Binary Relation Analyzer & Property Checker

A Discrete Mathematics Python application and interactive web interface for parsing, testing, and visualizing binary relations on a given set $A$.

🌐 Live Web Application: https://relations-liart.vercel.app/

The application evaluates fundamental mathematical properties, determines whether a relation is an Equivalence Relation or a Partial Order (Poset), generates adjacency relation matrices, and renders SVG directed graph diagrams.

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🌟 Features

• Six Fundamental Relation Properties:

  • Reflexive: $\forall x \in A, (x, x) \in R$
  • Irreflexive: $\forall x \in A, (x, x) \notin R$
  • Symmetric: $\forall x, y \in A, (x, y) \in R \implies (y, x) \in R$
  • Antisymmetric: $\forall x, y \in A, (x, y) \in R \land (y, x) \in R \implies x = y$
  • Asymmetric: $\forall x, y \in A, (x, y) \in R \implies (y, x) \notin R$
  • Transitive: $\forall x, y, z \in A, (x, y) \in R \land (y, z) \in R \implies (x, z) \in R$

• Separate Classification Cards:

  • Equivalence Relation: Evaluates $\text{Reflexive} + \text{Symmetric} + \text{Transitive}$.
  • Partial Order (Poset): Evaluates $\text{Reflexive} + \text{Antisymmetric} + \text{Transitive}$.
  • Includes a requirement checklist with green (✓) and red (✗) indicators for each condition.

• Dynamic Preset Relation Generator:

  • Generates relation pairs directly from the elements currently typed in Set A:
    • Equality ($=$): Pairs where $a = b$.
    • Divides ($\mid$): Pairs where $a \mid b$ ($b \bmod a = 0$).
    • Less than ($<$): Pairs where $a < b$.
    • Greater than ($>$): Pairs where $a > b$.
    • Greater or Equal ($\ge$): Pairs where $a \ge b$.
    • Empty ($\emptyset$): Fills empty relation $R = \emptyset$.

• Visual Representations:

  • Adjacency Relation Matrix: Grid table showing $1$ for pairs in $R$ and $0$ otherwise, with highlighted diagonal self-loop cells.
  • SVG Directed Graph: SVG graph diagram arranging nodes on a circle with directed arrows and curved self-loops.

• User Experience & Themes:

  • Live Preview: Formats $R = {(1,2), (3,1)}$ in real-time as you type flat space-separated pairs.
  • Dark & Light Mode: Theme toggle button with localStorage memory and OS theme detection.
  • Error Validation: Displays inline warnings for odd element counts or elements not present in set A.

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📁 Project Structure

RELATONS/
├── relations.py          # Core mathematical parsing & property checking functions
├── app.py                # Flask web server, matrix builder, & SVG graph generator
├── main.py               # Interactive CLI terminal application
├── test_relations.py     # Unit test suite built with Python's unittest module
├── templates/
│   └── index.html        # Web app HTML template with theme switcher & live preview JS
├── static/
│   └── style.css         # CSS design system supporting Dark & Light themes
├── requirements.txt      # Python dependencies for Vercel deployment
├── vercel.json           # Vercel serverless build configuration
└── README.md             # Project documentation

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🚀 Getting Started

1. Access the Live Web Application

The app is deployed on Vercel: 👉 https://relations-liart.vercel.app/

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2. Run Locally

Start the local Flask development server:

pip install -r requirements.txt
python app.py

Open your browser and navigate to http://127.0.0.1:5000.

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3. Run the Command-Line Interface (CLI)

Run the interactive terminal app:

python main.py

Example terminal interaction:

Enter set A: 1, 2, 3
Enter relation R: 1 1 2 2 3 3 1 2 2 3 1 3

R = {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)}
-----------------------------------------------------------------
ANALYSIS RESULTS:
- Reflexive:     YES
- Irreflexive:   NO
- Symmetric:     NO
- Antisymmetric: YES
- Asymmetric:    NO
- Transitive:    YES

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4. Run Automated Unit Tests

Execute the unit test suite built with Python's built-in unittest module:

python test_relations.py

Tests cover:

• Equality Relation ($=$)
• Strict Order Relation ($<$)
• Symmetric Non-Transitive Relation
• Divides Relation ($\mid$)
• Empty Relation on Non-Empty Set
• Empty Set ($A = \emptyset$)
• Input errors (odd element count, element not in A, duplicate pairs)

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🛠️ Built With

• Python: Core logic & algorithms (no external third-party math libraries)
• Flask: Lightweight Web Server
• Vercel: Serverless Cloud Hosting
• HTML5 & Vanilla CSS3: Responsive UI, CSS Variables, Glassmorphism, Dark/Light Mode
• SVG: Pure vector graph rendering
• unittest: Native Python test suite