Mathematical Expressions

Matplotlib - Mathematical Expressions (TeX/LaTeX)

Matplotlib includes a built-in parser and layout engine that understands a subset of TeX (specifically, LaTeX-like math markup). This allows you to embed beautifully typeset mathematical formulas and symbols directly into your plot titles, labels, annotations, and legends.

Using MathText

To include mathematical expressions, simply enclose the TeX markup within a pair of dollar signs ($) in any Matplotlib text string (e.g., in ax.set_title(), ax.text(), ax.set_xlabel()).

It’s highly recommended to use raw strings (prefixing the string with r) for text containing math markup. This prevents Python from interpreting backslashes (\) as escape sequences before Matplotlib sees them.

# Correct way using raw string:
plt.title(r'$\alpha > \beta$')

# Incorrect way (backslash might be misinterpreted):
# plt.title('$\alpha > \beta$')

Common Syntax:

• Greek Letters: $\alpha$, $\beta$, $\gamma$, $\Delta$, $\Omega$ (e.g., r'$\Delta y / \Delta x$')
• Subscripts: Use underscore (_). Example: r'$x_i$' renders as xᵢ.
• Superscripts: Use caret (^). Example: r'$E = mc^2$' renders as E = mc².
• Fractions: $\frac{numerator}{denominator}$. Example: r'$\frac{1}{2}$' renders as ½.
• Roots: $\sqrt{expression}$. Example: r'$\sqrt{b^2 - 4ac}$' renders the quadratic formula part.
• Summation/Integrals: $\sum$, $\int$. Example: r'$\sum_{i=0}^N i^2$' renders Σᵢ<0xD0><0x96>₀ᴺ i².
• Accents: $\hat{x}$, $\bar{y}$, $\vec{z}$.
• Font Styles:
• • $\mathrm{Roman}$
• • $\mathit{Italic}$
• • $\mathbf{Bold}$
• • $\mathcal{CALLIGRAPHIC}$
• Spacing: Use \ (backslash space), \,, \:, \; for different amounts of space.
• Symbols: Many common math symbols are supported: $\pm$, $\times$, $\leq$, $\geq$, $\neq$, $\approx$, $\infty$ etc.

Example Usage

import matplotlib.pyplot as plt
import numpy as np

t = np.arange(0.0, 2.0, 0.01)
s = np.sin(2 * np.pi * t)

fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(t, s)

# Title with Greek letters and subscripts
ax.set_title(r'Plot of $sin(2 pi t)$ where $alpha_i > \beta_i$', fontsize=16)

# Axis labels with math
ax.set_xlabel(r'Time $t$ (s)', fontsize=12)
ax.set_ylabel(r'Voltage $V$ (mV)', fontsize=12)

# Text annotation with a formula using different fonts
ax.text(0.5, 0.6, r'Amplitude $mathcal{A} = \sqrt{x^2 + y^2}$',
        fontsize=14, color='blue')

# Annotation with a fraction
ax.text(1.2, -0.5, r'Phase shift: $\phi = \frac{\pi}{2}$',
        fontsize=14, color='green')

ax.grid(True)
plt.tight_layout()
plt.show()

This code generates a sine wave plot where the title, axis labels, and text annotations include properly typeset mathematical expressions and symbols using Matplotlib’s MathText engine.

Full LaTeX Integration (Optional)

For users who need the full power of a LaTeX installation (e.g., for specific packages or complex layouts not supported by the internal engine), Matplotlib can be configured to use an external LaTeX compiler. This requires having a working LaTeX distribution installed on your system.

To enable it, set the text.usetex rcParam:

# Requires a LaTeX installation
# plt.rcParams.update({
#     "text.usetex": True,
#     "font.family": "serif",
#     "font.serif": ["Computer Modern Roman"], # Or other LaTeX font
# })

# Example using LaTeX
# plt.title(r'Full LaTeX example: $int_0^infty e^{-x^2} dx = rac{sqrt{pi}}{2}$')
# plt.show()

Using the built-in MathText is generally sufficient and more portable, but the option for full LaTeX exists for advanced users.