Add mutating arithmetic for SRows

[lgoettgens]

Add mutating arithmetics for SRow with the interface from AA. Inspired by oscar-system/Oscar.jl#4228 (comment) by @fingolfin .
Furthermore, make some of the existing functions easier to use by letting them coerce scalars (if needed) and add automatic workarounds for assertions.

I tested the new methods locally using test_mutating_op_like_* from AA. Unfortunately, for CI this does not work atm as there is too much expected missing for SRows (like random elements, zero, ...).

This currently contains #1658 to avoid conflicts.

@fingolfin could you have a look at the methods added here as well?

[lgoettgens]

Is the failure something known that sometimes crashes?

Error in testset ModAlgAss/Lattices/Lattices.jl:
Error During Test at /home/runner/work/Hecke.jl/Hecke.jl/test/testdefs.jl:20
  Got exception outside of a @test
  LoadError: Matrix must be square
  Stacktrace:
    [1] error(s::String)
      @ Base ./error.jl:35
    [2] det
      @ ~/work/Hecke.jl/Hecke.jl/src/LinearAlgebra/FakeFmpqMat.jl:357 [inlined]
    [3] _coprime_integral_ideal_class(a::Hecke.AlgAssAbsOrdIdl{MatAlgebra{QQFieldElem, QQMatrix}, MatAlgebraElem{QQFieldElem, QQMatrix}}, b::Hecke.AlgAssAbsOrdIdl{MatAlgebra{QQFieldElem, QQMatrix}, MatAlgebraElem{QQFieldElem, QQMatrix}})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/AlgAssAbsOrd/PicardGroup.jl:922
    [4] _is_principal_non_maximal(I::Hecke.AlgAssAbsOrdIdl{MatAlgebra{QQFieldElem, QQMatrix}, MatAlgebraElem{QQFieldElem, QQMatrix}})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/NumFieldOrd/NfOrd/PicardGroup.jl:363
    [5] _is_principal_with_data_etale(a::Hecke.AlgAssAbsOrdIdl{MatAlgebra{QQFieldElem, QQMatrix}, MatAlgebraElem{QQFieldElem, QQMatrix}}; local_freeness::Bool)
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/AlgAssAbsOrd/PicardGroup.jl:488
    [6] _is_principal_with_data_etale
      @ ~/work/Hecke.jl/Hecke.jl/src/AlgAssAbsOrd/PicardGroup.jl:478 [inlined]
    [7] #_is_principal_with_data#4748
      @ ~/work/Hecke.jl/Hecke.jl/src/AlgAssAbsOrd/PIP.jl:44 [inlined]
    [8] _is_isomorphic_with_isomorphism_same_ambient_module(L::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix}, M::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix}, ::Val{true})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/ModAlgAss/Lattices/Morphisms.jl:289
    [9] _is_isomorphic(L::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix}, M::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix}, with_iso_val::Val{true})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/ModAlgAss/Lattices/Morphisms.jl:[334](https://github.com/thofma/Hecke.jl/actions/runs/11477268995/job/31938971542?pr=1659#step:7:337)
   [10] is_isomorphic_with_isomorphism(L::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix}, M::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/ModAlgAss/Lattices/Morphisms.jl:303
   [11] is_free_with_basis(L::Hecke.ModAlgAssLat{Hecke.AlgAssAbsOrd{GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}, GroupAlgebraElem{QQFieldElem, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}}, Hecke.ModAlgAss{QQField, QQMatrix, GroupAlgebra{QQFieldElem, MultTableGroup, MultTableGroupElem}}, QQMatrix})
      @ Hecke ~/work/Hecke.jl/Hecke.jl/src/ModAlgAss/Lattices/Morphisms.jl:394
   [12] top-level scope
      @ ~/work/Hecke.jl/Hecke.jl/test/ModAlgAss/Lattices/Lattices.jl:5

[fingolfin]

Looks good to me, thanks

[codecov]

Codecov Report

Attention: Patch coverage is 51.96078% with 49 lines in your changes missing coverage. Please review.

Project coverage is 75.88%. Comparing base (66ab098) to head (c5fb659).
Report is 12 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Sparse/Row.jl	52.00%	48 Missing ⚠️
src/Sparse/ZZRow.jl	50.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1659      +/-   ##
==========================================
+ Coverage   75.84%   75.88%   +0.03%     
==========================================
  Files         361      361              
  Lines      113694   113865     +171     
==========================================
+ Hits        86234    86409     +175     
+ Misses      27460    27456       -4     

Files with missing lines	Coverage Δ
src/Sparse/ZZRow.jl	91.25% <50.00%> (+0.02%)	⬆️
src/Sparse/Row.jl	74.73% <52.00%> (-4.23%)	⬇️

... and 43 files with indirect coverage changes

[thofma]

needs a rebase as #1658 has been merged

P.S.: Have not seen this error before. Trying to reproduce it locally. Should be unrelated to the changes here.

[fingolfin]

typo in title: arithmetcs

[fingolfin]

Orthogonal to this PR, but: Since you now handle b==0 at the start, the iszero(a.values[i]) check above the fold can only return true if the coefficient ring is not a domain. So it could be strengthened to something like !is_domain_type(T) && iszero(a.values[i]).

Since is_domain_type is a trait depending only on T, the compiler can eliminate the is_domain_type(T) check -- if it returns true it can elide the if block, and if it is false we the same code we have currently.

[fingolfin]

But this can easily wait for a follow-up PR. (Also scale_row! and scale_row_right! could be merged)

[thofma]

What is planned with respect to tests?

[lgoettgens]

We have some generic functions in AA that test if the mutating ops are properly implemented. But as I wrote above, it is not that easy to apply them here, but I do my best to somehow put that together

[thofma]

I was not sure whether this comment means that we want to

1. merge this here without tests,
2. wait for a test function from AA, or
3. add ad hoc tests.

[lgoettgens]

Wait with merging until I have time to look into this on Monday

[lgoettgens]

I added some tests regarding zero! and add!. For mul! and addmul! the test function (by fault) tries to multiply two SRows which of course errors. Nemocas/AbstractAlgebra.jl#1892 will provide a workaround.
With the corresponding branch from AA deved, these tests succeed locally for me.

The two options now (@thofma needs to decide between):

1. Merge now. Once Adapt test_mutating_op_like_(add)mul to work with scalar mul as well Nemocas/AbstractAlgebra.jl#1892 is available, uncomment the tests in a future PR.
2. Wait until Adapt test_mutating_op_like_(add)mul to work with scalar mul as well Nemocas/AbstractAlgebra.jl#1892 is available, uncomment the tests then, and then merge.

[thofma]

Let's wait for 2)