Discrete Structures

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🚀 Overview

Discrete Structures MCP Server is a comprehensive Model Context Protocol server that brings 21 powerful mathematical tools to AI assistants like Claude Desktop, Cline, and Zed. Perfect for students, educators, and developers working with discrete mathematics, data structures, algorithms, and cryptography.

Why Choose This Server?

• 🎯 21 Production-Ready Tools across 4 categories
• 📚 Educational Focus with step-by-step visualizations
• 🔒 Enterprise Cryptography (RSA, AES, Caesar, Vigenere)
• 📊 Algorithm Visualizations for sorting and graph algorithms
• 🧮 Boolean Logic with CNF/DNF conversion
• 🔢 Number Theory including prime factorization and modular arithmetic
• ⚡ Fast Installation via uvx discrete-structures-mcp
• 🌐 MCP Registry Listed for easy discovery

✨ Features

🧮 Logic Tools (5 tools) evaluate_boolean - Evaluate boolean expressions with truth tables generate_truth_table - Complete truth table generation simplify_boolean - Boolean algebra simplification convert_to_cnf - Conjunctive Normal Form conversion convert_to_dnf - Disjunctive Normal Form conversion 🔢 Number Theory Tools (5 tools) is_prime - Primality testing with explanations prime_factors - Complete prime factorization gcd_lcm - Greatest Common Divisor & Least Common Multiple modular_arithmetic - Modular operations (add, multiply, power) euler_totient - Euler's φ function calculation

📊 Algorithm Visualizers (6 tools) visualize_bubble_sort - O(n²) sorting with comparisons visualize_quick_sort - O(n log n) divide-and-conquer visualize_merge_sort - Stable merge sort visualization visualize_binary_search - O(log n) search algorithm visualize_dijkstra - Shortest path in weighted graphs visualize_bfs_dfs - Graph traversal algorithms 🔐 Cryptography Tools (5 tools) caesar_cipher - Classical shift cipher (educational) vigenere_cipher - Polyalphabetic substitution rsa_encrypt_decrypt - RSA public-key cryptography aes_encrypt_decrypt - AES-256 symmetric encryption generate_rsa_keys - Secure RSA key pair generation

📦 Installation

⚡ Quick Install (Recommended)

# Install and run directly with uvx
uvx discrete-structures-mcp

📥 Install with pip

# Install globally
pip install discrete-structures-mcp

# Run the server
discrete-structures-mcp

🛠️ Development Installation

# Clone the repository
git clone https://github.com/ZohaibCodez/discrete-structures-ai-platform.git
cd discrete-structures-ai-platform/mcp-server

# Install with uv
uv sync

# Run locally
uv run discrete-structures-mcp

🎯 Quick Start

Usage with Claude Desktop

Add to your claude_desktop_config.json:

{
  "mcpServers": {
    "discrete-structures": {
      "command": "uvx",
      "args": ["discrete-structures-mcp"]
    }
  }
}

Usage with Other MCP Clients

Compatible with any MCP client:

• Cline - VS Code extension
• Zed - Modern code editor
• Continue - AI code assistant
• Custom MCP clients via Python SDK

💻 Example Tool Calls

from mcp.client.session import ClientSession
from mcp.client.stdio import StdioServerParameters, stdio_client

server_params = StdioServerParameters(
    command="uvx",
    args=["discrete-structures-mcp"]
)

async with stdio_client(server_params) as (read, write):
    async with ClientSession(read, write) as session:
        await session.initialize()
        
        # List available tools
        tools = await session.list_tools()
        print([tool.name for tool in tools.tools])
        
        # Call a tool
        result = await session.call_tool("gcd_lcm", {"numbers": "48,18"})
        print(result)

💻 Example Tool Calls

🔢 Number Theory Examples

Calculate GCD and LCM

# Find greatest common divisor and least common multiple
result = await session.call_tool("gcd_lcm", {
    "numbers": "48,18,24"
})
# Output: {"gcd": 6, "lcm": 144, "explanation": "..."}

Prime Factorization

result = await session.call_tool("prime_factors", {
    "number": "84"
})
# Output: {"factors": [2, 2, 3, 7], "factorization": "2² × 3 × 7"}

Modular Arithmetic

result = await session.call_tool("modular_arithmetic", {
    "operation": "power",
    "base": "3",
    "exponent": "5",
    "modulus": "7"
})
# Output: {"result": 5, "explanation": "3^5 mod 7 = 5"}

🧮 Boolean Logic Examples

Generate Truth Table

result = await session.call_tool("generate_truth_table", {
    "expression": "(A & B) | (~A & C)"
})
# Returns: Complete truth table with all input combinations

Simplify Boolean Expression

result = await session.call_tool("simplify_boolean", {
    "expression": "(A & B) | (A & ~B)"
})
# Output: {"simplified": "A", "steps": ["..."]}

Convert to CNF

result = await session.call_tool("convert_to_cnf", {
    "expression": "(A | B) & (C | D)"
})
# Output: Expression in Conjunctive Normal Form

📊 Algorithm Visualization Examples

Visualize Bubble Sort

result = await session.call_tool("visualize_bubble_sort", {
    "array": "64,34,25,12,22,11,90"
})
# Returns: Step-by-step sorting with comparisons and swaps

Binary Search

result = await session.call_tool("visualize_binary_search", {
    "array": "1,3,5,7,9,11,13,15",
    "target": "7"
})
# Output: Search path with index calculations

Dijkstra's Algorithm

result = await session.call_tool("visualize_dijkstra", {
    "graph": "A-B:4,A-C:2,B-C:1,B-D:5,C-D:8",
    "start": "A",
    "end": "D"
})
# Returns: Shortest path with distances

🔐 Cryptography Examples

RSA Encryption

# Generate keys
keys = await session.call_tool("generate_rsa_keys", {
    "key_size": "2048"
})

# Encrypt message
encrypted = await session.call_tool("rsa_encrypt_decrypt", {
    "action": "encrypt",
    "message": "Hello World",
    "public_key": keys["public_key"]
})

# Decrypt message
decrypted = await session.call_tool("rsa_encrypt_decrypt", {
    "action": "decrypt",
    "ciphertext": encrypted["ciphertext"],
    "private_key": keys["private_key"]
})

AES Encryption

result = await session.call_tool("aes_encrypt_decrypt", {
    "action": "encrypt",
    "text": "Sensitive Data",
    "key": "my-secret-key-32-characters-long"
})
# Output: {"ciphertext": "...", "iv": "...", "tag": "..."}

Caesar Cipher

result = await session.call_tool("caesar_cipher", {
    "action": "encrypt",
    "text": "HELLO",
    "shift": "3"
})
# Output: {"result": "KHOOR", "explanation": "Each letter shifted by 3"}

🎓 Use Cases

• Computer Science Education - Teach algorithms and data structures
• Cryptography Learning - Understand encryption methods
• Mathematics Research - Number theory and discrete math
• Algorithm Analysis - Visualize complexity and performance
• Code Interviews - Practice common algorithmic problems
• Academic Projects - Implement mathematical concepts

🏗️ Technical Stack

• Language: Python 3.11+
• Framework: Model Context Protocol (MCP)
• Math Libraries: SymPy, NumPy
• Crypto: Python Cryptography library
• Graphs: NetworkX
• Build: UV package manager

📊 Performance

• Startup Time: < 2 seconds
• Response Time: < 100ms for most operations
• Memory: < 50MB baseline
• Concurrency: Async/await support

🔒 Security Note

Educational Purpose: Caesar and Vigenere ciphers are for learning only. Use AES or RSA for real-world encryption.

🤝 Contributing

We welcome contributions! Here's how to get started:

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Commit changes (git commit -m 'Add amazing feature')
4. Push to branch (git push origin feature/amazing-feature)
5. Open a Pull Request

See CONTRIBUTING.md for detailed guidelines.

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🔗 Links & Resources

Official Links

• 🏠 Homepage: GitHub Repository
• 📦 PyPI Package: discrete-structures-mcp
• 🌐 MCP Registry: Official Listing
• 📝 Documentation: README
• 🐛 Issue Tracker: Report Bugs

Community

• 💬 Discussions: GitHub Discussions
• 📢 Announcements: Watch repository for updates
• 🤝 Contributing: See contribution guide

MCP Resources

• 📖 MCP Documentation: modelcontextprotocol.io
• 🛠️ MCP SDK: Python SDK
• 🌟 MCP Servers: Community Servers

📈 Project Stats

🙏 Acknowledgments

• Model Context Protocol team at Anthropic
• SymPy and NumPy communities
• Python Cryptography developers
• NetworkX graph library maintainers
• All contributors and users

📞 Support

• 📧 Email: Open an issue for support
• 💬 Discussions: Use GitHub Discussions
• 🐛 Bugs: Report via Issues
• 💡 Features: Request via Issues with enhancement label

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