CAScad — Computer Algebra System Notebook

An interactive, browser-based computer algebra notebook with multi-kernel support and reactive cell evaluation.

Live Demo (if deployed via GitHub Pages)

Features

• Multi-kernel support — Switch between Giac/Xcas (default) and CortexJS Compute Engine via a toolbar selector
• Reactive DAG execution — Cells automatically re-evaluate when their dependencies change, powered by Observable Runtime
• Visual math input — LaTeX-style editing with MathLive and a custom virtual keyboard (fractions, integrals, sums, products, Greek letters)
• MathJSON-first pipeline — Math cells use MathJSON internally: MathField -> MathJSON -> kernel, LaTeX used only for display
• Interactive 2D plots — plot(sin(x)), plotfunc, plotparam, plotpolar, plotimplicit, plotfield, plotcontour, plotode, plotseq rendered with JSXGraph (zoom, pan, coordinates)
• 3D surface plots — plotfunc(x^2+y^2,[x,y]) rendered with WebGL
• Statistical charts — histogram, barplot, camembert, boxwhisker, scatterplot
• Geometry — circle, segment, point and more
• LaTeX output — Results rendered with KaTeX
• Internationalization — 10 languages: English, French, Spanish, German, Greek, Arabic (RTL), Hindi, Russian, Chinese, Japanese
• Export/Import — Save and reload notebooks as JSON (v5 format with kernel field, backward-compatible with v1–v4)
• Reactive/Manual toggle — Switch between automatic cascade and manual cell-by-cell execution
• Command discovery — search_commands(), list_categories(), suggest_commands() and more for exploring available functions

Kernels

Kernel	Description	Status
Giac/Xcas	Full-featured CAS — algebra, calculus, plots, linear algebra, programming	Default, requires giac.js
CortexJS Compute Engine	Symbolic computation — simplify, factor, differentiate, integrate	Loaded from CDN

The active kernel is selected via the toolbar dropdown. The choice is persisted in localStorage and saved in notebook files (v5 format).

Getting Started

1. Download giac.js and place it in the project root
2. Serve the directory with any static HTTP server:

   npx serve .
   # or
   python3 -m http.server

3. Open http://localhost:3000 (or :8000) in a modern browser
4. Wait for "Giac ready" status, then start computing

Note: A local HTTP server is required because the project uses ES module imports. Opening index.html directly via file:// will not work.

Project Structure

index.html              HTML shell (header, toolbar, notebook container)
css/
  notebook.css          All styles
js/
  kernel-registry.js    Multi-kernel abstraction and registry
  kernel-giac.js        Giac/Xcas kernel adapter
  kernel-compute-engine.js  CortexJS Compute Engine kernel adapter
  i18n.js               Internationalization (10 locales)
  giac-init.js          CortexJS Compute Engine + Giac initialization
  mathjson-xcas.js      MathJSON -> Xcas string converter
  state.js              Shared application state
  io.js                 Export/Import + utilities
  plot-rendering.js     2D/3D plot rendering (SVG, gr2d, JSXGraph, WebGL)
  reactive-dag.js       Reactive DAG with Observable Runtime
  cells.js              Cell management, debug panel, mode switching
  execution.js          Cell execution engine
  command-discovery.js  Command search, browse, and suggest functions
  actions.js            Global actions (run all, delete, move)
  boot.js               Startup sequence, virtual keyboard config, demo cells
assets/
  CAScad.png            Visual identity / logo
examples/
  giac-js/              Example notebooks for Giac/Xcas kernel
  compute-engine/       Example notebooks for CortexJS Compute Engine
giac.js                 Giac/Xcas engine (asm.js, not included — download separately)

Examples

The notebook comes pre-loaded with demo cells covering:

Category	Examples
Reactive chain	a := 5, a^2, b := a + 3
Calculus	\frac{x^4-1}{x^2+1}, \int \frac{1}{x^2+1} dx, \frac{d}{dx}(\sin(x) \cdot e^x), \lim_{x\to 0} \frac{\sin(x)}{x}
Finite sums/products	\sum_{k=1}^{n} k, \prod_{k=1}^{n} k, \sum_{k=1}^{10} k^2
Infinite series	\sum_{n=1}^{\infty} \frac{1}{n^2} (Basel), \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1} (Leibniz)
Algebra	solve(x^2 - 3*x + 2 = 0, x), eigenvalues([[1,2],[3,4]])
2D plots	plot(sin(x)), plotfunc([sin(x),cos(x)],x), plotimplicit(x^2+y^2-1,x,y)
3D plots	plotfunc(x^2+y^2,[x,y]), plotfunc(sin(x)*cos(y),[x,y])
Statistics	histogram(...), barplot(...), camembert(...), boxwhisker(...), scatterplot(...)
Geometry	circle(0,2); segment([0,0],[2,0]); point(1,1)

P2P Transfer (Phone → PC)

Transfer a notebook from your phone to your PC without needing a webcam on the PC side. Uses WebRTC for direct browser-to-browser communication — notebook data never passes through any server.

Prerequisites

• Two devices (phone + PC) with internet access
• Modern browser (Chrome 83+, Firefox 80+, Safari 15+, Edge 83+)
• Phone must have a camera for QR scanning

How to Use

1. On the PC, click 📲 Receive from Phone in the toolbar — a QR code appears
2. On the phone, click 📷 Scan QR and scan the PC's QR code
3. Both devices show a 4-digit confirmation code — verify they match
4. The notebook transfers automatically from phone to PC
5. Review and confirm to load the notebook

The connection uses PeerJS Cloud for signaling and Google STUN for NAT traversal. All notebook data travels over a DTLS-encrypted WebRTC data channel.

Transfer Methods Comparison

Method	PC Webcam	Internet	Size Limit	Speed
Static QR	No	No	~2 KB	Instant
Animated QR (Fountain)	No	No	Unlimited	5-30s
URL Sharing	No	Yes	~2 KB	Instant
File Export/Import	No	No	Unlimited	Manual
P2P Transfer	No	Yes	Unlimited	<10s

When to use P2P Transfer: You want to send a large notebook from phone to PC, the PC has no webcam, and both devices have internet access.

Keyboard Shortcuts

Shortcut	Action
Shift+Enter	Run current cell
Ctrl+Enter	Run current cell + add new cell
Ctrl+Shift+Enter	Run current cell only (no reactive cascade)

Technology Stack

• Giac/Xcas (asm.js) — Computer algebra engine (default kernel)
• CortexJS Compute Engine — Symbolic computation engine (alternative kernel)
• MathLive — Math input web component
• KaTeX — LaTeX rendering
• JSXGraph — Interactive 2D/3D plots
• Observable Runtime — Reactive dependency graph
• No build step, no bundler — pure browser ES2020+

Related Projects

• Giac/Xcas — Computer algebra system by Bernard Parisse
• KaTeX — Fast LaTeX math rendering for the web
• JSXGraph — Interactive geometry and function plotting in the browser
• Observable Runtime — Reactive dataflow runtime for dependency graphs
• MathLive — Web component for math input editing
• CortexJS Compute Engine — LaTeX/MathJSON parsing and symbolic computation

Credits

• Giac/Xcas by Bernard Parisse
• MathLive by Arno Gourdol
• Virtual keyboard layout inspired by B. Parisse's math2d.html

License

GPL-3.0 — See LICENSE.txt