setup SolveCtx for number fields

[fieker]

to see a difference in inv it needs AA #2177. Solve should improve immedaitely, the rest I don't know

[codecov]

Codecov Report

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✅ Project coverage is 88.14%. Comparing base (d0033a4) to head (27dba1e).
⚠️ Report is 5 commits behind head on master.

Files with missing lines	Patch %	Lines
src/antic/nf_elem.jl	0.00%	6 Missing ⚠️

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[joschmitt]

Unfortunately, the magic does not seem to work:

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

julia> A = K[1;;];

julia> B = K[1//2;;];

julia> can_solve_with_solution(A, B)
(true, [1])

Weirdly enough

julia> Nemo.AbstractAlgebra._can_solve_with_solution_fflu(A, B)
(true, [1//2], 1)

works.

[joschmitt]

The matrices are actually made integral in AbstractAlgebra: https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 . So for this to work, the _common_denominator would need to be

function AbstractAlgebra.Solve._common_denominator(A::MatElem{AbsSimpleNumFieldElem})
  d = ZZ(1)
  @inbounds for j in 1:ncols(A)
    for i in 1:nrows(A)
      d = lcm(d, denominator(A[i, j]))
    end
  end
  return d
end

Then at least my small example works.

[fieker]

On Wed, Oct 01, 2025 at 06:10:42AM -0700, Johannes Schmitt wrote: joschmitt left a comment (Nemocas/Nemo.jl#2149) Unfortunately, the magic does not seem to work: ``` julia> K, a = cyclotomic_field(3, :a); julia> A = K[1;;]; julia> B = K[1//2;;]; julia> can_solve_with_solution(A, B) (true, [1])

To hazard a guess: the 3rd return value (the denominator) is ignored

…

``` Weirdly enough ``` julia> Nemo.AbstractAlgebra._can_solve_with_solution_fflu(A, B) (true, [1//2], 1) ``` works. -- Reply to this email directly or view it on GitHub: #2149 (comment) You are receiving this because you authored the thread. Message ID: ***@***.***>

[fieker]

On Wed, Oct 01, 2025 at 06:17:50AM -0700, Johannes Schmitt wrote: joschmitt left a comment (Nemocas/Nemo.jl#2149) The matrices are actually made integral in AbstractAlgebra: https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 . So for this to work, the `_common_denominator` would need to be ``` function AbstractAlgebra.Solve._common_denominator(A::MatElem{AbsSimpleNumFieldElem}) d = ZZ(1) @inbounds for j in 1:ncols(A) for i in 1:nrows(A) d = lcm(d, denominator(A[i, j])) end end return d end ``` Then at least my small example works.

Try `can_solve_with_solution(4*A, B)` the dens are handled badly. somewhere. In fields having a den of 1 always should maybe affect performance, but not correctness...

…

-- Reply to this email directly or view it on GitHub: #2149 (comment) You are receiving this because you authored the thread. Message ID: ***@***.***>

[joschmitt]

On Wed, Oct 01, 2025 at 06:17:50AM -0700, Johannes Schmitt wrote: joschmitt left a comment (Nemocas/Nemo.jl#2149) The matrices are actually made integral in AbstractAlgebra: https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 . So for this to work, the _common_denominator would need to be function AbstractAlgebra.Solve._common_denominator(A::MatElem{AbsSimpleNumFieldElem}) d = ZZ(1) @inbounds for j in 1:ncols(A) for i in 1:nrows(A) d = lcm(d, denominator(A[i, j])) end end return d end Then at least my small example works.
Try can_solve_with_solution(4*A, B) the dens are handled badly. somewhere. In fields having a den of 1 always should maybe affect performance, but not correctness...
…
-- Reply to this email directly or view it on GitHub: #2149 (comment) You are receiving this because you authored the thread. Message ID: @.***>

julia> can_solve_with_solution(4*A, B)
(true, [1//8])

Seems to be fine?

I would say the problem is that https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 calls a numerator function that is not compatible with the constant denominator 1.

[fieker]

On Wed, Oct 01, 2025 at 06:34:45AM -0700, Johannes Schmitt wrote: joschmitt left a comment (Nemocas/Nemo.jl#2149) > On Wed, Oct 01, 2025 at 06:17:50AM -0700, Johannes Schmitt wrote: joschmitt left a comment ([Nemocas/Nemo.jl#2149](#2149)) The matrices are actually made integral in AbstractAlgebra: https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 . So for this to work, the `_common_denominator` would need to be ``` function AbstractAlgebra.Solve._common_denominator(A::MatElem{AbsSimpleNumFieldElem}) d = ZZ(1) @inbounds for j in 1:ncols(A) for i in 1:nrows(A) d = lcm(d, denominator(A[i, j])) end end return d end ``` Then at least my small example works. > Try `can_solve_with_solution(4*A, B)` the dens are handled badly. somewhere. In fields having a den of 1 always should maybe affect performance, but not correctness... > […](#) > -- Reply to this email directly or view it on GitHub: [#2149 (comment)](#2149 (comment)) You are receiving this because you authored the thread. Message ID: ***@***.***> ``` julia> can_solve_with_solution(4*A, B) (true, [1//8]) ``` Seems to be fine?

I got a 1//4...

…

I would say the problem is that https://github.com/Nemocas/AbstractAlgebra.jl/blob/96790541de6f246c39f848a7c941f74413d673bb/src/Solve.jl#L1139 calls a `numerator` function that is not compatible with the constant denominator 1. -- Reply to this email directly or view it on GitHub: #2149 (comment) You are receiving this because you authored the thread. Message ID: ***@***.***>

[fieker]

there are 2 things: common_den(matrix) needs to match den(elem) since we scale by matrix(den) to obtain elem == numerator
The other is that the den must ot be in Z it has to be base_ring(A), try can_solve_with_solution(inv(a)*A, B)
Both are hopefully adressed.
And the AA tests are/ were flawed: a special Field(F2) is constructed that was lacking conversion from Int and -