# 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
```bash
# 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:
```bash
# 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
```python
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:
```python
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:
```bash
# 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.
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The platform combines computational tools with formal proof systems to create an integrated environment for mathematical research and education.\n\n## Features\n\n### Core Mathematical Objects\n- **Set Theory**: Mathematical sets with standard operations (union, intersection, difference)\n- **Function Theory**: Mathematical functions with composition and evaluation\n- **Number Theory**: Prime numbers, GCD/LCM, factorization algorithms\n\n### Proof System\n- **Formal Proofs**: Structured proof representation with axioms, theorems, and proof steps\n- **Theorem Management**: Create, verify, and organize mathematical theorems\n- **Logical Framework**: Support for direct proofs, proof by contradiction, and more\n\n### Number Theory Toolkit\n- **Prime Generation**: Sieve of Eratosthenes for efficient prime computation\n- **Sequences**: Fibonacci numbers, perfect numbers, Collatz sequences\n- **Conjectures**: Goldbach conjecture verification, twin prime detection\n- **Advanced Tools**: Euler's totient function, Chinese Remainder Theorem\n\n### Visualization & Graphics\n- **Function Plotting**: Visualize mathematical functions with customizable ranges\n- **Sequence Visualization**: Plot mathematical sequences with annotations\n- **Prime Distribution**: Graphical analysis of prime number patterns\n- **Collatz Trajectories**: Visualize the famous 3n+1 problem paths\n- **Comparative Analysis**: Side-by-side sequence comparisons\n\n## Installation\n\n```bash\n# Clone the repository\ngit clone https://github.com/Vooblin/eternal-math.git\ncd eternal-math\n\n# Install dependencies\npip install -e .\n```\n\n## Quick Start\n\n### Interactive CLI\n\nStart the interactive command-line interface:\n\n```bash\n# After installation\neternal-math\n\n# Or directly with Python\npython -m eternal_math.cli\n```\n\nThe CLI provides interactive access to all mathematical functions:\n\n```\neternal-math> primes 30\n\ud83d\udd0d Prime numbers up to 30:\n [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]\n Found 10 primes\n\neternal-math> fibonacci 8\n\ud83c\udf00 First 8 Fibonacci numbers:\n [0, 1, 1, 2, 3, 5, 8, 13]\n Golden ratio approximation: 1.625000\n\neternal-math> help\n\ud83d\udcda Eternal Math CLI Commands:\n[... complete help menu ...]\n```\n\n### Python API\n\n```python\nfrom eternal_math import sieve_of_eratosthenes, fibonacci_sequence, twin_primes\n\n# Generate prime numbers up to 50\nprimes = sieve_of_eratosthenes(50)\nprint(f\"Primes: {primes}\")\n\n# Generate Fibonacci sequence\nfib = fibonacci_sequence(10)\nprint(f\"Fibonacci: {fib}\")\n\n# Find twin prime pairs\ntwins = twin_primes(30)\nprint(f\"Twin primes: {twins}\")\n```\n\n### Visualization Features\n\nCreate stunning mathematical visualizations:\n\n```python\nfrom eternal_math import MathVisualizer\n\n# Initialize visualizer\nviz = MathVisualizer()\n\n# Plot mathematical functions\nviz.plot_function(\"x**2\", title=\"Quadratic Function\")\nviz.plot_function(\"sin(x)\", x_range=(-6, 6))\n\n# Visualize sequences\nfrom eternal_math import fibonacci_sequence, sieve_of_eratosthenes\n\nfib = fibonacci_sequence(15)\nviz.plot_sequence([float(x) for x in fib], title=\"Fibonacci Numbers\")\n\n# Prime distribution analysis\nprimes = sieve_of_eratosthenes(100)\nviz.plot_prime_distribution(primes, 100)\n\n# Interactive CLI visualization commands\n# eternal-math> plot sin(x)\n# eternal-math> plotseq fibonacci 10\n# eternal-math> plotprimes 50\n# eternal-math> plotcollatz 3,7,15\n```\n```\n\n## Examples\n\nRun the number theory exploration example:\n\n```bash\npython examples/number_theory_exploration.py\n```\n\n## Testing\n\nRun the complete test suite:\n\n```bash\n# Run all tests\npytest tests/\n\n# Run specific test modules\npytest tests/test_core.py\npytest tests/test_number_theory.py\npytest tests/test_proofs.py\npytest tests/test_cli.py\n\n# Or run individual modules (legacy method)\npython -m tests.test_core\npython -m tests.test_number_theory\n```\n\n## Project Structure\n\n```\neternal-math/\n\u251c\u2500\u2500 eternal_math/ # Main package\n\u2502 \u251c\u2500\u2500 core.py # Core mathematical objects\n\u2502 \u251c\u2500\u2500 proofs.py # Proof system and logic\n\u2502 \u251c\u2500\u2500 number_theory.py # Number theory utilities\n\u2502 \u2514\u2500\u2500 cli.py # Interactive command-line interface\n\u251c\u2500\u2500 tests/ # Test suite\n\u2502 \u251c\u2500\u2500 test_cli.py # CLI functionality tests\n\u2502 \u2514\u2500\u2500 ... # Other test modules\n\u251c\u2500\u2500 examples/ # Usage examples\n\u2514\u2500\u2500 pyproject.toml # Project configuration\n```\n\n## Contributing\n\nThis is an open-source project. 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