#!/usr/bin/env python
# coding: utf-8

# (myst-content/math)=
# # Math and equations
# 
# Jupyter Book uses [MathJax](http://docs.mathjax.org/) for typesetting math in your HTML book build.
# This allows you to have LaTeX-style mathematics in your online content.
# This page shows you a few ways to control this.
# 
# :::{seealso}
# For more information about equation numbering,
# see the [MathJax equation numbering documentation](http://docs.mathjax.org/en/v2.7-latest/tex.html#automatic-equation-numbering).
# :::
# 
# :::{tip}
# 
# By default MathJax version 2 is currently used.
# If you are using a lot of math, you may want to try using version 3, which claims to improve load speeds by 60 - 80%:
# 
# ```yaml
# sphinx:
#   config:
#     mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
# ```
# 
# See the [Sphinx documentation](sphinx:sphinx.ext.mathjax) for details.
# 
# :::
# 
# ## In-line math
# 
# To insert in-line math use the `$` symbol within a Markdown cell.
# For example, the text `$this_{is}^{inline}$` will produce: $this_{is}^{inline}$.

# ## Math blocks
# 
# You can also include math blocks for separate equations. This allows you to focus attention
# on more complex or longer equations, as well as link to them in your pages. To use a block
# equation, wrap the equation in either `$$` or `\begin` statements.
# 
# For example,
# 
# ```latex
# $$
#   \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}
# $$
# ```
# 
# results in:
# 
# $$
#   \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}
# $$

# or, by adding to your `_config.yml`:
# 
# ```yaml
# parse:
#   myst_extended_syntax: true
# ```
# 
# you can use:
# 
# ```latex
# \begin{gather*}
# a_1=b_1+c_1\\
# a_2=b_2+c_2-d_2+e_2
# \end{gather*}
# 
# \begin{align}
# a_{11}& =b_{11}&
#   a_{12}& =b_{12}\\
# a_{21}& =b_{21}&
#   a_{22}& =b_{22}+c_{22}
# \end{align}
# ```
# 
# which results in:
# 
# \begin{gather*}
# a_1=b_1+c_1\\
# a_2=b_2+c_2-d_2+e_2
# \end{gather*}
# 
# \begin{align}
# a_{11}& =b_{11}&
#   a_{12}& =b_{12}\\
# a_{21}& =b_{21}&
#   a_{22}& =b_{22}+c_{22}
# \end{align}
# 
# :::{seealso}
# The MyST guides to [dollar math syntax](myst-parser:syntax/math), [LaTeX math syntax](myst-parser:syntax/amsmath), and [how MyST-Parser works with MathJax](myst-parser:syntax/mathjax).
# 
# For advanced use, also see how to [define MathJax TeX Macros](sphinx/tex-macros).
# :::

# ### Numbering equations
# 
# If you'd like to number equations so that you can refer to them later, use the **math directive**.
# It looks like this:
# 
# ````md
# ```{math}
# :label: my_label
# my_math
# ```
# ````
# 
# For example, the following code:
# 
# ````md
# ```{math}
# :label: my_label
# w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}
# ```
# ````
# 
# will generate
# 
# ```{math}
# :label: my_label
# w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}
# ```
# 
# Alternatively you can use the dollar math syntax with a prefixed label:
# 
# ```md
# $$
#   w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}
# $$ (my_other_label)
# ```
# 
# which generates
# 
# $$
#   w_{t+1} = (1 + r_{t+1}) s(w_t) + y_{t+1}
# $$ (my_other_label)
# 
# :::{note}
# Labels cannot start with an integer, or they won't be able to be referenced and
# will throw a warning message if referenced. For example, `:label: 1` and `:label: 1eq` cannot
# be referenced.
# :::
# 
# ### Linking to equations
# 
# If you have created an equation with a label, you can link to it from within your text
# (and across pages!).
# 
# You can refer to the equation using the label that you've provided by using
# the `{eq}` role. For example:
# 
# ```md
# - A link to an equation directive: {eq}`my_label`
# - A link to a dollar math block: {eq}`my_other_label`
# ```
# 
# results in
# 
# - A link to an equation directive: {eq}`my_label`
# - A link to a dollar math block: {eq}`my_other_label`
# 
# :::{note}
# `\labels` inside LaTeX environment are not currently identified, and so cannot be referenced.
# We hope to implement this in a future update (see [executablebooks/MyST-Parser#202](https://github.com/executablebooks/MyST-Parser/issues/202))!
# :::
