Integrate OpenBLASLUFactorization into existing test suite

- Add OpenBLASLUFactorization to basictests.jl alongside other factorizations
- Include in resolve.jl subtype iteration tests
- Add to preferences.jl algorithm availability tests
- Remove separate test file in favor of integrated testing

Author: claude

test/basictests.jl

@@ -287,6 +287,9 @@ end
         push!(test_algs, MKLLUFactorization())
     end
 
+    # Always test OpenBLAS since it's a direct dependency
+    push!(test_algs, OpenBLASLUFactorization())
+
     # Test BLIS if extension is available
     if Base.get_extension(LinearSolve, :LinearSolveBLISExt) !== nothing
         push!(test_algs, BLISLUFactorization())

test/preferences.jl

@@ -190,6 +190,12 @@ using Preferences
             println("✅ MKLLUFactorization confirmed working")
         end
 
+        # Test OpenBLAS (always available as a dependency)
+        sol_openblas = solve(prob, OpenBLASLUFactorization())
+        @test sol_openblas.retcode == ReturnCode.Success
+        @test norm(A * sol_openblas.u - b) < 1e-8
+        println("✅ OpenBLASLUFactorization confirmed working")
+        
         # Test Apple Accelerate if available
         if LinearSolve.appleaccelerate_isavailable()
             sol_apple = solve(prob, AppleAccelerateLUFactorization())

test/resolve.jl

@@ -19,7 +19,8 @@ for alg in vcat(InteractiveUtils.subtypes(AbstractDenseFactorization),
        ]) &&
        (!(alg == AppleAccelerateLUFactorization) ||
         LinearSolve.appleaccelerate_isavailable()) &&
-       (!(alg == MKLLUFactorization) || LinearSolve.usemkl)
+       (!(alg == MKLLUFactorization) || LinearSolve.usemkl) &&
+       (!(alg == OpenBLASLUFactorization) || true)  # OpenBLAS is always available as a dependency
         A = [1.0 2.0; 3.0 4.0]
         alg in [KLUFactorization, UMFPACKFactorization, SparspakFactorization] &&
             (A = sparse(A))