[dimpase]

ArithmeticVoronoi is now registered in General. Update the Julia provider from dimpase/arithmetic_voronoi to dimpase/ArithmeticVoronoi.jl and exercise fresh GL, SL and PSL complexes and integral homology using Julia and HAP, without Magma, a C++ build or stored complexes.

The Julia job runs seven record-based examples and a direct hap_voronoi_complex call in one process: quadratic GL/SL/PSL in rank two, GL/SL over the integers in rank three, Gaussian GL in rank three, and PSL(2,Z). It checks cell-orbit counts and H₁/H₂ where specified, and verifies that later computations preserve earlier complexes. The tutorial gives the shorter direct Julia calls, installation commands and the supported field/lattice scope. HAP's existing dispatcher already accepts the general records; its added test checks that a rational PSL request is passed through unchanged.

The provider is pinned to public commit c6942b9. Its rational request and projective-complex API extends registered v0.1.0, so the tutorial explicitly installs that same revision. PSL quotients by the full scalar centre. Real-quadratic SL/PSL cell complexes, nonmaximal orders and nonfree lattices remain unsupported by this provider.

Also fix InverseMutable for IsHapQuotientElement: it currently constructs a HapOppositeElement. This breaks direct products of finite stabilizers in PSL homology. A separate GAP regression checks the inverse type, inverse identities and a finite direct product; it runs in ordinary HAP tests without Julia. Existing Magma defaults are unchanged.

Validation against HAP 85917bcb:

• GAP dispatcher and quotient-element regressions pass; GAPDoc parses and validates the complete tutorial.
• Tutorial installation succeeds in a new Julia environment using the public pinned revision and Julia 1.13.3.
• Full HAP integration suite: 416 checks pass, including rational/PSL complexes, Gaussian rank-three homology and higher-rank presentations.
• GitHub CI passes on minimal, latest and development GAP, and the Julia job passes all 39 checks. The examples take 2m32s in one process on GitHub, plus 17.6s package loading. They also pass in the fresh local environment.
• The provider's prior independent Magma/VMH comparisons agree for SL/PSL H₁ and scalar centres over Z (rank 3), Q(sqrt(-7)) (rank 2), and the Gaussian and Eisenstein integers (rank 3), including the centre of order three.

CI is green, and complete GAPDoc composition, parsing and validation passed locally, too.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 43.00%. Comparing base (85917bc) to head (c21e5fc).

Additional details and impacted files

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##           master     #169   +/-   ##
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  Coverage   43.00%   43.00%           
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  Files         383      383           
  Lines       69324    69324           
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  Hits        29816    29816           
  Misses      39508    39508           

Files with missing lines	Coverage Δ
lib/FreeGmodules/wordOperations.gi	67.65% <100.00%> (ø)

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