Error when trying to solve for polynomial of certain type

[TorkelE]

I have a project where I generate lots of models and find their steady states using HC. However, I find that quite often I get HC errors for various inputs. Here is one example:

using DynamicPolynomials
import HomotopyContinuation
HomotopyContinuation.@var X1 X2 X3

poly1 = HomotopyContinuation.System([
    -0.18704475670296675*X3 - 0.023748976311324048*X3^4 - 2.1429687752634874*(X2^3)*X3 - 0.6874329414442399*(X1^3)*X3 + 7.8759081760412375*(X1^3)*(X2^3) - 0.2720916404005911*(X2^3)*(X3^4) - 0.08728300610911549*(X1^3)*(X3^4) - 7.8759081760412375(X1^3)*(X2^3)*X3 - (X1^3)*(X2^3)*(X3^4),
    -6.3789556272117505*X1 + 2.2623861285717575*X3^3 - 2.2623861285717575*X1*X3^3 - 2.8195698102334017X1^4 - (X1^4)*X3^3,
    -0.8988646055564954*X2 - 0.41957276727278686*X2*X3^3 - 2.1423330484461474*(X1^3)*X2 + (X1^3)*X3^3 - (X1^3)*X2*X3^3
])
result = HomotopyContinuation.solve(poly1) # Works

# Same input, but with `DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}` type
poly2 = DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[
    -0.18704475670296675*X3 - 0.023748976311324048*X3^4 - 2.1429687752634874*(X2^3)*X3 - 0.6874329414442399*(X1^3)*X3 + 7.8759081760412375*(X1^3)*(X2^3) - 0.2720916404005911*(X2^3)*(X3^4) - 0.08728300610911549*(X1^3)*(X3^4) - 7.8759081760412375(X1^3)*(X2^3)*X3 - (X1^3)*(X2^3)*(X3^4),
    -6.3789556272117505*X1 + 2.2623861285717575*X3^3 - 2.2623861285717575*X1*X3^3 - 2.8195698102334017X1^4 - (X1^4)*X3^3,
    -0.8988646055564954*X2 - 0.41957276727278686*X2*X3^3 - 2.1423330484461474*(X1^3)*X2 + (X1^3)*X3^3 - (X1^3)*X2*X3^3
]
result = HomotopyContinuation.solve(poly2) # ERROR: ArgumentError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer

So, things work for poly1 but not poly2. The only difference is that poly2 have a specific type designated (which is the type of the polynomial when I generated it from my reaction system model).

[TorkelE]

Just an update on this. Checking, it seems like poly2 basically reduces to [0.0, 0.0, 0.0], which I presume causes the issue. Maybe this is a general thing when you try to assign this type, and thus is it me getting that type that is causing the problem?

julia> import HomotopyContinuation

julia> HomotopyContinuation.@var X1 X2 X3
(X1, X2, X3)

julia> poly = DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[
               -0.18704475670296675*X3 - 0.023748976311324048*X3^4 - 2.1429687752634874*(X2^3)*X3 - 0.6874329414442399*(X1^3)*X3 + 7.8759081760412375*(X1^3)*(X2^3) - 0.2720916404005911*(X2^3)*(X3^4) - 0.08728300610911549*(X1^3)*(X3^4) - 7.8759081760412375(X1^3)*(X2^3)*X3 - (X1^3)*(X2^3)*(X3^4),
               -6.3789556272117505*X1 + 2.2623861285717575*X3^3 - 2.2623861285717575*X1*X3^3 - 2.8195698102334017X1^4 - (X1^4)*X3^3,
               -0.8988646055564954*X2 - 0.41957276727278686*X2*X3^3 - 2.1423330484461474*(X1^3)*X2 + (X1^3)*X3^3 - (X1^3)*X2*X3^3
           ]
3-element Vector{Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Float64}}:
 2.73250847e-315
 2.73250847e-315
 2.73250847e-315

[TorkelE]

If I then try this type: DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, DynamicPolynomials.Graded{DynamicPolynomials.LexOrder}}, which is what I usually expected in Catalyst, the polynomial looks OK, but

begin #problematic HC example.
    import HomotopyContinuation
    HomotopyContinuation.@var X1 X2 X3
    poly = DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, DynamicPolynomials.Graded{DynamicPolynomials.LexOrder}}[
        -0.18704475670296675*X3 - 0.023748976311324048*X3^4 - 2.1429687752634874*(X2^3)*X3 - 0.6874329414442399*(X1^3)*X3 + 7.8759081760412375*(X1^3)*(X2^3) - 0.2720916404005911*(X2^3)*(X3^4) - 0.08728300610911549*(X1^3)*(X3^4) - 7.8759081760412375(X1^3)*(X2^3)*X3 - (X1^3)*(X2^3)*(X3^4),
        -6.3789556272117505*X1 + 2.2623861285717575*X3^3 - 2.2623861285717575*X1*X3^3 - 2.8195698102334017X1^4 - (X1^4)*X3^3,
        -0.8988646055564954*X2 - 0.41957276727278686*X2*X3^3 - 2.1423330484461474*(X1^3)*X2 + (X1^3)*X3^3 - (X1^3)*X2*X3^3
    ]
    result = HomotopyContinuation.solve(poly)
end

yields a

ERROR: MethodError: no method matching coefficient_type(::Vector{Polynomial{DynamicPolynomials.Commutative{…}, Graded{…}}})
The function `coefficient_type` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  coefficient_type(::Union{AbstractVector{PT}, Type{PT}, Type{<:AbstractVector{PT}}, PT}) where {T, PT<:AbstractPolynomialLike{T}}
   @ MultivariatePolynomials ~/.julia/packages/MultivariatePolynomials/iTfZE/src/term.jl:139

Stacktrace:
 [1] system_with_coefficents_as_params(F::Vector{…}; variables::Vector{…}, variable_groups::Nothing)
   @ HomotopyContinuation.ModelKit ~/.julia/packages/HomotopyContinuation/HdN5z/src/model_kit/symbolic.jl:1450
 [2] solver_startsolutions(F::Vector{…}, starts::Nothing; parameters::Vector{…}, variables::Vector{…}, variable_ordering::Vector{…}, variable_groups::Nothing, target_parameters::Nothing, kwargs::@Kwargs{})
   @ HomotopyContinuation ~/.julia/packages/HomotopyContinuation/HdN5z/src/solve.jl:100
 [3] solver_startsolutions (repeats 2 times)
   @ ~/.julia/packages/HomotopyContinuation/HdN5z/src/solve.jl:86 [inlined]
 [4] solve(args::Vector{…}; show_progress::Bool, threading::Bool, catch_interrupt::Bool, target_parameters::Nothing, stop_early_cb::Function, transform_result::Nothing, transform_parameters::typeof(identity), flatten::Nothing, target_subspaces::Nothing, kwargs::@Kwargs{})
   @ HomotopyContinuation ~/.julia/packages/HomotopyContinuation/HdN5z/src/solve.jl:473
 [5] solve(args::Vector{Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}}})
   @ HomotopyContinuation ~/.julia/packages/HomotopyContinuation/HdN5z/src/solve.jl:433
 [6] top-level scope
   @ ~/Desktop/Research Projects/GRN discovery - playground/playground_hc_based_oscillation_finder.jl:210
Some type information was truncated. Use `show(err)` to see complete types.

[PBrdng]

Internally, all systems are converted to System. It seems that the function MultivariatePolynomials.coefficient_type is not implemented for your specific type.

[TorkelE]

Got it, thanks! i have added some additional conversions to my method, so it works now.