New linear solving interface + more upstream changes

[joschmitt]

The functions solve, can_solve, can_solve_with_solution, can_solve_with_solution_and_kernel and kernel (for matrices) now use the "new" interface from AbstractAlgebra.
This is a breaking change and needs a Hecke update.

I put everything on top of #3366 so that OSCAR works with the newest Nemo/AbstractAlgebra. Will rebase once #3366 is merged.

Closes #1062 🥳 🎉

[codecov]

Codecov Report

Merging #3350 (d0af366) into master (82f6440) will decrease coverage by 0.03%.
Report is 2 commits behind head on master.
The diff coverage is 84.33%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3350      +/-   ##
==========================================
- Coverage   82.08%   82.06%   -0.03%     
==========================================
  Files         556      556              
  Lines       74072    74075       +3     
==========================================
- Hits        60805    60792      -13     
- Misses      13267    13283      +16     

Files	Coverage Δ
...ntal/FTheoryTools/src/FamilyOfSpaces/attributes.jl	100.00% <100.00%> (ø)
.../FTheoryTools/src/LiteratureModels/constructors.jl	92.64% <100.00%> (ø)
...rimental/FTheoryTools/src/TateModels/attributes.jl	93.84% <100.00%> (ø)
...mental/FTheoryTools/src/TateModels/constructors.jl	97.43% <100.00%> (ø)
...FTheoryTools/src/WeierstrassModels/constructors.jl	95.58% <100.00%> (ø)
experimental/FTheoryTools/src/auxiliary.jl	94.87% <100.00%> (ø)
experimental/GITFans/src/GITFans.jl	94.22% <100.00%> (ø)
experimental/GModule/Brueckner.jl	87.96% <100.00%> (ø)
experimental/GModule/Cohomology.jl	67.46% <100.00%> (ø)
experimental/GaloisGrp/src/Solve.jl	74.20% <100.00%> (ø)
... and 49 more

... and 2 files with indirect coverage changes

[fieker]

I think we need a function nullity - to return the rank of the kernel only...

[joschmitt]

I add it to the list of future improvements.

[joschmitt]

There is a type inference problem on nightly. It already happens only with Hecke (but not only with Nemo):

julia> function foo(R::MPolyRing)
           return [ x for x in gens(R) ]
       end
foo (generic function with 1 method)

julia> K, a = cyclotomic_field(3, "a");

julia> Kx, (x, y) = K["x", "y"];

julia> @code_warntype foo(Kx)
MethodInstance for foo(::AbstractAlgebra.Generic.MPolyRing{AbsSimpleNumFieldElem})
  from foo(R::MPolyRing) @ Main REPL[2]:1
Arguments
  #self#::Core.Const(foo)
  R::AbstractAlgebra.Generic.MPolyRing{AbsSimpleNumFieldElem}
Body::Any
1 ─ %1 = Main.gens::Core.Const(AbstractAlgebra.gens)
│   %2 = (%1)(R)::AbstractVector{<:AbstractAlgebra.Generic.MPoly{AbsSimpleNumFieldElem}}
│   %3 = Base.Generator(Base.identity, %2)::Base.Generator{I, typeof(identity)} where I<:(AbstractVector{<:AbstractAlgebra.Generic.MPoly{AbsSimpleNumFieldElem}})
│   %4 = Base.collect(%3)::Any
└──      return %4

@thofma can/should we do something about this?

[fingolfin]

Regarding the new invalidation: open an issue with the details (we can look at it with help of JET at some point), but otherwise move on.

[thofma]

Not clear if this is about invalidations.

julia> @inferred gens(Kx)
ERROR: return type Vector{AbstractAlgebra.Generic.MPoly{AbsSimpleNumFieldElem}} does not match inferred return type AbstractVector{<:AbstractAlgebra.Generic.MPoly{AbsSimpleNumFieldElem}}
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] top-level scope
   @ REPL[11]:1

julia> @code_warntype gens(Kx)
[...]
Body::Vector{AbstractAlgebra.Generic.MPoly{AbsSimpleNumFieldElem}}
[...]

This is inconsistent and one of them is lying.

[thofma]

There is something dodgy in AA, where we rely on some compiler heuristic. Not sure what exactly broke it. I think I have a fix in Nemocas/AbstractAlgebra.jl#1611. Can you confirm that this fixes the issue @joschmitt?

[joschmitt]

There is something dodgy in AA, where we rely on some compiler heuristic. Not sure what exactly broke it. I think I have a fix in Nemocas/AbstractAlgebra.jl#1611. Can you confirm that this fixes the issue @joschmitt?

Yes, this also solves the original failure in the nightly tests here.

[lgoettgens]

This should get backported, right?

[thofma]

This should be backported. It includes two breaking changes to the linear algebra, which are long overdue. Clean up kernel and clean up indexing.

I adjusted the book two weeks ago for the indexing changes (#3276) is the corresponding OSCAR PR) and the book does not use kernel of matrices.

CC: @fieker