What is in here is an outgrowth of Vincent Reverdy's CppCon 2023 presentation Symbolic Calculus for High-performance Computing From Scratch Using C++23, a pdf of which is contained in this repository. Here is a link to the YouTube video.

If paired with a library like gcem will allow use for this entirely at compile time, that is, compile within constexpr and consteval contexts. Here is a working example linked with gcem. The code here uses the Standard Library, so until C++26 (or later), constexpr will not compile with certain expressions; but switching between using std math or gcem math is a matter of replacing std:: by gcem::, so if you feel like making the switch it's immediate – check out the example on godbolt...

lam.symbols is a c++ module and is a part of LAM. It has been extended from it's original state to implement some of the exercises for the reader left at the end of the original presentation.

You will need cmake 3.31.6 or later, ninja, and a compiler that cmake supports with import std;. lam.symbols depends on the c++ standard library.

First of all grab a copy:

git clone www.github.com/colinrford/symbols
cd symbols

then, in the directory symbols

mkdir build && cd build
cmake .. -G Ninja

and so long as this succeeds, run

ninja

Your Cmake mileage may vary, on macOS with homebrew-installed clang++, cmake may not find and link everything properly, and I have had to add more flags in the build commands. You may be able to get away with a simple cmake .. and ninja.

import lam.symbols;
using namespace lam::symbols;

constexpr symbol x, y;
constexpr auto expr = (x + y) - y;  // Simplifies to just x at compile time

static_assert(expr(x = 5, y = 10) == 5);  // Verified at compile time!

For now there is but one example included. It computes at compile time the trajectory of Io about Jupiter. An associated Python script will call the c++ program - the trajectory is already computed - which will print 500 svgs; the script converts them with librsvg or inkscape for feeding into ffmpeg, which will stitch the svgs together for a short mp4 video.

The example will not build if it cannot find librsvg, inkscape, or ffmpeg.

ninja orbital_mechanics
cd examples/orbital-motion
python make_video.py

More interesting examples on the way.