include("HittingSet.jl")

module Engine

include("Engine.Algebraic.jl")
include("Engine.Numerical.jl")

using .Algebraic
using .Numerical

export Construction, mprod, codimension, dimension

end

# ~~~ sandbox setup ~~~

using Random
using Distributions
using LinearAlgebra
using AbstractAlgebra
using HomotopyContinuation
using GLMakie

CoeffType = Rational{Int64}

spheres = [Engine.Sphere{CoeffType}() for _ in 1:3]
tangencies = [
  Engine.AlignsWithBy{CoeffType}(
    spheres[n],
    spheres[mod1(n+1, length(spheres))],
    CoeffType(1)
  )
  for n in 1:3
]
ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
##ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
Engine.realize(ctx_tan_sph, output = :m2)
##freedom = Engine.dimension(ideal_tan_sph)
##println("Three mutually tangent spheres: $freedom degrees of freedom")

# --- test rational cut ---

##coordring = base_ring(ideal_tan_sph)
##vbls = Variable.(symbols(coordring))

# test a random witness set
##system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
##norm2 = vec -> real(dot(conj.(vec), vec))
##rng = MersenneTwister(6071)
##n_planes = 6
##samples = []
##for _ in 1:n_planes
##  real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))
##  for soln in real_solns
##    if all(norm2(soln - samp) > 1e-4*length(gens(coordring)) for samp in samples)
##      push!(samples, soln)
##    end
##  end
##end
##println("Found $(length(samples)) sample solutions")

# show a sample solution
##function show_solution(ctx, vals)
##  # evaluate elements
##  real_vals = real.(vals)
##  disp_points = [Engine.Numerical.evaluate(pt, real_vals) for pt in ctx.points]
##  disp_spheres = [Engine.Numerical.evaluate(sph, real_vals) for sph in ctx.spheres]
##  
##  # create scene
##  scene = Scene()
##  cam3d!(scene)
##  scatter!(scene, disp_points, color = :green)
##  for sph in disp_spheres
##    mesh!(scene, sph, color = :gray)
##  end
##  scene
##end