MathematicalTransforms

A Python library that facilitates symbolic and numerical mathematical transforms, designed for computational tasks in engineering, science, and education. The library provides a modular framework for transforms such as Fourier, Laplace, Hankel, Wavelet, Radon, and Z transforms, ensuring ease of extension and robust test coverage.

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Features

Transforms

• Fourier Transform: Symbolic and numerical computation for signal analysis.
• Laplace Transform: Symbolic and numerical computation for systems analysis.
• Hankel Transform: A mathematical tool used in various fields including optics.
• Wavelet Transform: Decomposition of signals for multi-resolution analysis.
• Radon Transform: Utilized in image reconstruction.
• Z Transform: Analysis and processing of discrete signals.

Utilities

• Reusable symbolic computation utilities powered by SymPy.
• Numerical data handling using NumPy and Scipy.
• Constant definitions and general-purpose functions for seamless integration.

Testing Framework

• Comprehensive tests for all transforms.
• Modular test classes for easy integration of new functionality.

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Installation

Prerequisites

• Python 3.8 or newer
• pip for package management

Installation Steps

1. Clone the repository:

   git clone https://github.com/yourusername/MathematicalTransforms.git
   cd MathematicalTransforms

2. Install dependencies:

   pip install -r requirements.txt

Dependencies

The requirements.txt includes:

• sympy: Symbolic mathematics library
• numpy: Numerical computing library
• z3-solver: Symbolic solver
• mpmath: Precision mathematics
• matplotlib: Data visualization
• scikit-image: Image processing utilities

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Usage

Example: Fourier Transform

from sympy import symbols, sin
from transforms.fourier import FourierTransform

# Define a symbolic function
t = symbols('t')
function = sin(t)

# Initialize Fourier Transform
ft = FourierTransform(
   function, 
   t=t
)

# Compute symbolic transform
symbolic_transform = ft.transformed_function
print("Symbolic Fourier Transform:", symbolic_transform)

# Numerical data transform
data = [1, 2, 3, 4]
numerical_transform = ft.transform_data(data)
print("Numerical Fourier Transform:", numerical_transform)

Example: Laplace Transform

from sympy import symbols, exp
from transforms.laplace import LaplaceTransform

# Define a symbolic function
s = symbols('s')
function = exp(-s)

# Initialize Laplace Transform
lt = LaplaceTransform(
   function=function,
   s=s
)

# Compute symbolic transform
symbolic_transform = lt.transformed_function
print("Symbolic Laplace Transform:", symbolic_transform)

Testing

Run all tests to verify functionality:

python -m testing.run_all_tests

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Project Structure

MathematicalTransforms/
├── transforms/
│   ├── fourier.py                # Fourier Transform implementation
│   ├── laplace.py                # Laplace Transform implementation
│   ├── wavelet.py                # Wavelet Transform implementation
│   ├── base_transform/           # Base classes for extensibility
├── utils/
│   ├── util.py                   # General utility functions
│   ├── sympy_math.py             # Symbolic computation utilities
│   ├── consts.py                 # Predefined constants
├── testing/
│   ├── tests/                    # Unit tests for transforms
│   ├── run_all_tests.py          # Main test runner
├── requirements.txt              # Project dependencies
├── README.md                     # Documentation

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Extensibility

Adding a new transform is simple:

1. Create a new file in the transforms folder.
2. Define a new class inheriting from BaseTransform.
3. Implement the following methods:
   • _compute_transform_function
   • _compute_inverse_transform_function
   • (Optional) Custom methods for numerical transforms.

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Contribution Guidelines

We welcome contributions to improve functionality, fix bugs, or add features!

1. Fork the repository.
2. Create a new branch:

   git checkout -b feature-name

3. Commit your changes:

   git commit -m "Add feature-name"

4. Push to your fork:

   git push origin feature-name

5. Submit a pull request.

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License

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

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Acknowledgments

• Built using SymPy for symbolic mathematics and NumPy for numerical processing.
• Inspired by mathematical transformations in engineering and physics.
• This Readme is partly generated by AI (ChatGpt) for formatting reasons.