fix: use full_equations when generating HomotopyContinuationProblem

Author: AayushSabharwal

ext/MTKHomotopyContinuationExt.jl

@@ -192,7 +192,12 @@ function MTK.HomotopyContinuationProblem(
     end
 
     dvs = unknowns(sys)
-    eqs = equations(sys)
+    # we need to consider `full_equations` because observed also should be
+    # polynomials (if used in equations) and we don't know if observed is used
+    # in denominator.
+    # This is not the most efficient, and would be improved significantly with
+    # CSE/hashconsing.
+    eqs = full_equations(sys)
 
     denoms = []
     eqs2 = map(eqs) do eq
@@ -216,6 +221,9 @@ function MTK.HomotopyContinuationProblem(
     end
 
     sys2 = MTK.@set sys.eqs = eqs2
+    # remove observed equations to avoid adding them in codegen
+    MTK.@set! sys2.observed = Equation[]
+    MTK.@set! sys2.substitutions = nothing
 
     nlfn, u0, p = MTK.process_SciMLProblem(NonlinearFunction{true}, sys2, u0map, parammap;
         jac = true, eval_expression, eval_module)

test/extensions/homotopy_continuation.jl

@@ -76,6 +76,11 @@ end
     @mtkbuild sys = NonlinearSystem([((x^2) / sin(x))^2 + x ~ 0])
     @test_warn ["Unrecognized", "sin"] @test_throws "not a polynomial" HomotopyContinuationProblem(
         sys, [])
+
+    @variables y = 2.0
+    @mtkbuild sys = NonlinearSystem([x^2 + y^2 + 2 ~ 0, y ~ sin(x)])
+    @test_warn ["Unrecognized", "sin"] @test_throws "not a polynomial" HomotopyContinuationProblem(
+        sys, [])
 end
 
 @testset "Rational functions" begin
@@ -122,4 +127,21 @@ end
         end
     end
     @test prob.denominator([2.0, 4.0], p)[1] <= 1e-8
+
+    @testset "Rational function in observed" begin
+        @variables x=1 y=1
+        @mtkbuild sys = NonlinearSystem([x^2 + y^2 - 2x - 2 ~ 0, y ~ (x - 1) / (x - 2)])
+        prob = HomotopyContinuationProblem(sys, [])
+        @test any(prob.denominator([2.0], parameter_values(prob)) .≈ 0.0)
+        @test_nowarn solve(prob; threading = false)
+    end
+end
+
+@test "Non-polynomial observed not used in equations" begin
+    @variables x=1 y
+    @mtkbuild sys = NonlinearSystem([x^2 - 2 ~ 0, y ~ sin(x)])
+    prob = HomotopyContinuationProblem(sys, [])
+    sol = @test_nowarn solve(prob; threading = false)
+    @test sol[x] ≈ √2.0
+    @test sol[y] ≈ sin(√2.0)
 end