Add conversion methods between OSCAR and HomotopyContinuation as a julia extension

.github/workflows/CI.yml

@@ -364,6 +364,51 @@ jobs:
         with:
           token: ${{ secrets.CODECOV_TOKEN }}
 
+  exts:
+    runs-on: ${{ matrix.os }}
+    continue-on-error: ${{ contains(matrix.julia-version, 'nightly') }}
+    timeout-minutes: 60
+    strategy:
+      fail-fast: false
+      matrix:
+        julia-version:
+          - '1.10'
+          - '1.12'
+          - '1.13-nightly'
+          - 'nightly'
+        os: ['ubuntu-latest']
+    env:
+      OSCAR_TEST_SUBSET: "exts"
+    steps:
+      - uses: actions/checkout@v6
+      - name: "Set up Julia"
+        uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.julia-version }}
+      - uses: julia-actions/cache@v2
+        with:
+          cache-name: julia-cache;workflow=${{ github.workflow }};julia=${{ matrix.julia-version }};arch=${{ runner.arch }}
+          include-matrix: false
+          cache-scratchspaces: false
+      - name: "Inject HomotopyContinuation as test dependencies"
+        continue-on-error: true
+        run: |
+          sed -i -e "s/\[deps\]/[deps]\nHomotopyContinuation = \"f213a82b-91d6-5c5d-acf7-10f1c761b327\"/" test/Project.toml
+      - uses: julia-actions/julia-runtest@v1
+        with:
+          annotate: ${{ matrix.julia-version == '1.10' }}
+          coverage: ${{ matrix.julia-version == '1.10' }}
+      - name: "Process code coverage"
+        if: matrix.julia-version == '1.10'
+        uses: julia-actions/julia-processcoverage@v1
+        with:
+          directories: src,experimental
+      - name: "Upload coverage data to Codecov"
+        if: matrix.julia-version == '1.10'
+        continue-on-error: true
+        uses: codecov/codecov-action@v5
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }}
 
 # adapted from gap-system/gap
   slack-notification:

Project.toml

@@ -32,6 +32,12 @@ cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 f4ncgb_jll = "160f184c-7e1a-5d95-af1f-70d62a450302"
 lib4ti2_jll = "1493ae25-0f90-5c0e-a06c-8c5077d6d66f"
 
+[weakdeps]
+HomotopyContinuation = "f213a82b-91d6-5c5d-acf7-10f1c761b327"
+
+[extensions]
+HomotopyContinuationExt = "HomotopyContinuation"
+
 [compat]
 AbstractAlgebra = "0.48.0"
 AlgebraicSolving = "0.10.4"
@@ -61,3 +67,4 @@ cohomCalg_jll = "0.32.0"
 f4ncgb_jll = "0.300.300"
 julia = "1.10"
 lib4ti2_jll = "1.6.10"
+HomotopyContinuation = "2.15"

ext/HomotopyContinuationExt.jl

@@ -0,0 +1,53 @@
+module HomotopyContinuationExt
+
+using Oscar, HomotopyContinuation
+
+import HomotopyContinuation: HomotopyContinuation, Variable
+
+"""
+    Expression(f::MPolyRingElem)
+
+Takes a polynomial `f` an `MPolyRingElem` and converts it into a
+`HomotopyContinuation.Expression`. The `HomotopyContinuation.Variable`
+objects used in the expression have the same names as the generators
+in the `parent(f)` (including brackets as in `x[1]`).
+"""
+function HomotopyContinuation.Expression(f::MPolyRingElem)
+  # Get a list of HomotopyContinuation variables whose names are the
+  # same as the ones in the Oscar polynomial f.
+  v = Variable.(symbols(parent(f)))
+  # Make the HomotopyContinuation expression
+  sum(Float64(c) * prod(v[i]^e for (i,e) in enumerate(a)) for (c,a) in coefficients_and_exponents(f))
+end
+
+"""
+    System(I::MPolyIdeal; args...)
+
+Takes an `MPolyIdeal` and turns it into a `HomotopyContinuation.System`
+containing the ideal generators. It forwards all `args` to `HomotopyContinuation.System`.
+"""
+HomotopyContinuation.System(I::MPolyIdeal; args...) = HomotopyContinuation.System(Expression.(gens(I)); args...)
+
+"""
+    solve(I::MPolyIdeal; args...)
+
+Call `HomotopyContinuation.solve` on the `HomotopyContinuation.System` derived
+from `I` forwarding all `args`.
+"""
+HomotopyContinuation.solve(I::MPolyIdeal; show_progress=false, args...) = HomotopyContinuation.solve(HomotopyContinuation.System(I); show_progress, args...)
+
+HomotopyContinuation.witness_set(I::MPolyIdeal; show_progress=false, args...) = HomotopyContinuation.witness_set(HomotopyContinuation.System(I); show_progress, args...)
+
+"""
+    dim(I::MPolyIdeal)
+
+Compute the dimension of `I` numerically.
+"""
+function HomotopyContinuation.dim(I::MPolyIdeal)
+  # This is provided by HomotopyContinuation.jl and computes the
+  # dimension based on the Jacobian rank at a random point.
+  F = HomotopyContinuation.System(I)
+  return HomotopyContinuation.nvariables(F) - rank(HomotopyContinuation.fixed(F))
+end
+
+end

test/exts.jl

@@ -0,0 +1,15 @@
+using HomotopyContinuation
+
+@testset "Extensions" begin
+  @testset "HomotopyContinuation" begin
+    Qxy, (x, y) = QQ[:x, :y]
+    I = ideal([x^2 - x * y + y^3, y^2 - x - 4//5])
+    @test iszero(HomotopyContinuation.dim(I))
+    result = Oscar.nsolve(I)
+    @test [r.multiplicity for r in result.path_results] == [1, 1, 1, 1]
+
+    J = ideal([x^2 - x * y + y^3])
+    ws = Oscar.witness_set(J)
+    @test length(ws.R) == 3
+  end
+end

test/runtests.jl

@@ -139,7 +139,8 @@ test_subsets = Dict(
                      :book => [
                                "test/book/test.jl",
                      ],
-  :oscar_db => ["experimental/OscarDB/test/runtests.jl"]
+                 :oscar_db => ["experimental/OscarDB/test/runtests.jl"],
+                     :exts => ["test/exts.jl"]
 )
 
 tests_on_main = Dict(