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Start interface to Macaulay2

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I did this to try out Macaulay2's "triangularize" function, but that
turns out to use Maple for rings with more than three variables.
This commit is contained in:
Aaron Fenyes 2024-02-16 12:47:06 -08:00
parent 3170a933e4
commit 74529048de
3 changed files with 64 additions and 36 deletions
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69
engine-proto/Engine.jl
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@ -33,44 +33,45 @@ tangencies = [
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)
freedom = Engine.dimension(ideal_tan_sph)
println("Three mutually tangent spheres: $freedom degrees of freedom")
##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))
##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")
##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
##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