LieAlgebras: reduce allocations

[lgoettgens]

some representative workload comparisons between 4a5b96d (two days old master) and this PR branch

  ___   ____   ____    _    ____
 / _ \ / ___| / ___|  / \  |  _ \   |  Combining ANTIC, GAP, Polymake, Singular
| | | |\___ \| |     / _ \ | |_) |  |  Type "?Oscar" for more information
| |_| | ___) | |___ / ___ \|  _ <   |  Manual: https://docs.oscar-system.org
 \___/ |____/ \____/_/   \_\_| \_\  |  1.2.0-DEV #master 4a5b96d 2024-09-28
 \___/ |____/ \____/_/   \_\_| \_\  |  1.2.0-DEV #lg/Lie-allocs ed5c5dd 2024-09-30
 
julia> using BenchmarkTools

julia> @btime basis($(special_linear_lie_algebra(QQ, 7)));
  79.304 μs (2497 allocations: 134.00 KiB)	# master
  7.550 μs (193 allocations: 42.50 KiB)		# this PR

julia> @btime root_system([(:D, 12), (:E, 6)]);
  7.043 ms (314018 allocations: 5.89 MiB)	# master
  3.032 ms (47004 allocations: 2.53 MiB)	# this PR

julia> @btime lie_algebra(QQ, $(Oscar.LieAlgebras._struct_consts(QQ, root_system(:F, 4), fill(true, 20))), check=true); # this is heavily used in testing
  6.746 s (88755679 allocations: 3.65 GiB)	# master
  37.229 ms (1103389 allocations: 37.98 MiB)	# this PR

julia> @btime lie_algebra(QQ, $(root_system(:B, 10)));
  60.045 ms (1213748 allocations: 66.03 MiB)	# master
  47.319 ms (623167 allocations: 40.60 MiB)	# this PR

julia> @btime Oscar.LieAlgebras._cartan_subalgebra($(special_linear_lie_algebra(QQ, 7))); # internal function to circumvent caching
  3.072 s (9245963 allocations: 1.41 GiB)	# master
  386.819 ms (1110135 allocations: 217.34 MiB)  # this PR

julia> @btime Oscar.LieAlgebras._root_system_and_chevalley_basis($(special_linear_lie_algebra(QQ, 7))); # internal function to circumvent caching
  3.137 s (11603843 allocations: 1.73 GiB)	# master
  884.441 ms (2280864 allocations: 451.74 MiB) 	# this PR

the release of Nemocas/Nemo.jl#1872 will reduce allocations in some cases even further

[codecov]

Codecov Report

Attention: Patch coverage is 98.39572% with 3 lines in your changes missing coverage. Please review.

Project coverage is 84.71%. Comparing base (4a5b96d) to head (f1b177d).
Report is 2 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/LieAlgebras/src/LinearLieAlgebra.jl	87.50%	1 Missing ⚠️
experimental/LieAlgebras/src/Types.jl	91.66%	1 Missing ⚠️
experimental/LieAlgebras/test/RootSystem-test.jl	98.30%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4165      +/-   ##
==========================================
+ Coverage   84.69%   84.71%   +0.01%     
==========================================
  Files         628      628              
  Lines       84449    84608     +159     
==========================================
+ Hits        71527    71674     +147     
- Misses      12922    12934      +12     

Files with missing lines	Coverage Δ
experimental/LieAlgebras/src/AbstractLieAlgebra.jl	98.91% <100.00%> (-0.01%)	⬇️
experimental/LieAlgebras/src/LieAlgebra.jl	89.29% <100.00%> (+0.21%)	⬆️
experimental/LieAlgebras/src/LieAlgebraIdeal.jl	43.75% <100.00%> (ø)
experimental/LieAlgebras/src/LieAlgebraModule.jl	90.70% <100.00%> (+0.03%)	⬆️
experimental/LieAlgebras/src/LieAlgebras.jl	100.00% <ø> (ø)
experimental/LieAlgebras/src/LieSubalgebra.jl	58.71% <100.00%> (ø)
experimental/LieAlgebras/src/RootSystem.jl	92.47% <100.00%> (+2.18%)	⬆️
experimental/LieAlgebras/src/Util.jl	100.00% <100.00%> (ø)
...rimental/LieAlgebras/test/LinearLieAlgebra-test.jl	100.00% <ø> (ø)
experimental/LieAlgebras/src/LinearLieAlgebra.jl	95.97% <87.50%> (+0.11%)	⬆️
... and 2 more

... and 4 files with indirect coverage changes

[lgoettgens]

According to the CI logs, this reduces time/allocations of the relevant tests as follows (on ubuntu-1.10, compared to https://github.com/oscar-system/Oscar.jl/actions/runs/11118011606):

• experimental/LieAlgebras/test/AbstractLieAlgebra-test.jl: 84.75s, 45.8GB => 22.72s => 8.4GB
• experimental/LieAlgebras/test/LieAlgebra-test.jl 14.96s, 4.4GB => 4.7s => 1.4GB
• experimental/LieAlgebras/test/LieAlgebraModule-test.jl 30.43s, 12.5GB => 23.76s, 11.6GB

[fingolfin]

Nice