feat: arbitrary base rings for AlgAssAbsOrd #1728
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Codecov ReportAttention: Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #1728 +/- ##
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- Coverage 76.53% 76.40% -0.13%
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Files 360 360
Lines 113622 113864 +242
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+ Hits 86961 86999 +38
- Misses 26661 26865 +204
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- To generalize some constructions, we need to replace FakeFmpqMat with QQMatrix. Since both have different behaviour for `hnf` related functions, we first make the names of the methods for FakeFmpqMat unique.
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We can compute trivial examples: Compute a maximal |
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@fieker this here is to algebras over global fields, what |
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This was referenced Feb 1, 2025
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On Fri, Jan 31, 2025 at 02:44:59PM -0800, Tommy Hofmann wrote:
We can compute trivial examples: Compute a maximal $\mathbf{F}_3[X]$-order in $\mathrm{M}_2(\mathbf{F}_3[X])$ and a maximal $R$-order, where $R$ is the degree localization.
```
julia> F = GF(3);
julia> K, x = rational_function_field(F, :x);
julia> Fx = K.fraction_field.base_ring; # without words
julia> Finvx = localization(K, degree);
julia> A = matrix_algebra(K, 2);
julia> A.is_simple = 1
1
julia> maximal_order(any_order(A, Fx))
Order of Matrix algebra of dimension 4 over Rational function field over F with basis matrix
[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1]
julia> maximal_order(any_order(A, Finvx))
Order of Matrix algebra of dimension 4 over Rational function field over F with basis matrix
[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1]
```
This is cool stuff!
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