to

julia> @time G = matrix_space(ZZ, 22, 22)([integral(a*b) for a in g for b in g]);
 11.136035 seconds (163.40 M allocations: 4.268 GiB, 41.75% gc time, 0.75% compilation time)

for me. Ping @micjoswig , @benlorenz

[HechtiDerLachs]

I am now at

julia> C = Oscar.SimplicialCochainComplex(ZZ, K);

julia> # automated version which seeks out a single generator for the top cohomology
       A = Oscar.DGAlgCohRing(C)
Oscar.DGAlgCohRing{ZZRingElem}(Free module of rank 16 over integer ring --> Free module of rank 120 over integer ring --> Free module of rank 560 over integer ring --> Free module of rank 720 over integer ring --> Free module of rank 288 over integer ring
, Free module of rank 1 over integer ring --> Free module of rank 0 over integer ring --> Free module of rank 22 over integer ring --> Free module of rank 0 over integer ring --> Free module of rank 1 over integer ring
, #undef, #undef, #undef, #undef, #undef)

julia> Oscar.set_volume_form!(A);

julia> g = small_generating_set(A, 2); r = 22;

julia> @time G = matrix_space(ZZ, r, r)([integral(a*b) for a in g[1:r] for b in g[1:r]])
  1.735812 seconds (28.81 M allocations: 897.702 MiB, 27.27% gc time, 4.95% compilation time)

There is a subtlety here: If you suppress the output when creating A, the simplified_cochain_complex is not computed. This seems to lead to a different small_generating_set for which computations of the intersection matrices take much longer!

However, this is by design of simplify for complexes: It computes the simplification lazy and given the information that has already been discovered. The printing triggers these starting from 0, otherwise we start at degree 2 directly. We have these phenomena often in commutative algebra. The same led to the tests timing out in until yesterday (@benlorenz probably remembers). So there's not so much we can/want to do about this, I guess. The good news is that you can get your result now within less than two seconds.

@benlorenz wanted to have another look whether some of the caching here can be done more reasonably in conjunction with polymake's internals.

[micjoswig]

Improvement looks impressive. Thanks.

[fieker]

@HechtiDerLachs @benlorenz will discuss this for the next step

[benlorenz]

I now made the simplicial complex cache the faces in a julia datatype, while we could avoid many unnecessary calls it still helps quite a bit and brings the time down to about 2 seconds now. (It took 12 seconds without the cache and using the polymake sets directly, since they still need some amount of copying to be able to do the relevant operations)

[HechtiDerLachs]

Looks good. Thanks @benlorenz !

[benlorenz]

There is a weird failure in the Ring conformance tests for the DGAlgCohRing type:

https://github.com/oscar-system/Oscar.jl/actions/runs/31386085115/job/93748941519?pr=6074#step:11:4713

Basic functions: Test Failed at /home/oscarci-tester/ssd-data/ssd-runner-22/julia/packages/AbstractAlgebra/V9Znx/ext/TestExt/Rings-conformance-tests.jl:104
  Expression: equality(a + b, b + a)
   Evaluated: equality(0, 0)
  Stacktrace:
   [1] macro expansion
     @ ~/ssd-data/ssd-runner-22/_work/_tool/julia/1.13-nightly/x64/share/julia/stdlib/v1.13/Test/src/Test.jl:753 [inlined]
   [2] macro expansion
     @ ~/ssd-data/ssd-runner-22/julia/packages/AbstractAlgebra/V9Znx/ext/TestExt/Rings-conformance-tests.jl:104 [inlined]
   [3] macro expansion
     @ ~/ssd-data/ssd-runner-22/_work/_tool/julia/1.13-nightly/x64/share/julia/stdlib/v1.13/Test/src/Test.jl:1961 [inlined]
   [4] macro expansion
     @ ~/ssd-data/ssd-runner-22/julia/packages/AbstractAlgebra/V9Znx/ext/TestExt/Rings-conformance-tests.jl:73 [inlined]
   [5] macro expansion
     @ ~/ssd-data/ssd-runner-22/_work/_tool/julia/1.13-nightly/x64/share/julia/stdlib/v1.13/Test/src/Test.jl:1961 [inlined]
   [6] test_NCRing_interface(R::NCRing; reps::Any)
     @ TestExt ~/ssd-data/ssd-runner-22/julia/packages/AbstractAlgebra/V9Znx/ext/TestExt/Rings-conformance-tests.jl:26
Test Summary:                                                                                            | Pass  Fail  Total   Time
simplicial_cohomology                                                                                    | 4563     1   4564  12.0s
  NCRing interface for Oscar.DGAlgCohRing{ZZRingElem}(Free module of rank 4 over integer ring --> Free module of rank 5 over integer ring --> Free module of rank 2 over integer ring
, Free module of rank 1 over integer ring --> Free module of rank 0 over integer ring --> Free module of rank 0 over integer ring
, SubquoModule{ZZRingElem}[Submodule with 1 generator
  1: e[1] + e[2] + e[3] + e[4]
represented as subquotient with no relations, Subquotient of submodule with 3 generators
  1: -e[1] + e[3] - e[5]
  2: e[4] + e[5]
  3: e[1] + e[2]
by submodule with 4 generators
  1: -e[1] - e[2]
  2: e[1] - e[3] - e[4]
  3: e[2] + e[3] - e[5]
  4: e[4] + e[5], Subquotient of submodule with 2 generators
  1: e[1]
  2: e[2]
by submodule with 5 generators
  1: e[1]
  2: -e[1]
  3: e[1] + e[2]
  4: -e[2]
  5: e[2]], #undef, #undef, #undef, #undef, #undef) of type Oscar.DGAlgCohRing{ZZRingElem}              | 4554     1   4555   3.4s
    Functions for types and parents of rings                                                            |   23           23   1.6s
    Constructors                                                                                        |   25           25   0.0s
    Basic functions                                                                                     |  410     1    411   1.4s
    Adhoc operations with Integers                                                                      |  360          360   0.2s
    Adhoc operations with Integers{Int64}()                                                             |  360          360   0.0s
    Adhoc operations with Integers{UInt64}()                                                            |  360          360   0.0s
    Adhoc operations with Integers{UInt8}()                                                             |  360          360   0.0s
    Basic functionality for noncommutative rings only                                                   |   60           60   0.0s
    Unsafe ring operators                                                                               | 2595         2595   0.1s

This did happen twice now, but only for julia 1.13 (1.13.0-rc1.105). Once the current re-run of the failures is done I would try to restart all jobs to see if this appears anywhere else.

[codecov]

Codecov Report

❌ Patch coverage is 91.66667% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.81%. Comparing base (ca196fb) to head (fc222ab).
⚠️ Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
...tal/DoubleAndHyperComplexes/src/cohomology_ring.jl	90.62%	3 Missing ⚠️
...ndHyperComplexes/src/Objects/simplicial_complex.jl	87.50%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6074      +/-   ##
==========================================
- Coverage   83.83%   83.81%   -0.03%     
==========================================
  Files         789      789              
  Lines      108512   108548      +36     
==========================================
+ Hits        90971    90977       +6     
- Misses      17541    17571      +30     

Files with missing lines	Coverage Δ
src/Combinatorics/SimplicialComplexes.jl	94.19% <100.00%> (+0.23%)	⬆️
...ndHyperComplexes/src/Objects/simplicial_complex.jl	87.32% <87.50%> (-12.68%)	⬇️
...tal/DoubleAndHyperComplexes/src/cohomology_ring.jl	65.48% <90.62%> (-7.99%)	⬇️

... and 4 files with indirect coverage changes

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[benlorenz]

There is a weird failure in the Ring conformance tests for the DGAlgCohRing type:

...

This did happen twice now, but only for julia 1.13 (1.13.0-rc1.105). Once the current re-run of the failures is done I would try to restart all jobs to see if this appears anywhere else.

I can reproduce this locally, but only with 1.13-rc2 (It did not happen with 1.13-rc1 which I tried before).