8000 Disallow standard quaternion algebras in characteristic 2 by thofma · Pull Request #1793 · thofma/Hecke.jl · GitHub
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Disallow standard quaternion algebras in characteristic 2 #1793

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Merged
merged 1 commit into from
Mar 8, 2025
Merged

Disallow standard quaternion algebras in characteristic 2 #1793

merged 1 commit into from
Mar 8, 2025

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thofma
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@thofma thofma commented Mar 8, 2025
  • these are not quaternion algebras, so don't allow constructing them

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thofma commented Mar 8, 2025

@wfsteiner: regarding nilpotency of elements:

julia> k = GF(2); kt, t = rational_function_field(k, "t")
(Rational function field over k, t)

julia> A = (Hecke.QuaternionAlgebra(kt, kt(t), kt(t + 1)))
Quaternion algebra over
kt
defined by i^2 = t, j^2 = t + 1

julia> radical(Hecke.StructureConstantAlgebra(A)[1])
Ideal
  of dimension 2
  in structure constant algebra of dimension 4 over kt
  with basis matrix
    [1   0   1//(t + 1)   1//(t + 1)]
    [0   1   t//(t + 1)   1//(t + 1)]

julia> _, i, j, k = basis(A);

julia> (1 + 1//(t + 1) * j + 1//(t + 1)*k)^2
(0) + (0) * i + (0) * j + (0) * k

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fix: quaternion algebras in characteristic 2
dac9e55 
- these are not quaternion algebras, so don't allow constructing them
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codecov bot commented Mar 8, 2025 •
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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 76.39%. Comparing base (eafebe0) to head (dac9e55).
Report is 1 commits behind head on master.

Additional details and impacted files 
@@            Coverage Diff             @@
##           master    #1793      +/-   ##
==========================================
- Coverage   76.45%   76.39%   -0.07%     
==========================================
  Files         362      362              
  Lines      114456   114457       +1     
==========================================
- Hits        87506    87435      -71     
- Misses      26950    27022      +72
Files with missing lines Coverage Δ
src/AlgAss/AlgQuat.jl 90.65% <100.00%> (+0.02%) ⬆️

... and 29 files with indirect coverage changes

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@thofma thofma merged commit f95dde4 into master Mar 8, 2025
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@thofma thofma deleted the th/quat branch March 8, 2025 14:47
@thofma thofma changed the title fix: quaternion algebras in characteristic 2 Disallow standard quaternion algebras in characteristic 2 Mar 8, 2025
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