cas-rs

cas-rs is an opinionated computer algebra system written in Rust, originally made for use with the Discord bot CalcBot. It is currently in a very early stage of development.

See below for a guide on the REPL and some code examples.

Features

• Simplification of algebraic expressions, learn more here
• Graphing calculator, learn more here
• Robust expression parser and evaluator with very human-friendly output
• Arbitrary precision arithmetic
• Real and complex numbers
• Radix notation (e.g. 2'1010 = 10)
• 60+ built-in functions, covering many expected use cases (see here)
• Powerful formatting options, including LaTeX code output
• Builtin REPL
• And more!

Quick start

Below are some routine examples of how cas-rs can be used.

REPL

cas-rs comes with a builtin scripting language called "CalcScript" along with a REPL to help you try out the library. CalcScript is a mostly imperative, expression-oriented language, and attempts to keep syntax and visual noise minimal, while still readable. See the examples/ directory for examples of basic programs written in CalcScript.

To install the REPL, run the following command (Rust needs to be installed):

cargo install cas-rs --locked

You can then run the REPL with:

cas-rs

Which will immediately drop you into a REPL session where you can run CalcScript code:

> x = (1 + sqrt(5))/2
1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408807538689175212663386222353693179318006077
> x == phi
true

To learn more about CalcScript and example REPL usage, see the cas-parser crate.

General expression evaluation

cas-rs can also be used as a library to evaluate CalcScript expressions. Here is an example of evaluating the expression x^2 + 5x + 6 where x = 2:

use cas_compute::numerical::{ctxt::Ctxt, eval::Eval};
use cas_parser::parser::{ast::Expr, Parser};

let mut parser = Parser::new("x^2 + 5x + 6");
let ast_expr = parser.try_parse_full::<Expr>().unwrap();

let mut ctxt = Ctxt::default();
ctxt.add_var("x", 2.into());

let result = ast_expr.eval(&mut ctxt).unwrap();
assert_eq!(result, 24.into());

Learn more about this in the cas-compute crate.

Graphing calculator

A customizable graphing calculator is provided with the cas-graph crate. You can create a graph of multiple functions and points, customize the appearance of the viewport, functions, and points, and render the graph to a PNG file (or any format supported by the cairo crate.

use cas_graph::Graph;
use std::fs::File;

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let surface = Graph::default()
        .try_add_expr("x^2 + 5x + 6").unwrap()
        .add_point((-5.0, 6.0))
        .add_point((-4.0, 2.0))
        .add_point((-3.0, 0.0))
        .add_point((-2.0, 0.0))
        .add_point((-1.0, 2.0))
        .center_on_points()
        .draw()?;

    let mut file = File::create("parabola.png")?;
    surface.write_to_png(&mut file)?;

    Ok(())
}

Output (note: colors were randomly chosen; random color selection is not included in the example code):

Acknowledgements

• Arbitrary precision arithmetic is implemented using the rug crate.
• The design of cas-parser is heavily inspired by the Rust compiler, syn, and ariadne.

lib.rs:

Contains the common ErrorKind trait used by all parsing and evaluation errors to display user-facing error messages.