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Engine prototype #13

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glen merged 133 commits from engine-proto into main 2024-10-21 03:18:48 +00:00
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1 changed files with 47 additions and 60 deletions
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engine-proto/Engine.jl
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@ -263,22 +263,9 @@ println("Two points on a sphere: ", freedom, " degrees of freedom")
# --- test rational cut --- # --- test rational cut ---
cut_coeffs = [
1 1 1 0 0 0 1 1 1 1 1;
2 1 1 0 0 0 1 2 1 1 1;
1 2 0 0 0 0 1 1 0 1 2
]
cut = [
sum(vcat(cf[1:3] .* a.coords, cf[4:6] .* b.coords, cf[7:end] .* (s.coords - [0, 0, 0, 0, 1])))
for cf in eachrow(cut_coeffs)
]
cut_ideal_ab_s = Generic.Ideal(base_ring(ideal_ab_s), [gens(ideal_ab_s); cut])
cut_freedom = Engine.dimension(cut_ideal_ab_s)
println("Two points on a sphere, after cut: ", cut_freedom, " degrees of freedom")
if cut_freedom == 0
coordring = base_ring(ideal_ab_s) coordring = base_ring(ideal_ab_s)
vbls = Variable.(symbols(coordring)) vbls = Variable.(symbols(coordring))
cut_system = System([eqns_ab_s; cut], variables = vbls) ##cut_system = CompiledSystem(System([eqns_ab_s; cut], variables = vbls))
##cut_result = HomotopyContinuation.solve(cut_system) ##cut_result = HomotopyContinuation.solve(cut_system)
##println("non-singular solutions:") ##println("non-singular solutions:")
##for soln in solutions(cut_result) ##for soln in solutions(cut_result)
@ -290,6 +277,7 @@ if cut_freedom == 0
##end ##end
# test a random witness set # test a random witness set
system = CompiledSystem(System(eqns_ab_s, variables = vbls))
max_slope = 2 max_slope = 2
binom = Binomial(2max_slope, 1/2) binom = Binomial(2max_slope, 1/2)
Random.seed!(6071) Random.seed!(6071)
@ -307,7 +295,7 @@ if cut_freedom == 0
display(cut_matrix) display(cut_matrix)
display(cut_offset) display(cut_offset)
cut_subspace = LinearSubspace(cut_matrix, cut_offset) cut_subspace = LinearSubspace(cut_matrix, cut_offset)
wtns = witness_set(System(eqns_ab_s, variables = vbls), cut_subspace) wtns = witness_set(system, cut_subspace)
append!(samples, solution.(filter(isreal, results(wtns)))) append!(samples, solution.(filter(isreal, results(wtns))))
end end
println("witness solutions:") println("witness solutions:")
@ -326,4 +314,3 @@ if cut_freedom == 0
println("center at origin: r² = $(round(1/k_sq, digits = 6)); x² + y² + z² = $(round(sum_sq, digits = 6))") println("center at origin: r² = $(round(1/k_sq, digits = 6)); x² + y² + z² = $(round(sum_sq, digits = 6))")
end end
end end
end