Add MacaulayLab to README (#29)

* Add MacaulayLab to README

* Specify to install julia package

Author: blegat

README.md

@@ -18,6 +18,16 @@ using TypedPolynomials
 @set x == z^2 && y == z^3
 ```
 
+The following example shows how to build an [basic semialgebraic set](http://www.mit.edu/~parrilo/cdc03_workshop/10_positivstellensatz_2003_12_07_02_screen.pdf)
+```julia
+using TypedPolynomials
+@polyvar x y
+@set x^2 + y^2 <= 1 # Euclidean ball
+# Cutting the algebraic variety https://en.wikipedia.org/wiki/Algebraic_variety#/media/File:Elliptic_curve2.png
+@set y^2 == x^3 - x && x <= 0
+@set y^2 == x^3 - x && x >= 1
+```
+
 ## Solving systems of algebraic equations
 
 Once the algebraic set has been created, you can check whether it is zero-dimensional and if it is the case, you can get the finite number of elements of the set simply by iterating over it, or by using `collect` to transform it into an array containing the solutions.
@@ -32,9 +42,13 @@ The code sample above solves the system of algbraic equations by first
 computing a *Gröbner basis* for the system, then the multiplication matrices
 and then a Schur decomposition of a random combination of these matrices.
 Additionally, SemialgebraicSets defines an interface that can be implemented by
-other solvers for these systems.
-This allows for instance to solve the systems with
-[homotopy continuation](https://www.juliahomotopycontinuation.org/):
+other solvers for these systems as shown in the following subsections.
+
+### Solve with [HomotopyContinuation.jl](https://www.juliahomotopycontinuation.org/)
+
+You can solve the system with
+[homotopy continuation](https://www.juliahomotopycontinuation.org/)
+as follows:
 ```julia
 julia> using HomotopyContinuation
 
@@ -55,14 +69,27 @@ julia> collect(V)
  [-3.0, -2.0]
 ```
 
-The following example shows how to build an [basic semialgebraic set](http://www.mit.edu/~parrilo/cdc03_workshop/10_positivstellensatz_2003_12_07_02_screen.pdf)
+### Solve with [MacaulayLab](http://www.macaulaylab.net/)
+
+You can solve the system with
+[MacaulayLab](http://www.macaulaylab.net/) as follows.
+First install [MacaulayLab.jl](https://github.com/blegat/MacaulayLab.jl)
+and then run the following:
 ```julia
-using TypedPolynomials
-@polyvar x y
-@set x^2 + y^2 <= 1 # Euclidean ball
-# Cutting the algebraic variety https://en.wikipedia.org/wiki/Algebraic_variety#/media/File:Elliptic_curve2.png
-@set y^2 == x^3 - x && x <= 0
-@set y^2 == x^3 - x && x >= 1
+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]
 ```
 
 [build-img]: https://github.com/JuliaAlgebra/SemialgebraicSets.jl/workflows/CI/badge.svg?branch=master