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Find real solutions for three mutually tangent spheres

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I'm not sure why the solver wasn't working before. It might've been just
an unlucky random number draw.
This commit is contained in:
Aaron Fenyes 2024-02-15 16:16:06 -08:00
parent ae5db0f9ea
commit ba365174d3
2 changed files with 19 additions and 19 deletions
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20
engine-proto/Engine.Algebraic.jl
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@ -186,16 +186,16 @@ function realize(ctx::Construction{T}) where T
# add relations to center, orient, and scale the construction
# [to do] the scaling constraint, as written, can be impossible to satisfy
# when all of the spheres have to go through the origin
##if !isempty(ctx.points)
## append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3])
##end
##if !isempty(ctx.spheres)
## append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4])
##end
##n_elts = length(ctx.points) + length(ctx.spheres)
##if n_elts > 0
## push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
##end
if !isempty(ctx.points)
append!(eqns, [sum(pt.coords[k] for pt in ctx.points) for k in 1:3])
end
if !isempty(ctx.spheres)
append!(eqns, [sum(sph.coords[k] for sph in ctx.spheres) for k in 3:4])
end
n_elts = length(ctx.points) + length(ctx.spheres)
if n_elts > 0
push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
end
(Generic.Ideal(coordring, eqns), eqns)
## [test] (nothing, eqns)

18
engine-proto/Engine.jl
View File

@ -59,13 +59,13 @@ tangencies = [
ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
##small_eqns_tan_sph = eqns_tan_sph
small_eqns_tan_sph = [
eqns_tan_sph;
spheres[2].coords - [1, 0, 0, 0, 1];
spheres[3].coords - [1, 0, 0, 0, -1];
]
small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph)
freedom = Engine.dimension(small_ideal_tan_sph)
##small_eqns_tan_sph = [
## eqns_tan_sph;
## spheres[2].coords - [1, 0, 0, 0, 1];
## spheres[3].coords - [1, 0, 0, 0, -1];
##]
##small_ideal_tan_sph = Generic.Ideal(base_ring(ideal_tan_sph), small_eqns_tan_sph)
freedom = Engine.dimension(ideal_tan_sph)
println("Three mutually tangent spheres, with two fixed: $freedom degrees of freedom")
##points = [Engine.Point{CoeffType}() for _ in 1:3]
@ -83,11 +83,11 @@ println("Three mutually tangent spheres, with two fixed: $freedom degrees of fre
# --- test rational cut ---
coordring = base_ring(small_ideal_tan_sph)
coordring = base_ring(ideal_tan_sph)
vbls = Variable.(symbols(coordring))
# test a random witness set
system = CompiledSystem(System(small_eqns_tan_sph, variables = vbls))
system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
norm2 = vec -> real(dot(conj.(vec), vec))
rng = MersenneTwister(6071)
n_planes = 3