MacaulayLab

MacaulayLab.jl is an interface to the MacaulayLab solver for algebraic equations. It exports the solvesystem function that is a thin wrapper on top of the solvesystem MATLAB function and use it to define the MacaylayLab.Solver object that implements the solver-independent SemialgebraicSets API for solving algebraic systems.

Consider the system of polynomial equations defined by x^2 + x == 6 and y == x + 1

To solve it with MacaulayLab directly, do

julia> using DynamicPolynomials, MacaulayLab

julia> @polyvar x y
(x, y)

julia> P = [x^2 + x - 6, y - x - 1]
2-element Vector{Polynomial{true, Int64}}:
 x² + x - 6
 -x + y - 1

julia> X, output = solvesystem(P);

julia> X
2×2 Matrix{Float64}:
  2.0   3.0
 -3.0  -2.0

julia> output
Dict{String, Any} with 8 entries:
  "residualsbeforeclustering" => [4.66294e-15, 9.76996e-15]
  "accuracybeforeclustering"  => 9.76996e-15
  "time"                      => 1.08337
  "nullities"                 => [0.0, 2.0, 2.0]
  "accuracy"                  => 9.76996e-15
  "residuals"                 => [4.66294e-15, 9.76996e-15]
  "shiftvalues"               => [6.57699, -5.28077]
  "solutions"                 => Any[[6.57699, -5.28077], [2.0, -3.0], [3.0, -2.0]]

To solve it with SemialgebraicSets interface, do

julia> using DynamicPolynomial, MacaulayLab, SemialgebraicSets

julia> solver = MacaulayLab.Solver()
MacaulayLab.Solver()

julia> V = @set x^2 + x == 6 && y == x + 1 solver
Algebraic Set defined by 2 equalities
 x^2 + x - 6.0 = 0
 -x + y - 1.0 = 0

julia> collect(V)
2-element Vector{Vector{Float64}}:
 [2.0000000000000004, 2.999999999999999]
 [-3.0000000000000004, -2.0000000000000004]

Installation

You can install MacaulayLab.jl through the Julia package manager:

] add https://github.com/blegat/MacaulayLab.jl

but you first need to make sure that you satisfy the requirements of the MATLAB.jl Julia package and that the MacaulayLab software is installed in your MATLAB™ installation.

Then, you will need to add the path to MATLAB:

julia> using MATLAB

julia> mat"addpath('/home/blegat/git/macaulaylab-public/Code')"

julia> mat"addpath('/home/blegat/git/macaulaylab-public/Database')"

julia> mat"savepath"