docs: overhaul README with supported expressions table and quickstart

Author: smakde

README.md

@@ -1,59 +1,74 @@
-## Edge Vision Mathifyer
-## Edge Vision + Math Engine (Quickstart Bundle)
+# Edge Vision + Math Engine
 
-This bundle contains two self-contained projects:
+[![CI](https://github.com/smakde/Edge-Vision-Mathifyer/actions/workflows/ci.yml/badge.svg)](https://github.com/smakde/Edge-Vision-Mathifyer/actions/workflows/ci.yml)
+[![Python 3.12](https://img.shields.io/badge/python-3.12-blue.svg)](https://www.python.org/downloads/)
+[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](LICENSE)
 
-1. **edge-vision/** — Real-time, privacy-preserving computer vision demo on local hardware with OpenCV.
-   - Streamlit UI that plays a sample video, measures FPS, and (optionally) uses a TFLite model if you add one.
-2. **math-engine/** — SymPy + NumPy solver for calculus/combinatorics/probability, with a Streamlit UI and Monte Carlo verification.
+Two self-contained projects in one repo:
 
-> Tip: Use two terminals (or tabs) to run both UIs.
+- **Math Engine** — symbolic solver with step-by-step explanations and Monte Carlo verification (SymPy + NumPy + SciPy)
+- **Edge Vision** — multi-algorithm computer vision demo running 4 CV pipelines side-by-side on local video (OpenCV)
 
 ---
 
-## 0) Create Python env (recommended)
+## Math Engine
 
+Symbolic solver supporting integrals, derivatives, limits, combinatorics, and probability — with LaTeX output and Monte Carlo cross-checks.
+
+### Quickstart
 ```bash
-python3 -m venv .venv && source .venv/bin/activate
-# Windows: .venv\Scripts\activate
+cd math-engine
+pip install -r requirements.txt
+streamlit run streamlit_app.py
 ```
 
+### Supported expressions
+
+| Type | Example |
+|------|---------|
+| Indefinite integral | `integral(sin(x)^2, x)` |
+| Definite integral | `integral(x^2, x, 0, 1)` |
+| Derivative | `diff(exp(x)*log(x), x)` |
+| nth-order derivative | `diff(x^5, x, 3)` |
+| Limit | `limit(sin(x)/x, x, 0)` |
+| Limit at infinity | `limit((1 + 1/x)**x, x, oo)` |
+| Combinations | `C(52, 5)` |
+| Permutations | `P(5, 2)` |
+| Factorial | `factorial(10)` |
+| Dice probability | `P(sum_{i=1..3} die() >= 10)` |
+| Binomial CDF | `P(binomial(10, 0.3) >= 4)` |
+| Normal tail | `P(normal(0, 1) > 1.96)` |
+
+All probability results include exact + Monte Carlo verification with 95% CI.
+
 ---
 
-## 1) Edge Vision — Run
+## Edge Vision
+
+Runs 4 CV algorithms simultaneously on a local video, with per-algorithm controls and processing metrics.
 
+### Algorithms
+- **Canny edges** — tunable low/high thresholds, edge density metric
+- **Sobel gradient** — magnitude map, mean gradient metric
+- **Contour detection** — Otsu threshold + contour filtering by area
+- **CLAHE equalisation** — adaptive histogram equalisation, contrast before/after
+
+### Quickstart
 ```bash
 cd edge-vision
 pip install -r requirements.txt
-# Run Streamlit dashboard (plays sample video and shows FPS)
 streamlit run apps/streamlit_app.py
 ```
-- Add your model at `edge-vision/models/model.tflite` (optional). If present, the app will try to run TFLite inference.
-- Otherwise, it will fall back to a simple OpenCV edge detector as a placeholder.
 
-CLI benchmark (optional):
-```bash
-python tools/benchmark.py --video data/sample.mp4
-```
+Add your own video at `edge-vision/data/sample.mp4` or use the included sample.
 
 ---
 
-## 2) Math Engine — Run
+## Tests
 
 ```bash
-cd math-engine
-pip install -r requirements.txt
-streamlit run streamlit_app.py
+pip install pytest pytest-cov scipy opencv-python-headless sympy numpy
+PYTHONPATH=math-engine:edge-vision pytest math-engine/tests/ edge-vision/tests/ -v
 ```
 
-Examples in the UI:
-- Calculus: `integral(sin(x)^2, x)`
-- Probability: `P(sum_{i=1..3} die() >= 10)`
-- Combinatorics: `C(10,3)`
-
----
-
-## Notes
-
-- `tflite-runtime` is platform-specific; we do **not** auto-install it. If you need it, install for your device (Raspberry Pi/ARM, etc.).
-- Everything runs locally and offline. Replace `data/sample.mp4` with your own footage for edge-vision.
+38 tests — 21 engine (integrals, derivatives, limits, combinatorics, probability) + 17 CV pipeline (shape, dtype, edge cases).