How To Plot An Expression In Python

In this tutorial, we will learn how to plot an expression using Python, with the help of popular libraries like NumPy, matplotlib, and SymPy. Plotting is an essential skill for visualizing and analyzing data, and Python makes it effortless to do so.

Step 1: Installing necessary libraries

In order to plot an expression in Python, we will need to install the following libraries:

1. NumPy: A fundamental library for numeric computing in Python
2. matplotlib: A popular plotting and data visualization library
3. SymPy: A library for symbolic mathematics

To install these libraries, open your terminal or command prompt and type the following command:

1	pip install numpy matplotlib sympy

Step 2: Import the necessary libraries

Once the libraries are installed, we need to import them. Add the following lines at the beginning of your Python script:

import numpy as np

import matplotlib.pyplot as plt

import sympy as sp

Step 3: Define the expression and range for the plot

Now, we need to define the expression that we want to plot. For this tutorial, let’s plot the simple quadratic function f(x) = x², but feel free to choose any function you like. We will also define the range for our x-axis.

x = sp.Symbol('x')

f_x = x**2

x_range = np.linspace(-10, 10, 1000)

In this code, we define the expression using the SymPy library and declare the variable x as a symbol. Then, we create the expression f_x for our quadratic function. Our x-axis range will go from -10 to 10, with 1000 equally spaced data points.

Step 4: Convert the expression to a NumPy function

For efficient computation and compatibility with the matplotlib library, it is essential to convert our symbolic expression to a NumPy function. To do this, we will use the sp.lambdify() method from the SymPy library:

1	f_x_np = sp.lambdify(x, f_x, 'numpy')

This method takes three arguments – the variable (x), the expression (f_x), and the output format (‘numpy’).

Step 5: Plot the expression

Finally, we can plot the expression using the matplotlib library. To do this, we will use the plt.plot() method and provide our x_range and the computed function values.

plt.plot(x_range, f_x_np(x_range))

plt.xlabel('x')

plt.ylabel('y')

plt.title('Plot of f(x) = x²')

plt.grid(True)

plt.show()

Output:

A plot of the quadratic function f(x) = x² with x-axis from -10 to 10

Complete Code