Update ArithmeticVoronoi provider and expand Julia homology examples

.github/scripts/voronoi-julia.jl

@@ -1,5 +1,5 @@
-# Run with the ArithmeticVoronoi environment pinned in ../workflows/CI.yml:
-# julia --startup-file=no --project=/path/to/arithmetic_voronoi \
+# Run with the ArithmeticVoronoi revision pinned in ../workflows/CI.yml:
+# julia --startup-file=no --project=/path/to/ArithmeticVoronoi.jl \
 #     .github/scripts/voronoi-julia.jl
 println("Loading the Julia provider and its dependencies...")
 flush(stdout)
@@ -21,34 +21,51 @@ dispatcher = GAP.Globals.VoronoiComplex
 println("HAP checkout: ", hap_root)
 println("Julia ", VERSION, "; OSCAR ", pkgversion(Oscar), "; GAP ", GAP.GAP_VERSION)
 
-@testset "Julia provider: GL2 over O_(Q(sqrt(-7)))" begin
-    enable_hap_julia_backend(; progress=true, resolution_length=3)
-    @test GAP.Globals.IsIdenticalObj(dispatcher, GAP.Globals.VoronoiComplex)
-
-    request = Dict(
-        "group" => "GL", "rank" => 2,
-        "field" => Dict("kind" => "quadratic", "discriminant" => -7),
-        "order" => Dict("kind" => "maximal"),
-        "lattice" => Dict("kind" => "free"),
+@testset "ArithmeticVoronoi: rational and quadratic groups" begin
+    enable_hap_julia_backend(;progress=true,resolution_length=3)
+    @test GAP.Globals.IsIdenticalObj(dispatcher,GAP.Globals.VoronoiComplex)
+    construct=GAP.evalstr("r -> VoronoiComplex(r : backend := \"julia\")")
+    # These are regression expectations from independent VMH/Magma, HAP stored
+    # resolutions and classical homology. All complexes here are computed fresh.
+    examples=(
+        (request=voronoi_request(-7),cells=[1,2,1],homology=([2,2,2],[2,12])),
+        (request=voronoi_request(5),cells=[2,4,5,4,1],homology=([0,2],[2,2,2,2])),
+        (request=voronoi_request(-7;group=:SL),cells=nothing,homology=([0,4],[12])),
+        (request=voronoi_request(-7;group=:PSL),cells=nothing,homology=([0,2],)),
+        (request=voronoi_request(;rank=3),cells=[1,1,2,1],homology=([2],[2,2])),
+        (request=voronoi_request(;rank=3,group=:SL),cells=nothing,homology=(Int[],)),
+        (request=voronoi_request(-4;rank=3),cells=[1,1,3,5,4,3,2],homology=([4],)),
     )
-    println("Request: ", request)
-    flush(stdout)
-    construct = GAP.evalstr("request -> VoronoiComplex(request : backend := \"julia\")")
-    # A fresh native enumeration, without Magma, stored complexes or a C++ build.
-    K = construct(GAP.GapObj(request; recursive=true))
-    @test GAP.Globals.IsHapNonFreeResolution(K)
-    cells = Int.(GAP.gap_to_julia(
-        GAP.evalstr("K -> List([0..2], n -> K!.dimension(n))")(K)))
-    @test cells == [1, 2, 1]
-    println("Cell orbits in dimensions 0, 1, 2: ", cells)
-
-    R = GAP.Globals.FreeGResolution(K, 3)
-    C = GAP.Globals.TensorWithIntegers(R)
-    # These invariants were independently checked with Magma/VMH;
-    # neither the example nor CI needs Magma to compute them.
-    for (degree, expected) in ((1, [2, 2, 2]), (2, [2, 12]))
-        invariants = sort(Int.(GAP.gap_to_julia(GAP.Globals.Homology(C, degree))))
-        println("H", degree, " invariant factors: ", invariants)
-        @test invariants == expected
+    first_complex=nothing
+    for (i,example) in enumerate(examples)
+        request=example.request
+        @testset "$(request)" begin
+            println("Request: ",request);flush(stdout)
+            started=time_ns()
+            K=construct(GAP.GapObj(request;recursive=true))
+            i==1 && (first_complex=K)
+            @test GAP.Globals.IsHapNonFreeResolution(K)
+            @test Int(GAP.evalstr("K -> K!.arithmeticVoronoi")(K).rank)==request["rank"]
+            @test GAP.evalstr("K -> K!.arithmeticVoronoi")(K).groupKind==GAP.GapObj(request["group"])
+            if !isnothing(example.cells)
+                cells=GAP.evalstr("{K,d} -> List([0..d-1], K!.dimension)")(K,length(example.cells))
+                @test Int.(GAP.gap_to_julia(cells))==example.cells
+            end
+            R=GAP.Globals.FreeGResolution(K,length(example.homology)+1)
+            C=GAP.Globals.TensorWithIntegers(R)
+            for (degree,expected) in enumerate(example.homology)
+                invariants=sort(Int.(GAP.gap_to_julia(GAP.Globals.Homology(C,degree))))
+                println("H",degree," invariant factors: ",invariants)
+                @test invariants==expected
+            end
+            println("Example time: ",round((time_ns()-started)/1e9;digits=2)," s");flush(stdout)
+        end
     end
+    # The direct Julia interface requires no record conversion or dispatcher.
+    K=hap_voronoi_complex(;group=:PSL,resolution_length=2)
+    R=GAP.Globals.FreeGResolution(K,2)
+    @test Int.(GAP.gap_to_julia(GAP.Globals.Homology(GAP.Globals.TensorWithIntegers(R),1)))==[6]
+    # Later computations must not overwrite an earlier object's captured data.
+    R=GAP.Globals.FreeGResolution(first_complex,3)
+    @test sort(Int.(GAP.gap_to_julia(GAP.Globals.Homology(GAP.Globals.TensorWithIntegers(R),2))))==[2,12]
 end

.github/workflows/CI.yml

@@ -45,7 +45,7 @@ jobs:
           token: ${{ secrets.CODECOV_TOKEN }}
 
   julia-voronoi:
-    name: Julia Voronoi example (GL2, D=-7)
+    name: Julia Voronoi examples (GL, SL and PSL)
     runs-on: ubuntu-latest
     permissions:
       contents: read
@@ -54,15 +54,15 @@ jobs:
       OPENBLAS_NUM_THREADS: '1'
     steps:
       - uses: actions/checkout@v7
-      - name: Check out the Julia provider and its pinned environment
+      - name: Check out the Julia provider at a tested revision
         uses: actions/checkout@v7
         with:
-          repository: dimpase/arithmetic_voronoi
-          ref: 007df75debde04c7469124891ac78d555d5de20b
+          repository: dimpase/ArithmeticVoronoi.jl
+          ref: c6942b97936e69a392ee88523fbf3574edcc6e26
           path: arithmetic-voronoi
       - uses: julia-actions/setup-julia@v3
         with:
-          version: '1.13.2'
+          version: '1'
       - uses: julia-actions/cache@v3
         with:
           delete-old-caches: 'false'
@@ -74,7 +74,7 @@ jobs:
         run: >-
           julia --startup-file=no --project=arithmetic-voronoi
           -e 'using Pkg; Pkg.precompile("ArithmeticVoronoi"; strict=true, timing=true)'
-      - name: Construct a fresh complex and check integral H1 and H2
+      - name: Construct fresh complexes and check integral homology
         run: >-
           julia --startup-file=no --project=arithmetic-voronoi
           .github/scripts/voronoi-julia.jl

lib/FreeGmodules/wordOperations.gi

@@ -459,7 +459,7 @@ InstallOtherMethod( InverseMutable,
 
 function(x) local w;
 w:=List(x!.element,InverseMutable);
-return Objectify(HapOppositeElement,
+return Objectify(HapQuotientElement,
                     rec(
                     element:=w) );
 end);

tst/testextra/quotient-elements.tst

@@ -0,0 +1,16 @@
+gap> START_TEST("quotient-elements.tst");
+gap> hapqinfo := InfoLevel(InfoWarning);;
+gap> SetInfoLevel(InfoWarning,0);
+gap> hapq := QuotientGroup((1,2,3,4,5,6),[(),(1,4)(2,5)(3,6)]);;
+gap> Print(IsHapQuotientElement(InverseMutable(hapq)),"\n");
+true
+gap> Print(InverseMutable(hapq)=hapq^-1,"\n");
+true
+gap> Print(hapq*InverseMutable(hapq)=One(hapq),"\n");
+true
+gap> Print(Size(DirectProduct(Group(hapq),Group(hapq))),"\n");
+9
+gap> SetInfoLevel(InfoWarning,hapqinfo);
+gap> Unbind(hapqinfo);
+gap> Unbind(hapq);
+gap> STOP_TEST("quotient-elements.tst", 1000);

tst/testextra/voronoi-backends.tst

@@ -16,6 +16,10 @@ gap> Print([haprequest.group,haprequest.rank,haprequest.field.radicand],"\n");
 gap> haprequest := VoronoiComplexGL(3,5 : backend := "hap-test");;
 gap> Print([haprequest.group,haprequest.rank,haprequest.field.radicand],"\n");
 [ "GL", 3, 5 ]
+gap> haprequest := rec(group:="PSL",rank:=4,field:=rec(kind:="rational"),
+> order:=rec(kind:="maximal"),lattice:=rec(kind:="free"));;
+gap> Print(IsIdenticalObj(haprequest,VoronoiComplex(haprequest : backend := "hap-test")),"\n");
+true
 gap> RegisterVoronoiBackend("hap-test-fail", request -> fail);
 gap> Print(VoronoiComplex(rec() : backend := "hap-test-fail"),"\n");
 fail

tutorial/tutorialBianchi.xml

@@ -474,8 +474,50 @@ radicand, not a field discriminant. Without the backend option, or with
 <C>backend := "magma"</C>, these two convenience functions retain the
 Magma implementation described above.
 <P/>
-A Julia package running with GAP.jl can register an in-process callback
+The Julia package
+<URL Text="ArithmeticVoronoi.jl">https://github.com/dimpase/ArithmeticVoronoi.jl</URL>
+computes these complexes natively and can register an in-process callback
 under the name <C>"julia"</C>. HAP itself does not install or load Julia.
+The rational request and projective-complex examples below extend the first
+registered release, v0.1.0. Install the tested provider revision used by this
+CI job in your chosen Julia environment, along with OSCAR for its GAP interface:
+<Log><![CDATA[
+import Pkg
+Pkg.add(url="https://github.com/dimpase/ArithmeticVoronoi.jl.git",
+        rev="c6942b97936e69a392ee88523fbf3574edcc6e26")
+Pkg.add("Oscar")
+]]></Log>
+The direct Julia interface loads HAP automatically:
+<Log><![CDATA[
+using ArithmeticVoronoi, Oscar
+import Oscar: GAP
+K = hap_voronoi_complex(-7; group=:PSL, resolution_length=3);
+R = GAP.Globals.FreeGResolution(K, 3);
+GAP.gap_to_julia(GAP.Globals.Homology(GAP.Globals.TensorWithIntegers(R), 1))
+# [0, 2]
+]]></Log>
+The integer argument here is a fundamental field discriminant. Omit it for
+rational coefficients: <C>hap_voronoi_complex(; rank=3, group=:SL)</C>
+computes a complex for <M>SL_3(\mathbb Z)</M>. The provider supports ranks
+at least two, rational and quadratic GL, and rational and imaginary-quadratic
+SL and PSL on free lattices over maximal orders. PSL divides by the full
+scalar centre. Real-quadratic SL/PSL complexes, nonmaximal orders and nonfree
+lattices are not supplied by this provider. The package's separate
+presentation algorithms cover real-quadratic SL/PSL too; they do not replace
+the equivariant cell data required by HAP.
+<P/>
+For HAP's record dispatcher in the same Julia session, first run
+<C>enable_hap_julia_backend()</C>. A rational example is:
+<Log><![CDATA[
+request := rec(group := "SL", rank := 3, field := rec(kind := "rational"),
+    order := rec(kind := "maximal"), lattice := rec(kind := "free"));
+K := VoronoiComplex(request : backend := "julia");
+]]></Log>
+These last commands use GAP syntax, which can be evaluated through GAP.jl.
+See the
+<URL Text="ArithmeticVoronoi HAP guide">https://github.com/dimpase/ArithmeticVoronoi.jl/blob/c6942b97936e69a392ee88523fbf3574edcc6e26/docs/src/hap_and_vmh.md</URL>
+for installation, the direct Julia calls and supported computations.
+<P/>
 An unregistered backend name is an error. Providers must supply complete stabilizers, the orientation action
 and equivariant boundaries; perfect forms or a group presentation alone
 do not suffice for higher homology. Standard HAP operations such as