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Try switching to compiled system

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This commit is contained in:
Aaron Fenyes 2024-02-10 00:59:50 -05:00
parent 34358a8728
commit becefe0c47
1 changed files with 47 additions and 60 deletions
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59
engine-proto/Engine.jl
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@ -263,38 +263,26 @@ println("Two points on a sphere: ", freedom, " degrees of freedom")
# --- 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)
vbls = Variable.(symbols(coordring))
cut_system = System([eqns_ab_s; cut], variables = vbls)
##cut_result = HomotopyContinuation.solve(cut_system)
##println("non-singular solutions:")
##for soln in solutions(cut_result)
## display(soln)
##end
##println("singular solutions:")
##for sing in singular(cut_result)
## display(sing.solution)
##end
coordring = base_ring(ideal_ab_s)
vbls = Variable.(symbols(coordring))
##cut_system = CompiledSystem(System([eqns_ab_s; cut], variables = vbls))
##cut_result = HomotopyContinuation.solve(cut_system)
##println("non-singular solutions:")
##for soln in solutions(cut_result)
## display(soln)
##end
##println("singular solutions:")
##for sing in singular(cut_result)
## display(sing.solution)
##end
# test a random witness set
max_slope = 2
binom = Binomial(2max_slope, 1/2)
Random.seed!(6071)
samples = []
for _ in 1:3
# test a random witness set
system = CompiledSystem(System(eqns_ab_s, variables = vbls))
max_slope = 2
binom = Binomial(2max_slope, 1/2)
Random.seed!(6071)
samples = []
for _ in 1:3
cut_matrix = rand(binom, freedom, length(gens(coordring))) .- max_slope
##cut_matrix = [
## 1 1 1 1 0 1 1 0 1 1 0;
@ -307,11 +295,11 @@ if cut_freedom == 0
display(cut_matrix)
display(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))))
end
println("witness solutions:")
for soln in samples
end
println("witness solutions:")
for soln in samples
display([vbls round.(soln, digits = 6)])
k_sq = abs2(soln[1])
if abs2(soln[end-2]) > 1e-12
@ -325,5 +313,4 @@ if cut_freedom == 0
sum_sq = sum(soln[[4, 7, 10]] .^ 2)
println("center at origin: r² = $(round(1/k_sq, digits = 6)); x² + y² + z² = $(round(sum_sq, digits = 6))")
end
end
end