Separate the algebraic and numerical parts of the engine

engine-proto/Engine.Numerical.jl

@@ -0,0 +1,25 @@
+module Numerical
+
+using AbstractAlgebra
+using HomotopyContinuation: Variable, Expression, System
+using ..Algebraic
+
+# --- polynomial conversion ---
+
+# hat tip Sascha Timme
+#   https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/issues/520#issuecomment-1317681521
+function Base.convert(::Type{Expression}, f::MPolyRingElem)
+  variables = Variable.(symbols(parent(f)))
+  f_data = zip(coefficients(f), exponent_vectors(f))
+  sum(cf * prod(variables .^ exp_vec) for (cf, exp_vec) in f_data)
+end
+
+# create a ModelKit.System from an ideal in a multivariate polynomial ring. the
+# variable ordering is taken from the polynomial ring
+function System(I::Generic.Ideal)
+  eqns = Expression.(gens(I))
+  variables = Variable.(symbols(base_ring(I)))
+  System(eqns, variables = variables)
+end
+
+end