Add support for SemialgebraicSets.jl

[saschatimme]

Finally(!) addresses #20.

Basic support:

julia> using HomotopyContinuation, SemialgebraicSets;

julia> solver = SemialgebraicSetsHCSolver(; compile = false) # possible to pass any solve option
SemialgebraicSetsHCSolver(; compile = false)

julia> @polyvar x y
(x, y)

julia> V = @set x^2 == 1 && y^2 == 2 solver
Algebraic Set defined by 2 equalities
 x^2 - 1.0 = 0
 y^2 - 2.0 = 0

julia> collect(V)
4-element Array{Array{Float64,1},1}:
 [1.0, 1.414213562373095]
 [1.0, -1.414213562373095]
 [-1.0, 1.414213562373095]
 [-1.0, -1.414213562373095]

There is now also a direct System constructor from an AbstractAlgebraicSet:

julia> V = @set x^2 == 1 && y^2 == 2
Algebraic Set defined by 2 equalities
 x^2 - 1.0 = 0
 y^2 - 2.0 = 0

julia> System(V; variables= [y, x])
System of length 2
 2 variables: y, x

 -1.0 + 1.0*x^2
 -2.0 + 1.0*y^2

@blegat Is this how you imagined it?

[saschatimme]

One question: I was wondering whether we should set the compile option to false by default here. Otherwise every system will trigger compilation. This obviously depends on the use case. Is this used to solve many small systems? Or can these also be larger?

[blegat]

Is this used to solve many small systems? Or can these also be larger?

That's a good point, it is indeed sometimes used to solve many small systems so compilation might be off by default.

[saschatimme]

Okay, I disabled the compilation by default