eternal-math 0.1.0

An open-source software platform for exploring, proving, and generating mathematical concepts

Eternal Math

An open-source software platform designed as a comprehensive, ever-evolving toolkit for exploring, proving, and generating mathematical concepts.

Overview

Eternal Math provides a Python-based framework for mathematical computation, theorem proving, and concept exploration. The platform combines computational tools with formal proof systems to create an integrated environment for mathematical research and education.

Features

Core Mathematical Objects

• Set Theory: Mathematical sets with standard operations (union, intersection, difference)
• Function Theory: Mathematical functions with composition and evaluation
• Number Theory: Prime numbers, GCD/LCM, factorization algorithms

Proof System

• Formal Proofs: Structured proof representation with axioms, theorems, and proof steps
• Theorem Management: Create, verify, and organize mathematical theorems
• Logical Framework: Support for direct proofs, proof by contradiction, and more

Number Theory Toolkit

• Prime Generation: Sieve of Eratosthenes for efficient prime computation
• Sequences: Fibonacci numbers, perfect numbers, Collatz sequences
• Conjectures: Goldbach conjecture verification, twin prime detection
• Advanced Tools: Euler's totient function, Chinese Remainder Theorem

Visualization & Graphics

• Function Plotting: Visualize mathematical functions with customizable ranges
• Sequence Visualization: Plot mathematical sequences with annotations
• Prime Distribution: Graphical analysis of prime number patterns
• Collatz Trajectories: Visualize the famous 3n+1 problem paths
• Comparative Analysis: Side-by-side sequence comparisons

Installation

# Clone the repository
git clone https://github.com/Vooblin/eternal-math.git
cd eternal-math

# Install dependencies
pip install -e .

Quick Start

Interactive CLI

Start the interactive command-line interface:

# After installation
eternal-math

# Or directly with Python
python -m eternal_math.cli

The CLI provides interactive access to all mathematical functions:

eternal-math> primes 30
🔍 Prime numbers up to 30:
   [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
   Found 10 primes

eternal-math> fibonacci 8
🌀 First 8 Fibonacci numbers:
   [0, 1, 1, 2, 3, 5, 8, 13]
   Golden ratio approximation: 1.625000

eternal-math> help
📚 Eternal Math CLI Commands:
[... complete help menu ...]

Python API

from eternal_math import sieve_of_eratosthenes, fibonacci_sequence, twin_primes

# Generate prime numbers up to 50
primes = sieve_of_eratosthenes(50)
print(f"Primes: {primes}")

# Generate Fibonacci sequence
fib = fibonacci_sequence(10)
print(f"Fibonacci: {fib}")

# Find twin prime pairs
twins = twin_primes(30)
print(f"Twin primes: {twins}")

Visualization Features

Create stunning mathematical visualizations:

from eternal_math import MathVisualizer

# Initialize visualizer
viz = MathVisualizer()

# Plot mathematical functions
viz.plot_function("x**2", title="Quadratic Function")
viz.plot_function("sin(x)", x_range=(-6, 6))

# Visualize sequences
from eternal_math import fibonacci_sequence, sieve_of_eratosthenes

fib = fibonacci_sequence(15)
viz.plot_sequence([float(x) for x in fib], title="Fibonacci Numbers")

# Prime distribution analysis
primes = sieve_of_eratosthenes(100)
viz.plot_prime_distribution(primes, 100)

# Interactive CLI visualization commands
# eternal-math> plot sin(x)
# eternal-math> plotseq fibonacci 10
# eternal-math> plotprimes 50
# eternal-math> plotcollatz 3,7,15

## Examples

Run the number theory exploration example:

```bash
python examples/number_theory_exploration.py

Testing

Run the complete test suite:

# Run all tests
pytest tests/

# Run specific test modules
pytest tests/test_core.py
pytest tests/test_number_theory.py
pytest tests/test_proofs.py
pytest tests/test_cli.py

# Or run individual modules (legacy method)
python -m tests.test_core
python -m tests.test_number_theory

Project Structure

eternal-math/
├── eternal_math/          # Main package
│   ├── core.py           # Core mathematical objects
│   ├── proofs.py         # Proof system and logic
│   ├── number_theory.py  # Number theory utilities
│   └── cli.py           # Interactive command-line interface
├── tests/                # Test suite
│   ├── test_cli.py      # CLI functionality tests
│   └── ...              # Other test modules
├── examples/             # Usage examples
└── pyproject.toml       # Project configuration

Contributing

This is an open-source project. Contributions are welcome! Please feel free to submit issues, feature requests, or pull requests.

License

MIT License - see LICENSE file for details.