Improve performance of strict transform under toric blowups

[paemurru]

I improved the speed of strict_transform for an arbitrary toric blowup. More precisely, I improved cox_ring_module_homomorphism, which is used for strict_transform, total_transform and strict_transform_with_index. The main time-saving techniques:

• using MPolyBuildCtx to create the polynomial, instead of iteratively adding terms to a polynomial,
• using Vector{Rational{Int64}} instead of Vector{QQFieldElem} for the vector ps,
• using Vector{Int64} for the vector ps in the special case where the denominators are 1.

Some small other improvements in the core loop:

• using first(exponents(g)) instead of collect(exponents(g))[1],
• using exps = [exps; exceptional_exp] instead of push!(exps, exceptional_exp) reduces allocated memory by about 35% --- I am puzzled why there is a difference here.

The function strict_transform now seems to be faster than the specialized _strict_transform in FTheoryTools that could compute strict transform only under blowups along smooth cones. So I removed the specialized function.

Also, I added a test for computing the strict transform when blowing up along an existing ray.

Benchmarks

I used the F-Theory computations from @HereAround . Namely, I first commented out lines 797--803 of experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl

  # For model 1511.03209 and resolution_index = 1, a particular resolution is available from an artifact
#   if has_attribute(m, :arxiv_id)
#     if resolution_index == 1 && arxiv_id(m) == "1511.03209"
#       model_data_path = artifact"FTM-1511-03209/1511-03209-resolved.mrdi"
#       return load(model_data_path)
#     end
#   end

and edited line 821 of the same file from for k in 1:nr_blowups to for k in 1:5 to have a faster test.

Then ran

h = literature_model(arxiv_id = "1511.03209")
@btime h_5 = resolve(h, 1)

Results

Previously:

julia> @btime h_5 = resolve(h, 1)
  190.106 s (44395903 allocations: 10.13 GiB)
Partially resolved global Tate model over a concrete base -- The F-theory geometry with most flux vacua based on arXiv paper 1511.03209 Eq. (2.11)

Now:

julia> @btime h_5 = resolve(h, 1)
  188.573 s (38064085 allocations: 6.42 GiB)
Partially resolved global Tate model over a concrete base -- The F-theory geometry with most flux vacua based on arXiv paper 1511.03209 Eq. (2.11)

Improvements

• time is roughly the same (the exact time changes by a few seconds every run),
• there are now 14% fewer allocation instances compared to the specialized function in FTheoryTools,
• 37% less memory used for allocations than the specialized function in FTheoryTools.

[codecov]

Codecov Report

Attention: Patch coverage is 86.66667% with 2 lines in your changes missing coverage. Please review.

Project coverage is 84.39%. Comparing base (1f7ded1) to head (46ad165).
Report is 123 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/FTheoryTools/src/auxiliary.jl	0.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4484      +/-   ##
==========================================
+ Coverage   84.37%   84.39%   +0.01%     
==========================================
  Files         672      672              
  Lines       88717    88690      -27     
==========================================
- Hits        74855    74847       -8     
+ Misses      13862    13843      -19     

Files with missing lines	Coverage Δ
.../FTheoryTools/src/AbstractFTheoryModels/methods.jl	78.00% <100.00%> (ø)
experimental/Schemes/src/ToricBlowups/methods.jl	96.07% <100.00%> (+0.24%)	⬆️
experimental/FTheoryTools/src/auxiliary.jl	79.83% <0.00%> (+3.83%)	⬆️

... and 4 files with indirect coverage changes

[HereAround]

Wow! That is cool! Thank you @paemurru I am very content with your changes!