📐 Symbolic Derivative Tool

A Python-based symbolic differentiation tool using Python's built-in AST. It computes symbolic derivatives of mathematical expressions and supports optimization with constraints using the Lagrange multiplier method, entropy calculations, and Jackson q-derivatives.

• ✅ Pure Symbolic Differentiation
• ✅ Support for basic arithmetic operations (+, -, *, /, **)
• ✅ Trigonometric functions (sin, cos, etc.)
• ✅ Exponential and logarithmic functions
• ✅ Chain rule, product rule, quotient rule, power rule
• ✅ Pretty-printed output with superscripts
• ✅ Lagrange Multiplier Method for constrained optimization
• ✅ Shannon, Renyi, and Tsallis Entropy calculations
• ✅ Jackson q-Derivative for quantum calculus

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🚀 Getting Started

🔧 Installation

1. Clone the repository:

git clone https://github.com/your-username/Symbolic-Derivative-Tool.git
cd Symbolic-Derivative-Tool

2. Install Dependencies:

pip install -r requirements.txt

3. 🚀 Usage

python main.py

You'll be prompted to choose between symbolic differentiation, Lagrange multiplier method, and advanced mathematical computations.

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🧪 Usage Examples

Example 1: Simple polynomial derivative

Choose an operation:
1. Symbolic Differentiation
2. Lagrange Multiplier Method
3. Advanced Mathematical Computations
> 1

Choose differentiation type:
1. Standard derivative
2. Jackson q-derivative
> 1

Function: f(x) = x**2 + 3*x
Variable to differentiate with respect to: x
📘 Symbolic derivative: 2x + 3

Example 2: Jackson q-Derivative

Choose differentiation type:
1. Standard derivative
2. Jackson q-derivative
> 2

Function: f(x) = x**2
q parameter: 2
Variable to differentiate with respect to: x
📘 Jackson q-derivative (q=2): 3x

Example 3: Lagrange Multiplier Method

Choose an operation:
1. Symbolic Differentiation
2. Lagrange Multiplier Method
3. Advanced Mathematical Computations
> 2

Objective function f: x**2 + y**2
Constraint function g: x + y
📘 Variables: x, y

📘 Lagrange Equations:
∇f = λ ∇g
∂f/∂x = λ ∂g/∂x
2x = λ 1
∂f/∂y = λ ∂g/∂y
2y = λ 1

📘 Constraint:
g(x,y,...) = c
x + y = c

Example 4: Shannon Entropy

Choose an operation:
1. Symbolic Differentiation
2. Lagrange Multiplier Method
3. Advanced Mathematical Computations
> 3

Choose computation:
1. Shannon Entropy
2. Renyi Entropy
3. Tsallis Entropy
> 1

Probabilities: 0.5, 0.3, 0.2
📘 Shannon Entropy: 1.4855 bits

Function: sin(x)
Variable to differentiate with respect to: x
📘 Symbolic derivative: cosx

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🧪 Testing

Run the unit tests to validate the functionality:

python -m pytest tests/ -v

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📁 Project Structure

Symbolic-Derivative-Tool/
├── main.py                 # Entry point
├── cli.py                  # Command-line interface with menu options
├── differentiator.py       # Core differentiation logic, gradient computation, and Jackson derivatives
├── entropy.py              # Entropy calculation functions (Shannon, Renyi, Tsallis)
├── parser.py               # Function parsing utilities
├── tests/                  # Unit tests
│   ├── test_parser.py
│   ├── test_differentiator.py
│   ├── test_entropy.py
│   └── test_cli.py
├── README.md
├── requirements.txt
└── LICENCE

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🧠 Author

Built with ❤️ and symbolic brainpower by Hincal Topcuoglu.

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📄 License

This project is licensed under the MIT License.