Matrix Solver

A web application for solving systems of linear equations using Cramer's rule. The solution is computed asynchronously via Celery workers, allowing users to track progress in real time.

Features

• User registration and JWT-based authentication
• Submit matrix systems (up to 12×12) for solving
• Asynchronous task processing with Celery + Redis
• Real-time progress tracking per task
• Task history with results and execution time
• Input via keyboard or .txt file upload
• Cancel in-progress tasks
• Scalable backend with multiple FastAPI replicas behind Nginx

Tech Stack

Layer	Technology
Frontend
Backend
Task Queue
Message Broker / Result Backend
Database
Reverse Proxy
Containerization

Project Structure

.
├── backend/
│   └── app/
│       ├── main.py          # FastAPI app entry point
│       ├── auth.py          # Registration, login, JWT
│       ├── tasks.py         # Celery task (Cramer's rule solver)
│       ├── tasks_routes.py  # REST endpoints for tasks
│       ├── models.py        # SQLAlchemy ORM models
│       ├── schemas.py       # Pydantic schemas
│       ├── crud.py          # DB helper functions
│       ├── db.py            # DB engine and session
│       └── celery_app.py    # Celery configuration
├── frontend/
│   ├── index.html
│   ├── style.css
│   └── app.js
├── nginx/
│   └── default.conf
├── create_tables.py         # DB initializer (runs on startup)
├── test_task.py             # CLI tool for testing solver
├── docker-compose.yml
├── Dockerfile
└── requirements.txt

Getting Started

Prerequisites

• Docker and Docker Compose

Configuration

Create a .env file in the project root:

DATABASE_URL=postgresql://postgres:yourpassword@db:5432/matrix_solver
POSTGRES_USER=postgres
POSTGRES_PASSWORD=yourpassword
POSTGRES_DB=matrix_solver
SECRET_KEY=your-secret-key-here
CELERY_BROKER_URL=redis://redis:6379/0
CELERY_BACKEND_URL=redis://redis:6379/1

Running the Application

# Build and start all services
docker compose up --build

# Initialize the database tables (first run)
docker compose run --rm backend python create_tables.py

The app will be available at http://localhost.

API documentation (Swagger UI) is available at http://localhost/docs.

Stopping

docker compose down

API Endpoints

Method	Path	Description
POST	/auth/register	Register a new user
POST	/auth/login	Log in and receive JWT
GET	/auth/me	Get current user info
POST	/tasks	Submit a new matrix task
GET	/tasks	List all tasks for the current user
GET	/tasks/{id}/status	Poll task status and progress
DELETE	/tasks/{id}	Cancel an in-progress task

Input Format

Keyboard Input

Enter the matrix row by row (space-separated values), then the right-hand side vector (space-separated):

2 1 -1
-3 -1 2
-2 1 2
---
8 -11 -3

File Upload (.txt)

The file must contain the matrix, a line with ---, and then the vector:

3 7 12
9 1 19
5 3 17
---
21 23 36

Limitations

• Maximum matrix size: 12×12 (due to the exponential complexity of Cramer's rule)
• Maximum concurrent active tasks per user: 10

CLI Testing Tool

You can test the Celery solver directly without the web UI:

python test_task.py

Follow the prompts to enter data from the keyboard or a .txt file. Requires a running Redis instance and Celery worker.

License

MIT License — see LICENSE for details.