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Evaluate and display elements

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This commit is contained in:
Aaron Fenyes 2024-02-12 20:34:12 -05:00
parent 1f173708eb
commit 6cf07dc6a1
2 changed files with 58 additions and 48 deletions
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16
engine-proto/Engine.Numerical.jl
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@ -2,7 +2,10 @@ module Numerical
using LinearAlgebra
using AbstractAlgebra
using HomotopyContinuation
using HomotopyContinuation:
Variable, Expression, AbstractSystem, System, LinearSubspace,
nvariables, isreal, witness_set, results
import GLMakie
using ..Algebraic
# --- polynomial conversion ---
@ -11,7 +14,7 @@ using ..Algebraic
# https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/issues/520#issuecomment-1317681521
function Base.convert(::Type{Expression}, f::MPolyRingElem)
variables = Variable.(symbols(parent(f)))
f_data = zip(AbstractAlgebra.coefficients(f), exponent_vectors(f))
f_data = zip(coefficients(f), exponent_vectors(f))
sum(cf * prod(variables .^ exp_vec) for (cf, exp_vec) in f_data)
end
@ -37,4 +40,13 @@ function real_samples(F::AbstractSystem, dim)
filter(isreal, results(witness_set(F, cut)))
end
AbstractAlgebra.evaluate(pt::Point, vals::Vector{<:RingElement}) =
GLMakie.Point3f([evaluate(u, vals) for u in pt.coords])
function AbstractAlgebra.evaluate(sph::Sphere, vals::Vector{<:RingElement})
radius = 1 / evaluate(sph.coords[1], vals)
center = radius * [evaluate(u, vals) for u in sph.coords[3:end]]
GLMakie.Sphere(GLMakie.Point3f(center), radius)
end
end