Give warning message when no solutions were computed

src/numerical_irreducible_decomposition.jl

@@ -284,6 +284,9 @@ function regeneration!(
     # it is covenient to use the WitnessSet wrapper here, because this also keeps track of the equation
     # as a linear subspace we take the linear subspace for out[1], that sets u=0.
     H = initialize_hypersurfaces(f, vars, linear_subspace(out[1]))
+    if any(H .== nothing)
+        return nothing
+    end
 
     # Initialize a cache
     Fᵢ = fixed(System(f[1:1], variables = vars), compile = false)
@@ -394,6 +397,9 @@ function initialize_hypersurfaces(f::Vector{Expression}, vars, L)
             start_system = :total_degree,
             show_progress = false,
         )
+        if isnothing(res)
+            return nothing
+        end
         S = solutions(res, only_nonsingular = true)
 
         out[i] = WitnessSet(h, L, S)
@@ -1402,6 +1408,9 @@ function numerical_irreducible_decomposition(
         endgame_options = endgame_options,
         kwargs...,
     )
+    if isnothing(Ws)
+        return nothing
+    end
     decompose(
         Ws;
         monodromy_options = monodromy_options,

src/solve.jl

@@ -499,7 +499,15 @@ end
 solve(S::Solver, R::Result; kwargs...) =
     solve(S, solutions(R; only_nonsingular = true); kwargs...)
 solve(S::Solver, s::AbstractVector{<:Number}; kwargs...) = solve(S, [s]; kwargs...)
-solve(S::Solver, starts; kwargs...) = solve(S, collect(starts); kwargs...)
+function solve(S::Solver, starts; kwargs...)
+    try
+        s = collect(starts)
+        solve(S, s; kwargs...)
+    catch
+        @warn "No solutions were found."
+        nothing
+    end
+end
 function solve(
     S::Solver,
     starts::AbstractArray;
@@ -508,6 +516,7 @@ function solve(
     threading::Bool = Threads.nthreads() > 1,
     catch_interrupt::Bool = true,
 )
+
     n = length(starts)
     progress = show_progress ? make_progress(n; delay = 0.3) : nothing
     init!(S.stats)

test/nid_test.jl

@@ -273,69 +273,22 @@
         @test degrees(NID)[0] == [1]
     end
 
-    #     @testset "426" begin
-    #         ### Example thanks to Julian Vill
-    #         @var a, b, c, d, e
-
-
-    #         f1 =
-    #             -18 * a^4 * c^5 + 27 * a^3 * b * c^5 - 9 * a^2 * b^2 * c^5 - 18 * a^4 * c^4 +
-    #             81 * a^3 * b * c^4 - 90 * a^2 * b^2 * c^4 + 27 * a * b^3 * c^4 - 9 * a^2 * c^6 +
-    #             c^8 - 18 * a^4 * c^3 + 81 * a^3 * b * c^3 - 126 * a^2 * b^2 * c^3 +
-    #             81 * a * b^3 * c^3 - 18 * b^4 * c^3 + 36 * a * b * c^5 - 9 * b^2 * c^5 +
-    #             c^7 +
-    #             27 * a^3 * b * c^2 - 90 * a^2 * b^2 * c^2 + 81 * a * b^3 * c^2 -
-    #             18 * b^4 * c^2 + 18 * a^2 * c^4 - 36 * a * b * c^4 - 8 * c^6 -
-    #             9 * a^2 * b^2 * c + 27 * a * b^3 * c - 18 * b^4 * c - 36 * a * b * c^3 +
-    #             18 * b^2 * c^3 +
-    #             7 * c^5 - 9 * a^2 * c^2 + 36 * a * b * c^2 - 2 * c^4 - 9 * b^2 * c + 7 * c^3 -
-    #             8 * c^2 +
-    #             c +
-    #             1
-
-    #         f2 =
-    #             -18 * a^4 * e^5 + 27 * a^3 * d * e^5 - 9 * a^2 * d^2 * e^5 - 18 * a^4 * e^4 +
-    #             81 * a^3 * d * e^4 - 90 * a^2 * d^2 * e^4 + 27 * a * d^3 * e^4 - 9 * a^2 * e^6 +
-    #             e^8 - 18 * a^4 * e^3 + 81 * a^3 * d * e^3 - 126 * a^2 * d^2 * e^3 +
-    #             81 * a * d^3 * e^3 - 18 * d^4 * e^3 + 36 * a * d * e^5 - 9 * d^2 * e^5 +
-    #             e^7 +
-    #             27 * a^3 * d * e^2 - 90 * a^2 * d^2 * e^2 + 81 * a * d^3 * e^2 -
-    #             18 * d^4 * e^2 + 18 * a^2 * e^4 - 36 * a * d * e^4 - 8 * e^6 -
-    #             9 * a^2 * d^2 * e + 27 * a * d^3 * e - 18 * d^4 * e - 36 * a * d * e^3 +
-    #             18 * d^2 * e^3 +
-    #             7 * e^5 - 9 * a^2 * e^2 + 36 * a * d * e^2 - 2 * e^4 - 9 * d^2 * e + 7 * e^3 -
-    #             8 * e^2 +
-    #             e +
-    #             1
-
-    #         f3 =
-    #             -9 * b^2 * c^5 * d^2 * e + 27 * b * c^5 * d^3 * e - 18 * c^5 * d^4 * e +
-    #             27 * b^3 * c^4 * d * e^2 - 90 * b^2 * c^4 * d^2 * e^2 +
-    #             81 * b * c^4 * d^3 * e^2 - 18 * c^4 * d^4 * e^2 - 18 * b^4 * c^3 * e^3 +
-    #             81 * b^3 * c^3 * d * e^3 - 126 * b^2 * c^3 * d^2 * e^3 +
-    #             81 * b * c^3 * d^3 * e^3 - 18 * c^3 * d^4 * e^3 - 18 * b^4 * c^2 * e^4 +
-    #             81 * b^3 * c^2 * d * e^4 - 90 * b^2 * c^2 * d^2 * e^4 +
-    #             27 * b * c^2 * d^3 * e^4 - 18 * b^4 * c * e^5 + 27 * b^3 * c * d * e^5 -
-    #             9 * b^2 * c * d^2 * e^5 - 9 * c^6 * d^2 * e - 9 * b^2 * c^5 * e^2 +
-    #             36 * b * c^5 * d * e^2 - 36 * b * c^4 * d * e^3 +
-    #             18 * c^4 * d^2 * e^3 +
-    #             18 * b^2 * c^3 * e^4 - 36 * b * c^3 * d * e^4 + 36 * b * c^2 * d * e^5 -
-    #             9 * c^2 * d^2 * e^5 - 9 * b^2 * c * e^6 +
-    #             c^8 +
-    #             c^7 * e - 8 * c^6 * e^2 + 7 * c^5 * e^3 - 2 * c^4 * e^4 + 7 * c^3 * e^5 -
-    #             8 * c^2 * e^6 +
-    #             c * e^7 +
-    #             e^8
-
-    #         F = System([f1; f2; f3], variables = [a, b, c, d, e])
-
-    #         N = nid(
-    #             F;
-    #             seed = 0xc7cca254,
-    #             endgame_options = EndgameOptions(; sing_accuracy = 1e-10),
-    #         )
-
-    #         @test ncomponents(N) == 1
-    #         @test degrees(N) == Dict(2 => [426])
-    #     end
+    @testset "solve a system without solutions" begin
+        using HomotopyContinuation
+        @var x[1:4]
+
+        I = [
+            13 * (x[1] + x[2]) - 61 * (x[2] + x[3]) + 48 * (x[1] + x[3]) -
+            61 * (x[1] + x[4]) +
+            48 * (x[2] + x[4]) +
+            13 * (x[3] + x[4]) +
+            1,
+            13 * (x[2]x[1] + x[1]^2 + x[2]^2) - 61(x[4]x[1] + x[1]^2 + x[4]^2) +
+            48(x[4]x[2] + x[2]^2 + x[4]^2) +
+            48(x[3]x[1] + x[1]^2 + x[3]^2) - 61(x[2]x[3] + x[2]^2 + x[3]^2) +
+            13(x[4] * x[3] + x[3]^2 + x[4]^2),
+        ]
+        b = nid(I)
+        @test isnothing(b)
+    end
 end

test/solve_test.jl

@@ -418,6 +418,27 @@
         @test s ≈ [s2[2], s2[1]]
     end
 
+    @testset "solve a system without solutions" begin
+        using HomotopyContinuation
+        @var x[1:4]
+
+        I = [
+            13 * (x[1] + x[2]) - 61 * (x[2] + x[3]) + 48 * (x[1] + x[3]) -
+            61 * (x[1] + x[4]) +
+            48 * (x[2] + x[4]) +
+            13 * (x[3] + x[4]) +
+            1,
+            13 * (x[2]x[1] + x[1]^2 + x[2]^2) - 61(x[4]x[1] + x[1]^2 + x[4]^2) +
+            48(x[4]x[2] + x[2]^2 + x[4]^2) +
+            48(x[3]x[1] + x[1]^2 + x[3]^2) - 61(x[2]x[3] + x[2]^2 + x[3]^2) +
+            13(x[4] * x[3] + x[3]^2 + x[4]^2),
+            randn(4)' * x - 1,
+            randn(4)' * x - 1,
+        ]
+        b = solve(I)
+        @test isnothing(b)
+    end
+
     @testset "change parameters" begin
         @var x a y b
         F = System([x^2 - a, x * y - a + b]; parameters = [a, b])
@@ -623,5 +644,7 @@
 
             @test length(R1) == 6
         end
+
+
     end
 end