feat: better detect and report non-polynomial systems

Author: AayushSabharwal

ext/MTKHomotopyContinuationExt.jl

@@ -2,7 +2,7 @@ module MTKHomotopyContinuationExt
 
 using ModelingToolkit
 using ModelingToolkit.SciMLBase
-using ModelingToolkit.Symbolics: unwrap
+using ModelingToolkit.Symbolics: unwrap, symtype
 using ModelingToolkit.SymbolicIndexingInterface
 using ModelingToolkit.DocStringExtensions
 using HomotopyContinuation
@@ -32,8 +32,25 @@ function is_polynomial(x, wrt)
     end
     if operation(x) == (^)
         b, p = arguments(x)
-        return is_polynomial(b, wrt) && !contains_variable(p, wrt)
+        is_pow_integer = symtype(p) <: Integer
+        if !is_pow_integer
+            if symbolic_type(p) == NotSymbolic()
+                @warn "In $x: Exponent $p is not an integer"
+            else
+                @warn "In $x: Exponent $p is not an integer. Use `@parameters p::Integer` to declare integer parameters."
+            end
+        end
+        exponent_has_unknowns = contains_variable(p, wrt)
+        if exponent_has_unknowns
+            @warn "In $x: Exponent $p cannot contain unknowns of the system."
+        end
+        base_polynomial = is_polynomial(b, wrt)
+        if !base_polynomial
+            @warn "In $x: Base is not a polynomial"
+        end
+        return base_polynomial && !exponent_has_unknowns && is_pow_integer
     end
+    @warn "In $x: Unrecognized operation $(operation(x)). Allowed polynomial operations are `*, +, -, ^`"
     return false
 end
 
@@ -124,7 +141,7 @@ function MTK.HomotopyContinuationProblem(
 
     for eq in eqs
         if !is_polynomial(eq.lhs, dvs) || !is_polynomial(eq.rhs, dvs)
-            error("Equation $eq is not a polynomial in the unknowns")
+            error("Equation $eq is not a polynomial in the unknowns. See warnings for further details.")
         end
     end
 

test/extensions/homotopy_continuation.jl

@@ -60,3 +60,29 @@ end
     sol = @test_nowarn solve(prob; threading = false)
     @test sol.retcode == ReturnCode.ConvergenceFailure
 end
+
+@testset "Parametric exponent" begin
+    @variables x = 1.0
+    @parameters n::Integer = 4
+    @mtkbuild sys = NonlinearSystem([x^n + x^2 - 1 ~ 0])
+    prob = HomotopyContinuationProblem(sys, [])
+    sol = solve(prob; threading = false)
+    @test SciMLBase.successful_retcode(sol)
+end
+
+@testset "Polynomial check and warnings" begin
+    @variables x = 1.0
+    @parameters n::Integer = 4
+    @mtkbuild sys = NonlinearSystem([x^n + x^2 - 1 ~ 0])
+    @test_warn ["Exponent", "not an integer", "@parameters"] @test_throws "not a polynomial" HomotopyContinuationProblem(
+        sys, [])
+    @mtkbuild sys = NonlinearSystem([x^1.5 + x^2 - 1 ~ 0])
+    @test_warn ["Exponent", "not an integer"] @test_throws "not a polynomial" HomotopyContinuationProblem(
+        sys, [])
+    @mtkbuild sys = NonlinearSystem([x^x - x ~ 0])
+    @test_warn ["Exponent", "unknowns"] @test_throws "not a polynomial" HomotopyContinuationProblem(
+        sys, [])
+    @mtkbuild sys = NonlinearSystem([((x^2) / (x + 3))^2 + x ~ 0])
+    @test_warn ["Base", "not a polynomial", "Unrecognized operation", "/"] @test_throws "not a polynomial" HomotopyContinuationProblem(
+        sys, [])
+end