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NID bug fixes #593

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merged 6 commits into from
Oct 1, 2024
Merged

NID bug fixes #593

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aff1f83
fix a bug in nid
PBrdng Oct 1, 2024
58c1b79
add one more test
PBrdng Oct 1, 2024
b5a9f4a
clean code
PBrdng Oct 1, 2024
27e2a99
add fallback for n_components
PBrdng Oct 1, 2024
21726da
export n_components
PBrdng Oct 1, 2024
5db3bbd
fix tests
PBrdng Oct 1, 2024
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2 changes: 1 addition & 1 deletion docs/src/witness_sets.md
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Original file line number Diff line number Diff line change
Expand Up @@ -42,7 +42,7 @@ NumericalIrreducibleDecomposition
```

```@docs
n_components
ncomponents
witness_sets
degrees
```
Expand Down
35 changes: 27 additions & 8 deletions src/numerical_irreducible_decomposition.jl
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Expand Up @@ -4,6 +4,7 @@ export NumericalIrreducibleDecomposition,
regeneration,
witness_sets,
decompose,
ncomponents,
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@PBrdng You should still keep for now an alias n_components = ncomponents around and export it. Otherwise this could break code

n_components,
seed

Expand Down Expand Up @@ -104,6 +105,7 @@ function update_progress!(progress::WitnessSetsProgress, W::Union{WitnessPoints,
showvalues = showvalues(progress),
)
end
update_progress!(progress::Union{Nothing,WitnessSetsProgress}, W::Nothing) = nothing
update_progress!(progress::Nothing) = nothing
finish_progress!(progress::Nothing) = nothing
function finish_progress!(progress::WitnessSetsProgress)
Expand Down Expand Up @@ -147,7 +149,7 @@ This is the core routine of the regeneration algorithm. It intersects a set of [
"""
function intersect_with_hypersurface!(
W::WitnessPoints{T1,T2,Vector{ComplexF64}},
X::WitnessPoints{T3,T4,Vector{ComplexF64}},
X::Union{WitnessPoints{T3,T4,Vector{ComplexF64}},Nothing},
F::AS,
H::WitnessSet{T5,T6,Vector{ComplexF64}},
u::Variable,
Expand All @@ -174,6 +176,11 @@ function intersect_with_hypersurface!(
deleteat!(P, m)
update_progress!(progress, W)

if isnothing(X)
return nothing
end


# Step 2:
# the points in P_next are used as starting points for a homotopy.
# where u^d-1 (u is the extra variable in u-regeneration) is deformed into g
Expand Down Expand Up @@ -203,10 +210,12 @@ function intersect_with_hypersurface!(

# here comes the loop for tracking
l_start = length(start)

for (i, s) in enumerate(start)
p = s[1]
p[end] = s[2] # the last entry of s[1] is zero. we replace it with a d-th root of unity.


res = track(tracker, p, 1)
if is_success(res) && is_finite(res) && is_nonsingular(res)
new = copy(tracker.state.solution)
Expand All @@ -217,6 +226,7 @@ function intersect_with_hypersurface!(
end



nothing
end

Expand Down Expand Up @@ -330,6 +340,7 @@ function is_contained!(
end
# check if x is among the points in U
_, added = add!(U, x, 0)

if added
return false
else
Expand Down Expand Up @@ -537,11 +548,14 @@ function regeneration!(
# we have already intersected X ∩ Hᵢ.
update_progress!(progress, true)
for (k, W) in reverse(E) # k = codim(W) for W in Ws
if k < min(i, n)
X = out[k+1]
if k < i
if k < n
X = out[k+1]
else
X = nothing
end
# here is the intersection step
# the next witness superset X is also passed to this function,
# because we add points that do not belong to W∩Hᵢ to X.
# if k < min(i,n), the next witness superset X is also passed to this function, because we add points that do not belong to W∩Hᵢ to X.
# at this point the equation for W is f[1:(i-1)]
intersect_with_hypersurface!(
W,
Expand All @@ -559,7 +573,10 @@ function regeneration!(
end
end



Fᵢ = fixed(System(f[1:i], variables = vars), compile = false)

# after the first loop that takes care of intersecting with Hᵢ
# we now check if we have added points that are already contained in
# witness sets of higher dimension.
Expand Down Expand Up @@ -1110,13 +1127,13 @@ witness_sets(N::NumericalIrreducibleDecomposition, dim::Int) = witness_sets(N, [
seed(N::NumericalIrreducibleDecomposition) = N.seed

"""
n_components(N::NumericalIrreducibleDecomposition;
ncomponents(N::NumericalIrreducibleDecomposition;
dims::Union{Vector{Int},Nothing} = nothing)

Returns the total number of components in `N`.
`dims` specifies the dimensions that should be considered.
"""
function n_components(
function ncomponents(
N::NumericalIrreducibleDecomposition;
dims::Union{Vector{Int},Nothing} = nothing,
)
Expand All @@ -1134,7 +1151,9 @@ function n_components(

out
end
n_components(N::NumericalIrreducibleDecomposition, dim::Int) = n_components(N, dims = [dim])
ncomponents(N::NumericalIrreducibleDecomposition, dim::Int) = ncomponents(N; dims = [dim])
n_components(N; dims = nothing) = ncomponents(N; dims = dims)
n_components(N, dim) = ncomponents(N; dims = [dim])

"""

Expand Down
31 changes: 25 additions & 6 deletions test/nid_test.jl
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Expand Up @@ -55,6 +55,9 @@
@test isa(N3, NumericalIrreducibleDecomposition)

# number of components
@test ncomponents(N3) == 4
@test ncomponents(N3, dims = [1, 2]) == 3
@test ncomponents(N3, 1) == 2
@test n_components(N3) == 4
@test n_components(N3, dims = [1, 2]) == 3
@test n_components(N3, 1) == 2
Expand All @@ -67,7 +70,7 @@

N_Hyp = numerical_irreducible_decomposition(Hyp)
@test degrees(N_Hyp) == Dict(3 => [5])
@test n_components(N_Hyp) == 1
@test ncomponents(N_Hyp) == 1
end

@testset "Curve of degree 6" begin
Expand All @@ -78,7 +81,7 @@

N_Curve = nid(Curve)
@test degrees(N_Curve) == Dict(1 => [6])
@test n_components(N_Curve) == 1
@test ncomponents(N_Curve) == 1
end

@testset "Overdetermined Test" begin
Expand All @@ -88,7 +91,7 @@

N_TwistedCubicSphere = nid(TwistedCubicSphere)
@test degrees(N_TwistedCubicSphere) == Dict(0 => [3])
@test n_components(N_TwistedCubicSphere) == 1
@test ncomponents(N_TwistedCubicSphere) == 1
end

@testset "Three Lines" begin
Expand All @@ -101,7 +104,7 @@

N_ThreeLines = nid(ThreeLines)
@test degrees(N_ThreeLines) == Dict(1 => [1; 1; 1])
@test n_components(N_ThreeLines) == 3
@test ncomponents(N_ThreeLines) == 3
end

@testset "Bricard6R" begin
Expand Down Expand Up @@ -198,7 +201,7 @@

N_Bricard6R = nid(Bricard6R)
@test degrees(N_Bricard6R) == Dict(1 => [8])
@test n_components(N_Bricard6R) == 1
@test ncomponents(N_Bricard6R) == 1
end

@testset "ACR" begin
Expand Down Expand Up @@ -242,6 +245,22 @@
end


@testset "Union of a sphere, a line, and a point" begin
@var x, y, z

S = [x^2 + y^2 + z^2 - 1] #The sphere
L = [2 * x - z, 2 * y - z] #The line (t,t,2t)
P = [x + y + 2 * z - 4, y - z, x - z] #The point (1,1,1)

F = System([s * l * p for s in S for l in L for p in P])

seed = rand(UInt32)
NID = numerical_irreducible_decomposition(F; seed = 0x7a4845b9)

@test ncomponents(NID, 0) == 1
@test degrees(NID)[0] == [1]
end

# @testset "426" begin
# ### Example thanks to Julian Vill
# @var a, b, c, d, e
Expand Down Expand Up @@ -304,7 +323,7 @@
# endgame_options = EndgameOptions(; sing_accuracy = 1e-10),
# )

# @test n_components(N) == 1
# @test ncomponents(N) == 1
# @test degrees(N) == Dict(2 => [426])
# end
end
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