Start interface to Macaulay2
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:
parent
3170a933e4
commit
74529048de
@ -29,6 +29,18 @@ end
|
|||||||
dimension(I::Generic.Ideal{U}, maxdepth = Inf) where {T <: RingElement, U <: MPolyRingElem{T}} =
|
dimension(I::Generic.Ideal{U}, maxdepth = Inf) where {T <: RingElement, U <: MPolyRingElem{T}} =
|
||||||
length(gens(base_ring(I))) - codimension(I, maxdepth)
|
length(gens(base_ring(I))) - codimension(I, maxdepth)
|
||||||
|
|
||||||
|
m2_ordering(R::MPolyRing) = Dict(
|
||||||
|
:lex => :Lex,
|
||||||
|
:deglex => :GLex,
|
||||||
|
:degrevlex => :GRevLex
|
||||||
|
)[ordering(R)]
|
||||||
|
|
||||||
|
string_m2(ring::MPolyRing) =
|
||||||
|
"QQ[$(join(symbols(ring), ", ")), MonomialOrder => $(m2_ordering(ring))]"
|
||||||
|
|
||||||
|
string_m2(f::MPolyRingElem) =
|
||||||
|
replace(string(f), "//" => "/")
|
||||||
|
|
||||||
# --- primitve elements ---
|
# --- primitve elements ---
|
||||||
|
|
||||||
abstract type Element{T} end
|
abstract type Element{T} end
|
||||||
@ -149,7 +161,10 @@ function Base.push!(ctx::Construction{T}, rel::Relation{T}) where T
|
|||||||
end
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
function realize(ctx::Construction{T}) where T
|
# output options:
|
||||||
|
# nothing - find a Gröbner basis
|
||||||
|
# :m2 - write a system of polynomials to a Macaulay2 file
|
||||||
|
function realize(ctx::Construction{T}; output = nothing) where T
|
||||||
# collect coordinate names
|
# collect coordinate names
|
||||||
coordnamelist = Symbol[]
|
coordnamelist = Symbol[]
|
||||||
eltenum = enumerate(Iterators.flatten((ctx.spheres, ctx.points)))
|
eltenum = enumerate(Iterators.flatten((ctx.spheres, ctx.points)))
|
||||||
@ -197,7 +212,16 @@ function realize(ctx::Construction{T}) where T
|
|||||||
push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
|
push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
|
||||||
end
|
end
|
||||||
|
|
||||||
(Generic.Ideal(coordring, eqns), eqns)
|
if output == :m2
|
||||||
|
file = open("macaulay2/construction.m2", "w")
|
||||||
|
write(file, string(
|
||||||
|
"coordring = $(string_m2(coordring))\n",
|
||||||
|
"eqns = {\n $(join(string_m2.(eqns), ",\n "))\n}"
|
||||||
|
))
|
||||||
|
close(file)
|
||||||
|
else
|
||||||
|
return (Generic.Ideal(coordring, eqns), eqns)
|
||||||
|
end
|
||||||
end
|
end
|
||||||
|
|
||||||
end
|
end
|
@ -33,44 +33,45 @@ tangencies = [
|
|||||||
for n in 1:3
|
for n in 1:3
|
||||||
]
|
]
|
||||||
ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
|
ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
|
||||||
ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
|
##ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
|
||||||
freedom = Engine.dimension(ideal_tan_sph)
|
Engine.realize(ctx_tan_sph, output = :m2)
|
||||||
println("Three mutually tangent spheres: $freedom degrees of freedom")
|
##freedom = Engine.dimension(ideal_tan_sph)
|
||||||
|
##println("Three mutually tangent spheres: $freedom degrees of freedom")
|
||||||
|
|
||||||
# --- test rational cut ---
|
# --- test rational cut ---
|
||||||
|
|
||||||
coordring = base_ring(ideal_tan_sph)
|
##coordring = base_ring(ideal_tan_sph)
|
||||||
vbls = Variable.(symbols(coordring))
|
##vbls = Variable.(symbols(coordring))
|
||||||
|
|
||||||
# test a random witness set
|
# test a random witness set
|
||||||
system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
|
##system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
|
||||||
norm2 = vec -> real(dot(conj.(vec), vec))
|
##norm2 = vec -> real(dot(conj.(vec), vec))
|
||||||
rng = MersenneTwister(6071)
|
##rng = MersenneTwister(6071)
|
||||||
n_planes = 6
|
##n_planes = 6
|
||||||
samples = []
|
##samples = []
|
||||||
for _ in 1:n_planes
|
##for _ in 1:n_planes
|
||||||
real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))
|
## real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))
|
||||||
for soln in real_solns
|
## for soln in real_solns
|
||||||
if all(norm2(soln - samp) > 1e-4*length(gens(coordring)) for samp in samples)
|
## if all(norm2(soln - samp) > 1e-4*length(gens(coordring)) for samp in samples)
|
||||||
push!(samples, soln)
|
## push!(samples, soln)
|
||||||
end
|
## end
|
||||||
end
|
## end
|
||||||
end
|
##end
|
||||||
println("Found $(length(samples)) sample solutions")
|
##println("Found $(length(samples)) sample solutions")
|
||||||
|
|
||||||
# show a sample solution
|
# show a sample solution
|
||||||
function show_solution(ctx, vals)
|
##function show_solution(ctx, vals)
|
||||||
# evaluate elements
|
## # evaluate elements
|
||||||
real_vals = real.(vals)
|
## real_vals = real.(vals)
|
||||||
disp_points = [Engine.Numerical.evaluate(pt, real_vals) for pt in ctx.points]
|
## 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]
|
## disp_spheres = [Engine.Numerical.evaluate(sph, real_vals) for sph in ctx.spheres]
|
||||||
|
##
|
||||||
# create scene
|
## # create scene
|
||||||
scene = Scene()
|
## scene = Scene()
|
||||||
cam3d!(scene)
|
## cam3d!(scene)
|
||||||
scatter!(scene, disp_points, color = :green)
|
## scatter!(scene, disp_points, color = :green)
|
||||||
for sph in disp_spheres
|
## for sph in disp_spheres
|
||||||
mesh!(scene, sph, color = :gray)
|
## mesh!(scene, sph, color = :gray)
|
||||||
end
|
## end
|
||||||
scene
|
## scene
|
||||||
end
|
##end
|
3
engine-proto/macaulay2/engine.m2
Normal file
3
engine-proto/macaulay2/engine.m2
Normal file
@ -0,0 +1,3 @@
|
|||||||
|
needsPackage "TriangularSets"
|
||||||
|
|
||||||
|
mprod = (v, w) -> (v#0*w#1 + w#0*v#1) / 2 - v#2*w#2 - v#3*w#3 - v#4*w#4
|
Loading…
Reference in New Issue
Block a user