Problem defining semialgebraicset

[matteodefra]

Hi,

I was trying to define a semialgebraic sets (composed by inequalities and equalities, but I focused only on equalities for the moment) and I'm stuck in the definition.
I cannot find a way to define an empty set, and then add iteratively constraint to it. I have the following code

@polyvar(t[1:4])
@polyvar(s[1:3])

# inequalities = Vector{MultivariatePolynomials.Polynomial}(undef,0)
inequalities = []
equalities = []
# K = BasicSemialgebraicSet{Float64,Polynomial{Float64,Float64}}()
# K = basic_semialgebraic_set(FullSpace(), [t[1]])

# add_inequality!( K, t[2] )

for j=1:n-1
	push!(inequalities, t[j])
	
	if j==1
		push!(inequalities, t[j]^2 - s[j]^2)
	elseif j==n-1
		push!(inequalities, t[j]^2 - (-s[j-1])^2)
	else
		push!(inequalities, t[j]^2 - (s[j]-s[j-1])^2)
	end

end

for j=1:n-2
	push!(inequalities, s[j]+smax)
	push!(inequalities, -s[j]+smax)

	g = s[j]
	for v in -smax:smax
		if v!=0
			g *= (s[j]-v)
		end
	end
	push!(equalities, g)
end

for j=1:n-1
	if j==1
		g1 = 0.25*t[j]^2 - 0.5*t[j]*(s[j]) - 0.25*s[j]^2 - 0.5*s[j] + distances[j]
		g2 = 0.25*t[j]^2 + 0.5*t[j]*(s[j]) - 0.25*s[j]^2 + 0.5*s[j] - distances[j]
		push!(inequalities, g1)
		push!(inequalities, g2)
	elseif j==n-1
		g1 = 0.25*t[j]^2 - 0.5*t[j]*(s[j-1]) - 0.25*s[j-1]^2 + 0.5*s[j-1] + distances[j]
		g2 = 0.25*t[j]^2 + 0.5*t[j]*(s[j-1]) - 0.25*s[j-1]^2 - 0.5*s[j-1] - distances[j]
		push!(inequalities, g1)
		push!(inequalities, g2)
	else
		g1 = 0.25*t[j]^2 - 0.5*t[j]*(s[j-1]+s[j]) - 0.25*s[j-1]^2 - 0.25*s[j]^2 + 0.5*s[j-1]*s[j] - 0.5*s[j] + 0.5*s[j-1] + distances[j]
		g2 = 0.25*t[j]^2 + 0.5*t[j]*(s[j-1]+s[j]) - 0.25*s[j-1]^2 - 0.25*s[j]^2 + 0.5*s[j-1]*s[j] + 0.5*s[j] - 0.5*s[j-1] - distances[j]
		push!(inequalities, g1)
		push!(inequalities, g2)
	end

end

where I define my polyvar and then I create multiple polynomials inequalities. Now, how can I transform all of these (the vector inequalities and equalities) into a set?
I tried the following ways

K = basic_semialgebraic_set(algebraic_set(equalities), inequalities)

# only inequalities
K = basic_semialgebraic_set(FullSpace(), inequalities)

But both of them failed. Even if try to expand all the inequalities with the @set macro

	K = @set t[1]>=0 && t[2]>=0 && t[3]>=0 && t[4]>=0 && t[1]^2>=s[1]^2 && t[2]^2>=(s[2]-s[1])^2 && t[3]^2>=(s[3]-s[2])^2 && t[4]^2>=(s[3])^2 && 
s[1]+smax>=0 && -s[1]+smax>=0 && s[2]+smax>=0 && -s[2]+smax>=0 && s[3]+smax>=0 && -s[3]+smax>=0 && 0.25*t[1]^2 - 0.5*t[1]*(s[1]) - 0.25*s[1]^2 - 0.5*s[1] + distances[1] && 
			0.25*t[1]^2 + 0.5*t[1]*(s[1]) - 0.25*s[1]^2 + 0.5*s[1] - distances[1] &&
			0.25*t[2]^2 - 0.5*t[2]*(s[1]+s[2]) - 0.25*s[1]^2 - 0.25*s[2]^2 + 0.5*s[1]*s[2] - 0.5*s[2] + 0.5*s[1] + distances[2] && 
			0.25*t[2]^2 + 0.5*t[2]*(s[1]+s[2]) - 0.25*s[1]^2 - 0.25*s[2]^2 + 0.5*s[1]*s[2] + 0.5*s[2] - 0.5*s[1] - distances[2] &&
			0.25*t[3]^2 - 0.5*t[3]*(s[2]+s[3]) - 0.25*s[2]^2 - 0.25*s[3]^2 + 0.5*s[2]*s[3] - 0.5*s[3] + 0.5*s[2] + distances[3] && 
			0.25*t[3]^2 + 0.5*t[3]*(s[2]+s[3]) - 0.25*s[2]^2 - 0.25*s[3]^2 + 0.5*s[2]*s[3] + 0.5*s[3] - 0.5*s[2] - distances[3] &&
			0.25*t[4]^2 - 0.5*t[4]*(s[3]) - 0.25*s[3]^2 + 0.5*s[3] + distances[4] &&
			0.25*t[4]^2 + 0.5*t[4]*(s[3]) - 0.25*s[3]^2 - 0.5*s[3] - distances[4]	

I get the following error

ERROR: LoadError: MethodError: no method matching length(::SemialgebraicSets.BasicSemialgebraicSet{Int64, MultivariatePolynomials.VectorPolynomial{Int64, MultivariatePolynomials.Term{Int64, TypedPolynomials.Monomial{(s₁, s₂, s₃, t₁, t₂, t₃, t₄), 7}}}, SemialgebraicSets.FullSpace})

Closest candidates are:
  length(::BenchmarkTools.Trial)
   @ BenchmarkTools ~/.julia/packages/BenchmarkTools/1i1mY/src/trials.jl:41
  length(::Combinatorics.CoolLexCombinations)
   @ Combinatorics ~/.julia/packages/Combinatorics/nV2DW/src/combinations.jl:137
  length(::Base.Iterators.Flatten{Tuple{}})
   @ Base iterators.jl:1193
  ...

[blegat]

The issue is that you are giving Vector{Any}. Maybe we can implement a fallback or a better error so let's keep this issue open. In the meantime, use this as work-around:

concretize(x) = convert.(mapreduce(typeof, promote_type, x), x)
K = basic_semialgebraic_set(FullSpace(), concretize(inequalities))
# or even
K = basic_semialgebraic_set(FullSpace(), identity.(inequalities))