Running the worksheets

The documentation of PaceControl.jl contains worksheets on certified computation for control. Each one is available as a web page, as a Jupyter notebook (.ipynb), as a Julia script (.jl) and as a Maple script (.mpl): the download links are at the top of each page.

1. Install Julia

Install Julia 1.11 or later with juliaup:

curl -fsSL https://install.julialang.org | sh      # macOS, Linux
winget install --name Julia --id 9NJNWW8PVKMN -e -s msstore   # Windows

2. Install PACE and its components

Start julia and type:

using Pkg
Pkg.Registry.add("General")
Pkg.Registry.add(url = "https://gitlab.inria.fr/pace/pace-julia-registry.git")
Pkg.activate(joinpath(homedir(), "pace-worksheets"))
Pkg.add(["PaceControl", "Nemo", "AbstractAlgebra", "IJulia"])

The registries are added once per Julia installation. The packages go into an environment of their own, in the folder pace-worksheets of your home directory. PaceControl brings PACE and its components; Nemo and AbstractAlgebra are used to write the polynomials. More on the PACE registry in the installation guide.

The worksheets call PACE only. To choose another implementation of an algorithm (rur_backend!, dv_backend!, zx_backend!) or another variant of the C library of LACE (lace_library!), see the PACE.jl documentation.

3. Run a notebook

Still in the same Julia session, declare a Jupyter kernel that uses this environment:

using IJulia
installkernel("Julia PACE", "--project=" * dirname(Base.active_project()))

Then download a notebook and open it with one of:

  • JupyterLab or Jupyter Notebook: in Julia, IJulia.jupyterlab(dir = pwd()) or IJulia.notebook(dir = pwd()) (if Jupyter is not installed, IJulia offers to install it); open the .ipynb file and choose the kernel Julia PACE.
  • VS Code, with the Julia and Jupyter extensions: open the .ipynb file and choose the kernel Julia PACE (top right).

Run the cells in order (Run All).

4. Run a Julia script

The .jl file is the same worksheet as a plain script:

julia --project=$HOME/pace-worksheets 04_hinf_norm.jl

A script shows only what it prints; to see the result of each step, use the notebook.

5. Run a Maple script

Install LACE for Maple (Maple 2026), then, from the folder of the downloaded file:

maple -q 04_hinf_norm.mpl