A comprehensive, efficient calculus calculator built with Python that handles derivatives, integrals, and complex mathematical operations with high precision and professional code quality.
Features • Installation • Usage • Examples • Documentation • Contributing
This Calculus Calculator is a powerful Python-based tool designed for students, educators, and mathematics enthusiasts. It provides a command-line interface for performing complex calculus operations, basic mathematics, and symbolic computations with ease and precision.
- Educational Focus: Perfect for learning and teaching calculus concepts
- Professional Code Quality: Well-structured, documented, and tested codebase
- Extensible Design: Easy to add new mathematical operations and formulas
- User-Friendly: Both interactive and command-line modes for different use cases
- No External Dependencies Required: Works with Python's built-in libraries (optional dependencies for advanced features)
| Operation | Description | Examples |
|---|---|---|
| Derivatives | Symbolic differentiation with multiple rules | Power rule, product rule, quotient rule, chain rule |
| Integrals | Indefinite and definite integration | Polynomial, trigonometric, exponential functions |
| Basic Math | Comprehensive arithmetic operations | Trigonometric, logarithmic, exponential functions |
| Formula Database | Extensive collection of mathematical formulas | Pre-loaded derivatives, integrals, and constants |
- ✅ Multiple Input Formats: Support for various mathematical notations (d/dx, ∫, derivative(), integral())
- ✅ High Precision: Decimal precision up to 28 digits for accurate calculations
- ✅ Formula Management: Organized database with easy formula lookup and extension
- ✅ Interactive Mode: User-friendly CLI with help, examples, and command history
- ✅ Batch Processing: Command-line argument support for automation and scripting
- ✅ Error Handling: Comprehensive validation with clear error messages
- Modular Design: Clean separation of concerns with dedicated calculation engines
- Extensible Framework: Plugin-style architecture for adding new operations
- Comprehensive Testing: Unit tests ensuring reliability and correctness
- Type Hints: Full type annotations for better code maintainability
- Documentation: Detailed inline documentation and usage examples
Calculus-Calculator/
│
├── 📄 calculator.py # Main application entry point and CLI
├── 📄 switch.py # Operation type detection and routing
├── 📄 parser.py # Expression parsing and tokenization
├── 📄 evaluator.py # Expression evaluation engine
├── 📄 utils.py # Mathematical utilities and helper functions
│
├── 📄 requirements.txt # Python dependencies
├── 📄 setup.py # Package installation configuration
├── 📄 README.md # Project documentation (this file)
├── 📄 Flowchart.drawio # Architecture diagram (editable)
├── 📄 Flowchart.png # Architecture diagram (image)
│
├── 📂 modules/ # Core calculation engines
│ ├── __init__.py
│ ├── derivative_engine.py # Symbolic differentiation engine
│ ├── integral_engine.py # Integration calculation engine
│ ├── basic_math.py # Elementary mathematics operations
│ └── formula_loader.py # Formula database management
│
├── 📂 data/ # Mathematical formulas database
│ ├── derivatives.txt # Derivative rules and formulas
│ ├── integrals.txt # Integration rules and formulas
│ ├── formulas.txt # General mathematical formulas
│ └── constants.txt # Mathematical constants (π, e, etc.)
│
└── 📂 tests/ # Unit tests and test utilities
├── __init__.py
├── test_calculator.py # Main calculator tests
└── test_utils.py # Utility function tests
- Python 3.8+ (Python 3.12 supported)
- pip (Python package manager)
- git (for cloning the repository)
# Clone the repository
git clone https://github.com/divyanshakya966/Calculus-Calculator.git
# Navigate to the project directory
cd Calculus-Calculator
# Install dependencies (optional - for advanced features)
pip install -r requirements.txt
# Run the calculator
python calculator.py# Clone and install in one go
git clone https://github.com/divyanshakya966/Calculus-Calculator.git
cd Calculus-Calculator
pip install -r requirements.txt
python calculator.py# Clone the repository
git clone https://github.com/divyanshakya966/Calculus-Calculator.git
cd Calculus-Calculator
# Install in editable mode
pip install -e .
# Run tests to verify installation
python -m pytest tests/The calculator works with Python's built-in libraries. If you don't need advanced features:
# Clone the repository
git clone https://github.com/divyanshakya966/Calculus-Calculator.git
cd Calculus-Calculator
# Run directly without installing dependencies
python calculator.py# Test basic functionality
python calculator.py "2 + 2"
# Expected output:
# ✅ Result:
# Expression: 2 + 2
# Type: basic_math
# Answer: 4Launch the calculator in interactive mode for step-by-step calculations:
python calculator.pyInteractive Session Example:
============================================================
🧮 ADVANCED CALCULUS CALCULATOR
============================================================
Supported Operations:
• Derivatives: d/dx[expression], derivative(expression)
• Integrals: ∫[expression]dx, integral(expression)
• Basic Math: +, -, *, /, ^, sqrt(), ln(), sin(), cos(), etc.
• Type 'help' for more commands, 'quit' to exit
------------------------------------------------------------
📝 Enter expression: d/dx[x^2 + 3x + 1]
✅ Result:
Expression: d/dx[x^2 + 3x + 1]
Type: derivative
Answer: 2x + 3
📝 Enter expression: quit
👋 Thank you for using Calculus Calculator!
Execute single calculations directly from the command line:
# Derivatives
python calculator.py "d/dx[x^3 + 2x^2 + x + 1]"
# Integrals
python calculator.py "integral(sin(x))"
# Basic Math
python calculator.py "sqrt(144) + 2^3"
# Complex expressions
python calculator.py "derivative(sin(x)*cos(x))"Use in scripts or batch files:
# Create a script to process multiple calculations
cat > calculations.sh << 'EOF'
#!/bin/bash
python calculator.py "d/dx[x^2]"
python calculator.py "integral(x)"
python calculator.py "sin(pi/2)"
EOF
chmod +x calculations.sh
./calculations.sh# Basic polynomial derivatives
Input: d/dx[x^3 + 2x^2 + x + 1]
Output: 3x^2 + 4x + 1
Input: derivative(5x^4 + 3x^2)
Output: 20x^3 + 6x
# Trigonometric derivatives
Input: d/dx[sin(x)]
Output: cos(x)
Input: derivative(sin(x)*cos(x))
Output: cos²(x) - sin²(x)
Input: diff(tan(x))
Output: sec²(x)
# Logarithmic and exponential derivatives
Input: d/dx[ln(x^2)]
Output: 2/x
Input: derivative(e^(x^2))
Output: 2x*e^(x^2)
Input: d/dx[log(x)]
Output: 1/(x*ln(10))# Basic polynomial integrals
Input: integral(x^2)
Output: x³/3 + C
Input: ∫[2x + 5]dx
Output: x² + 5x + C
Input: integral(x^4 + 3x^2)
Output: x⁵/5 + x³ + C
# Trigonometric integrals
Input: integral(sin(x))
Output: -cos(x) + C
Input: ∫[cos(x)]dx
Output: sin(x) + C
# Exponential and logarithmic integrals
Input: integral(e^x)
Output: e^x + C
Input: ∫[1/x]dx
Output: ln|x| + C# Arithmetic operations
Input: 2 + 3 * 4
Output: 14
Input: (5 + 3) * 2
Output: 16
# Power and roots
Input: 2^8
Output: 256
Input: sqrt(144)
Output: 12.0
Input: sqrt(2) * sqrt(8)
Output: 4.0
# Trigonometric functions
Input: sin(pi/2)
Output: 1.0
Input: cos(0)
Output: 1.0
Input: tan(pi/4)
Output: 1.0
# Logarithmic functions
Input: ln(e^2)
Output: 2.0
Input: log(1000)
Output: 3.0
# Complex expressions
Input: sqrt(16) + 2^3 + ln(e)
Output: 13.0
Input: sin(pi) + cos(pi/2)
Output: 0.0The interactive mode provides several helpful commands:
| Command | Description | Example Usage |
|---|---|---|
help |
Display comprehensive help information | Type help and press Enter |
examples |
Show example calculations with results | Type examples and press Enter |
quit |
Exit the calculator | Type quit, exit, or q |
| Notation | Format | Example |
|---|---|---|
| Standard | d/dx[expression] |
d/dx[x^2 + 3x] |
| Function-style | derivative(expression) |
derivative(sin(x)) |
| Alternative | diff(expression) |
diff(ln(x)) |
| Traditional | d(expression)/dx |
d(x^3)/dx |
| Notation | Format | Example |
|---|---|---|
| Mathematical | ∫[expression]dx |
∫[x^2]dx |
| Function-style | integral(expression) |
integral(2x + 1) |
| Short form | int(expression) |
int(sin(x)) |
| Definite | definite(expr, a, b) |
definite(x^2, 0, 5) |
Trigonometric Functions:
sin(x)- Sinecos(x)- Cosinetan(x)- Tangentasin(x)- Arc sineacos(x)- Arc cosineatan(x)- Arc tangentsec(x)- Secantcsc(x)- Cosecantcot(x)- Cotangent
Logarithmic Functions:
ln(x)- Natural logarithm (base e)log(x)- Common logarithm (base 10)log2(x)- Binary logarithm (base 2)
Exponential Functions:
exp(x)- e^xx^yorx**y- Power operationsqrt(x)- Square rootcbrt(x)- Cube root
Other Functions:
abs(x)- Absolute valuefloor(x)- Floor functionceil(x)- Ceiling functionround(x)- Round to nearest integer
piorπ- Pi (3.14159265358979...)e- Euler's number (2.71828182845904...)phiorφ- Golden ratio (1.61803398874989...)inf- Infinity
The calculator supports custom mathematical formulas. Add them to the appropriate data files:
# Format: function = derivative
# Example:
my_custom_function = my_custom_derivative
x^n = n*x^(n-1)
# Format: function = integral
# Example:
my_function = my_integral + C
x^n = x^(n+1)/(n+1) + C
# Format: [Category]
# formula_name = result
[Trigonometry]
sin^2(x) + cos^2(x) = 1
[Calculus]
derivative_of_constant = 0
# Format: name = value
# Example:
golden_ratio = 1.618033988749895
speed_of_light = 299792458
The modular architecture makes extension straightforward:
Edit switch.py to add new operation types:
self.patterns = {
'your_operation': [
r'your_pattern',
]
}Extend modules/basic_math.py:
def your_function(self, x):
# Implementation
return resultAdd new calculation engines in modules/:
class YourEngine:
def calculate(self, expression):
# Your logic
return resultSimply edit the appropriate .txt file in the data/ directory.
You can configure the calculator using environment variables:
# Set precision (default: 28)
export CALC_PRECISION=50
# Set debug mode
export CALC_DEBUG=true
# Run calculator
python calculator.pyThe project includes comprehensive unit tests to ensure reliability and correctness.
# Run all tests
python -m pytest tests/
# Run tests with verbose output
python -m pytest tests/ -v
# Run tests with coverage report
python -m pytest tests/ --cov=. --cov-report=html
# Run specific test file
python -m pytest tests/test_calculator.py
# Run specific test function
python -m pytest tests/test_calculator.py::test_derivative
# Run tests in parallel (faster)
python -m pytest tests/ -n autoThe test suite covers:
- ✅ Basic arithmetic operations
- ✅ Derivative calculations
- ✅ Integral calculations
- ✅ Trigonometric functions
- ✅ Logarithmic and exponential functions
- ✅ Expression parsing
- ✅ Error handling
- ✅ Edge cases
Follow the existing test structure when adding new tests:
# tests/test_your_feature.py
import pytest
from calculator import CalculusCalculator
def test_your_feature():
calc = CalculusCalculator()
result = calc.calculate("your_expression")
assert result['success'] == True
assert result['result'] == "expected_output"Tests are automatically run on every commit using GitHub Actions (if configured).
- Python 3.8+ - Primary programming language
- Built-in Libraries - math, decimal, re, typing, os, sys
- NumPy - Advanced numerical computations
- SciPy - Scientific computing functions
- SymPy - Symbolic mathematics
- Matplotlib - Plotting and visualization
- pytest - Testing framework
- pytest-cov - Code coverage reports
- setuptools - Package management
- PEP 8 - Python style guide compliance
- Type Hints - Full type annotations
- Docstrings - Comprehensive documentation
| Metric | Value | Notes |
|---|---|---|
| Precision | 28 decimal places | Configurable via Decimal module |
| Startup Time | < 1 second | Including formula loading |
| Calculation Speed | < 10ms | For typical expressions |
| Memory Usage | < 50MB | Base runtime |
| Max Expression Length | Unlimited | Limited only by available memory |
- ✅ 200+ mathematical formulas pre-loaded
- ✅ Unlimited custom formula support
- ✅ Multiple derivative rules (power, product, quotient, chain)
- ✅ Multiple integration techniques
- ✅ Symbolic computation for exact results
- ✅ Numerical computation for approximate results
| Component | Minimum | Recommended |
|---|---|---|
| Python Version | 3.8 | 3.10 or higher |
| RAM | 256 MB | 512 MB |
| Storage | 10 MB | 50 MB (with dependencies) |
| OS | Windows 7+, macOS 10.12+, Linux (any modern distro) | Latest versions |
Solution:
# Ensure you're in the correct directory
cd Calculus-Calculator
# Verify the modules directory exists
ls -la modules/
# Run from the project root
python calculator.pySolution:
# Verify data directory exists
ls -la data/
# Check file permissions
chmod +r data/*.txt
# If files are missing, restore from repository
git checkout data/Solution:
# Clear Python cache
find . -type d -name "__pycache__" -exec rm -rf {} +
find . -type f -name "*.pyc" -delete
# Reinstall dependencies
pip install -r requirements.txt --force-reinstallSolution:
- Verify input syntax matches supported notation
- Check for proper parentheses and brackets
- Use the
helpcommand for syntax examples - Review the examples section in this README
Solution:
# Make scripts executable
chmod +x calculator.py
# Run with python explicitly
python calculator.pyIf you encounter issues not listed here:
- Check Documentation: Review this README and inline code comments
- Search Issues: Look through existing GitHub issues
- Create Issue: Open a new issue with:
- Your Python version (
python --version) - Operating system
- Complete error message
- Steps to reproduce
- Your Python version (
- Contact: Reach out to the maintainer
All modules include comprehensive docstrings:
# View module documentation
python -c "import calculator; help(calculator)"
# View specific class documentation
python -c "from switch import CalculusRouter; help(CalculusRouter)"For developers extending the calculator:
- CalculusCalculator: Main calculator class
- CalculusRouter: Operation routing and detection
- DerivativeEngine: Symbolic differentiation
- IntegralEngine: Integration calculations
- BasicMathOperations: Elementary mathematics
- FormulaLoader: Formula database management
The calculator follows a layered architecture:
User Input → Parser → Router → Calculation Engine → Result
↓
Formula Database
- Input Layer: Accepts and validates user expressions
- Parsing Layer: Tokenizes and structures expressions
- Routing Layer: Determines operation type
- Engine Layer: Performs actual calculations
- Data Layer: Provides mathematical formulas and rules
We welcome contributions from the community! Whether you're fixing bugs, adding features, or improving documentation, your help is appreciated.
-
Fork the Repository
# Click the 'Fork' button on GitHub # Then clone your fork git clone https://github.com/YOUR_USERNAME/Calculus-Calculator.git
-
Create a Feature Branch
git checkout -b feature/amazing-feature # or git checkout -b bugfix/fix-issue-123 -
Make Your Changes
- Write clean, documented code
- Follow the existing code style
- Add tests for new features
- Update documentation as needed
-
Test Your Changes
# Run all tests python -m pytest tests/ # Check code style python -m flake8 . # Run your code manually python calculator.py
-
Commit Your Changes
git add . git commit -m "Add amazing feature" # Use conventional commit messages: # feat: Add new feature # fix: Fix bug # docs: Update documentation # test: Add tests # refactor: Refactor code
-
Push to Your Fork
git push origin feature/amazing-feature
-
Open a Pull Request
- Go to the original repository
- Click "New Pull Request"
- Describe your changes clearly
- Reference any related issues
- Follow PEP 8: Python style guide
- Use Type Hints: Add type annotations for functions
- Write Docstrings: Document all classes and functions
- Keep It Simple: Prefer readability over cleverness
- Write Tests: All new features must have tests
- Maintain Coverage: Don't decrease test coverage
- Test Edge Cases: Consider boundary conditions
- Run Tests Locally: Before submitting PR
- Update README: If adding features
- Add Examples: Show how to use new features
- Inline Comments: For complex logic
- API Documentation: For new public methods
- Use the bug report template
- Include reproduction steps
- Provide error messages
- Mention your environment
- Describe the feature clearly
- Explain why it's needed
- Provide use cases
- Consider implementation
- Fix typos and grammar
- Add examples
- Improve clarity
- Update outdated info
- Bug fixes
- New features
- Performance improvements
- Code refactoring
- Be Respectful: Treat everyone with respect
- Be Constructive: Provide helpful feedback
- Be Patient: Remember we're all volunteers
- Be Collaborative: Work together towards improvement
Contributors will be:
- Listed in the project's contributors page
- Mentioned in release notes
- Appreciated in the community!
This project is licensed under the MIT License - see the LICENSE file for details.
✅ Permissions:
- Commercial use
- Modification
- Distribution
- Private use
❌ Limitations:
- Liability
- Warranty
ℹ️ Conditions:
- License and copyright notice must be included
- Python - The powerful programming language that makes this possible
- Math Libraries - Built-in and external mathematical computation tools
- SymPy - Symbolic mathematics library for advanced features
- NumPy/SciPy - Numerical computing foundations
- Inspired by symbolic computation systems like Mathematica and Maple
- Educational tools for teaching calculus concepts
- The need for accessible, open-source mathematical software
- Python Community - For excellent mathematical libraries
- Mathematics Community - For open formulas and knowledge sharing
- Contributors - Everyone who has contributed to this project
- Users - For testing, feedback, and suggestions
- Mathematical formulas from various textbooks and references
- Calculus rules from standard mathematical literature
- Community feedback and suggestions
For Issues and Bugs:
For Questions and Discussions:
- 💬 Start a Discussion
- 📖 Read the Documentation
- 💡 Check the Examples section
For Feature Requests:
- ✨ Submit a Feature Request
- 🗳️ Vote on existing feature requests
Maintainer: Divyansh Shakya
- GitHub: @divyanshakya966
- Email: divyanshakya966@gmail.com
Repository: Calculus-Calculator
- 🔴 Critical Bugs: Within 24-48 hours
- 🟡 Feature Requests: Within 1 week
- 🟢 Questions: Within 2-3 days
Note: This is a community project maintained by volunteers. Response times may vary.
-
Graphical User Interface (GUI)
- Desktop application using Tkinter or PyQt
- Modern, intuitive design
- Real-time calculation preview
-
Web Interface
- Browser-based calculator
- No installation required
- Share calculations via URL
-
Mobile App
- iOS and Android versions
- Touch-optimized interface
- Offline capability
-
2D/3D Plotting
- Graph functions and their derivatives
- Visualize integrals as areas
- Interactive plot manipulation
-
Step-by-Step Solutions
- Show detailed calculation steps
- Educational explanations
- LaTeX-formatted output
-
Matrix Operations
- Matrix algebra
- Eigenvalues and eigenvectors
- Linear transformations
-
Differential Equations
- Solve ODEs and PDEs
- Numerical methods
- Symbolic solutions
-
Vector Calculus
- Gradient, divergence, curl
- Line and surface integrals
- Vector field visualization
-
Statistics & Probability
- Probability distributions
- Statistical tests
- Data analysis tools
-
LaTeX Export
- Export calculations as LaTeX
- Publication-ready formatting
- Equation editor integration
-
API Development
- RESTful API
- Python package on PyPI
- Integration with Jupyter notebooks
-
Cloud Sync
- Save calculation history
- Sync across devices
- Share with collaborators
-
Performance Optimization
- Parallel computation
- Caching mechanisms
- Memory optimization
-
Enhanced Error Messages
- More detailed error explanations
- Suggestions for corrections
- Interactive error resolution
-
Multi-language Support
- Interface translations
- Localized documentation
- Regional math notation
- Basic arithmetic operations
- Derivative calculations
- Integral calculations
- Trigonometric functions
- Logarithmic functions
- Interactive CLI mode
- Command-line arguments
- Formula database
- Unit tests
- Comprehensive documentation
- Enhanced error handling
- More mathematical functions
- Performance improvements
- Extended test coverage
Have ideas for new features? We'd love to hear them!
- Vote on Features: Star issues tagged with
enhancement - Suggest Features: Open a new issue with your idea
- Implement Features: Pick an item from the roadmap and contribute
If you find this project helpful, please consider:
⭐ Star this repository on GitHub
🐛 Report bugs to help improve the project
💡 Suggest features to make it even better
📢 Share with others who might benefit
🤝 Contribute code, documentation, or ideas
Made with ❤️ for mathematics enthusiasts, students, and educators worldwide
Empowering learning through open-source technology
🏠 Home • 📖 Documentation • 🐛 Issues • 💬 Discussions • ⭐ Star
© 2024 Divyansh Shakya. All rights reserved.
