# NumRoot
[](https://badge.fury.io/py/numroot)
[](https://www.python.org/downloads/)
Python package for numerical resolution of nonlinear equations with several numerical analysis methods.
## 🚀 Installation
```bash
pip install numroot
```
### Development installation
```bash
pip install numroot[dev]
```
## 📖 Quick use
```python
from numroot import NonlinearSolver
# Create a solver object
solver = NonlinearSolver()
# Define a function to analyse (example: x² - 2 = 0)
def f(x):
return x**2 - 2
# Bissection method
result = solver.bisection(f, x_a=0, x_b=2, epsilon=1e-6)
print(f"Root found: {result.root}") # ≈ 1.414
print(f"Number of iterations: {result.iterations}")
# Newton-Raphson method
def df(x):
return 2*x
result = solver.newton_raphson(f, df, x_0=1.5, epsilon=1e-6)
print(f"Root found: {result.root}") # ≈ 1.414
print(f"Number of iterations: {result.iterations}")
# Secant method
result = solver.secant(f, x_0=1.0, x_1=2.0, epsilon=1e-6)
print(f"Root found: {result.root}") # ≈ 1.414
print(f"Number of iterations: {result.iterations}")
```
## 🔧 Available methods
### Bissection method
- **Advantages**: Always convergent, robust
- **Disadvantages**: Slow convergence
- **Usage**: When you have an interval [a,b] where f(a) and f(b) have opposite signs
```python
result = solver.bisection(func, a, b, epsilon=1e-6, maxiter=100)
```
### Newton-Raphson method
- **Advantages**: Very fast quadratic convergence
- **Disadvantages**: Requires derivative, may diverge
- **Usage**: When you know the derivative and have a good initial estimate
```python
result = solver.newton_raphson(func, dfunc, x0, epsilon=1e-6, maxiter=100)
```
### Secant method
- **Advantages**: No derivative needed, super-linear convergence
- **Disadvantages**: Can be unstable with bad initial points.
- **Uses**: Compromise between bisection and Newton-Raphson
```python
result = solver.secant(func, x0, x1, epsilon=1e-6, maxiter=100)
```
## 🎯 Typical use cases
- Solving physical equations (trajectories, oscillations)
- Engineering calculations (balance points, intersections)
- Mathematical modeling (zeros of complex functions)
- Research and education in numerical analysis
## 📋 Requirements
- Python 3.8+
- NumPy >= 1.20.0
## 🔗 Links
- [Documentation complète](https://numroot.readthedocs.io/)
- [PyPI](https://pypi.org/project/numroot/)
- [Issues GitHub](https://github.com/Onniryss/numroot/issues)
- [Code source](https://github.com/Onniryss/numroot)
## 📈 Roadmap
- [ ] Systems of non-linear equations
- [ ] Ordinary differential equations
- [ ] Numerical optimization
- [ ] Graphical interface
- [ ] Interactive visualizations
## 📚 References
- [Geeks for Geeks - Secant method](https://www.geeksforgeeks.org/secant-method-of-numerical-analysis/)
- [Math Libretexts - Bisection Method](https://math.libretexts.org/Workbench/Numerical_Methods_with_Applications_(Kaw)/3:_Nonlinear_Equations/3.03:_Bisection_Methods_for_Solving_a_Nonlinear_Equation)
- [Math Libretexts - Newton-Raphson Method](https://math.libretexts.org/Workbench/Numerical_Methods_with_Applications_(Kaw)/3:_Nonlinear_Equations/3.04:_Newton-Raphson_Method_for_Solving_a_Nonlinear_Equation)
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