In this post, we'll discuss how to install Oscar on your personal computer. I'll assume a very little familiarity with programming, and none with any of the specific concepts or tools we'll discuss. Instead of doing the fastest possible thing to get started, I'd like to discuss why we're doing what we're doing along the way. This will lead us into a discussion of recent advances in software development over the past 20-25 years.
I want to clear up one subtlety in terminology. In order to do mathematical research with programming, you need (at least) two things:
A programming language, i.e. a set of commands that can be used to write computer programs. Things like if-statements, while-loops, for-loops, lists, and so on are part of the programming language. This is Turing-complete and a priori has nothing to do with any specific use cases, such as mathematical programming.
A standard library or framework, i.e. a set of functions which are provided out of the box for the user. This may include standard coding exercises like sorting a list, or very math-specific things like computing the class group of a number field.
This distinction can be confusing at times, because many computer algebra systems provide both a programming language and a framework, releasing them with the same name. One example of this is Macaulay2. On the other hand, we will use the Julia programming language, with Oscar as our framework.
Thus, to install Oscar it is enough to install Julia, and install various Julia packages (including Oscar itself).
It turns out that Oscar doesn't actually support Windows. This is ok though, because we can use Windows Subsystem for Linux (WSL), see the instructions on Oscar's website.
I highly recommend installing the Windows terminal. Among other things, it'll let you use math symbols like Ω or ≤ in your code.
If you're on a Mac, you'll need to install the Apple developer tools, see the instructions on Oscar's website.
Any programming language periodically have updates which add functionality, fix bugs, increase performance, and so on. It's nice to be able to use the latest version of your language, since it's likely to work better and faster. On the other hand, updating can be a pain, and even worse, sometimes you update and then it breaks your code.
Software engineers have dealt with thse issue for decades, and in the past 10-20 years the community seems to have converged on a solution. A version manager is a program that manages multiple versions of the language installed at once. For example, a while back Oscar was broken with Julia version 1.10 for some reason on my desktop computer. I used Julia version 1.8 for some of my research code. Eventually, whatever bug was causing the problem got fixed and I started using the latest version, which by that time was 1.11.
Julia's version mananger is called juliaup, which is a reference to rustup. Rust is a programming language that got really popular among software developers in the 2010s, and it has rave reviews. For example, it consistently wins the "most loved" technologies on the Stack Overflow Developer Survey. One of the reasons for Rust's popularity is the tools that surround it, including rustup, the version manager for Rust. As such, Rust has had a huge influence on software engineering since the mid-2010's. In particular, juliaup is designed to work in a very analogous way to rustup.
Rust has not yet been used that much for mathematics, but maybe this will change in the future: there are already people doing stuff with Gromov-Witten invariants and stable homotopy theory.
You can installed juliaup using the instructions in juliaup's README (if you're on Windows, make sure to use the "Linux" instructions in your WSL terminal).
To check if you've properly installed juliaup, you can type julia into the command line. You see a Julia prompt (if it doesn't work, you might need to restart the terminal window). This is called the Julia REPL, which stands for Read Evaluate Print Loop. You type commands into the REPL, and Julia prints out the output of the command. To verify that the REPL is working properly, you can try doing basic arithmetic:
julia> 2+2
4Once we've installed Julia, Oscar can simply be installed as a Julia package. A package is, roughly, a self-contained collection of code that's meant to be used by others, and a package manager is a program that downloads packages from the internet and takes care of installation and configuration.
Julia's package manager, known as Pkg, is modeled closely after cargo, the package manager for Rust. cargo also dates to the mid-2010's and has gotten rave reviews. Most modern package managers since then have either improved on or just copied the general design strategy of cargo.
To use Julia's package manager, open a Julia REPL (i.e. type julia into the command line if you haven't already) and press the end square bracket ]. The prompt should turn blue. Then type add Oscar and click enter. It'll take a while installing a bunch of things.
Julia's GPU libraries will work on most computers that were bought post-2020. The first thing you'll need to know is what brand of GPU you have. Your choices are Nvidia, AMD, Intel, or Apple. You should be able to find this in the system settings. Once you know the brand, the Julia library you install is listed here:
| Vendor | Julia Library Name |
|---|---|
| Nvidia | CUDA |
| AMD | ROCm |
| Intel | oneAPI |
| Apple | Metal |
I'll do the example of Nvidia. In this case, you'll go into package mode and run add CUDA. Then, regardless of what brand you're using, run add KernelAbstractions and add AcceleratedKernels.
An IDE (Integrated Development Environment) is basically a souped-up code editor with extra features that help you write code. You don't technically need an IDE to write code, but it can be a much nicer experience. Over the past few years, VS Code (short for Visual Studo Code) has become a very popular IDE. If you don't want to use VS Code, you can use any other IDE that you're familiar with, but here we'll focus on VS code.
First, you'll want to download and install VS Code from the VS Code website. Then, open VS Code. If you're on a Mac, you can now install all of the plugins you want– click the extensions icon on the left side, type julia into the search box. Find the "Julia Language Support" plugin, and click install.
If you're using Windows, you'll have to connect your VS Code to WSL. First, install the WSL extention by clicking the extensions icon on the left, and typing in wsl into the search bar. Find the WSL extension and click Install.
Next, go to the search bar at the very top of VS Code, and type in >wsl, and among the search options should be WSL: Connect to WSL. Choose this option, and VS Code will reload itself.
Now, you can install the Julia plugin (and any other plugins you may want). Click the extensions icon on the left again, type julia into the search bar, and click the Install in WSL option.
If you've got everything installed, go ahead and try it out! Type the following into the REPL (or just copy and paste the whole thing, including the julia> prompts), and see if you get the same results:
julia> using Oscar
julia> R, (x,y,z) = ZZ[:x,:y,:z]
(Multivariate polynomial ring in 3 variables over ZZ, ZZMPolyRingElem[x, y, z])
julia> I = ideal(R, x*y + z^2)
Ideal generated by
x*y + z^2
julia> Q, map = quo(R,I)
(Quotient of multivariate polynomial ring by ideal (x*y + z^2), Map: R -> Q)
julia> Q(y^2*x) == Q(-y*z^2)
trueText that is in monospace font means that you should type the code into the terminal and press enter.
Download Ubuntu from the Windows app store
Download Windows Terminal from the Windows app store
Open Windows Terminal (in Ubuntu)
curl -fsSL https://install.julialang.org | sh
julia (open a Julia REPL)
Type ] to enter package mode
add Oscar
Type backspace to exit package mode
using Oscar
Download and install VS Code
Install the WSL plugin
Run the command >WSL: Connect to WSL in VS Code
Install the Julia plugin in WSL
Launch a terminal
xcode-select --install, then confirm
curl -fsSL https://install.julialang.org | sh
julia (open a Julia REPL)
Type ] to enter package mode
add Oscar
Type backspace to exit package mode
using Oscar
Download and install VS Code
Install the Julia plugin