r"""
Writing mathematical expressions
================================

An introduction to writing mathematical expressions in Matplotlib.

You can use a subset TeX markup in any matplotlib text string by placing it
inside a pair of dollar signs ($).

Note that you do not need to have TeX installed, since Matplotlib ships
its own TeX expression parser, layout engine, and fonts.  The layout engine
is a fairly direct adaptation of the layout algorithms in Donald Knuth's
TeX, so the quality is quite good (matplotlib also provides a ``usetex``
option for those who do want to call out to TeX to generate their text (see
:doc:`/tutorials/text/usetex`).

Any text element can use math text.  You should use raw strings (precede the
quotes with an ``'r'``), and surround the math text with dollar signs ($), as
in TeX. Regular text and mathtext can be interleaved within the same string.
Mathtext can use DejaVu Sans (default), DejaVu Serif, the Computer Modern fonts
(from (La)TeX), `STIX <http://www.stixfonts.org/>`_ fonts (with are designed
to blend well with Times), or a Unicode font that you provide.  The mathtext
font can be selected with the customization variable ``mathtext.fontset`` (see
:doc:`/tutorials/introductory/customizing`)

Here is a simple example::

    # plain text
    plt.title('alpha > beta')

produces "alpha > beta".

Whereas this::

    # math text
    plt.title(r'$\alpha > \beta$')

produces ":mathmpl:`\alpha > \beta`".

.. note::
   Mathtext should be placed between a pair of dollar signs ($). To make it
   easy to display monetary values, e.g., "$100.00", if a single dollar sign
   is present in the entire string, it will be displayed verbatim as a dollar
   sign.  This is a small change from regular TeX, where the dollar sign in
   non-math text would have to be escaped ('\\\$').

.. note::
   While the syntax inside the pair of dollar signs ($) aims to be TeX-like,
   the text outside does not.  In particular, characters such as::

     # $ % & ~ _ ^ \ { } \( \) \[ \]

   have special meaning outside of math mode in TeX.  Therefore, these
   characters will behave differently depending on the rcParam ``text.usetex``
   flag.  See the :doc:`usetex tutorial </tutorials/text/usetex>` for more
   information.

Subscripts and superscripts
---------------------------

To make subscripts and superscripts, use the ``'_'`` and ``'^'`` symbols::

    r'$\alpha_i > \beta_i$'

.. math::

    \alpha_i > \beta_i

To display multi-letter subscripts or superscripts correctly,
you should put them in curly braces ``{...}``::

    r'$\alpha^{ic} > \beta_{ic}$'

.. math::

    \alpha^{ic} > \beta_{ic}

Some symbols automatically put their sub/superscripts under and over the
operator.  For example, to write the sum of :mathmpl:`x_i` from :mathmpl:`0` to
:mathmpl:`\infty`, you could do::

    r'$\sum_{i=0}^\infty x_i$'

.. math::

    \sum_{i=0}^\infty x_i

Fractions, binomials, and stacked numbers
-----------------------------------------

Fractions, binomials, and stacked numbers can be created with the
``\frac{}{}``, ``\binom{}{}`` and ``\genfrac{}{}{}{}{}{}`` commands,
respectively::

    r'$\frac{3}{4} \binom{3}{4} \genfrac{}{}{0}{}{3}{4}$'

produces

.. math::

    \frac{3}{4} \binom{3}{4} \stackrel{}{}{0}{}{3}{4}

Fractions can be arbitrarily nested::

    r'$\frac{5 - \frac{1}{x}}{4}$'

produces

.. math::

    \frac{5 - \frac{1}{x}}{4}

Note that special care needs to be taken to place parentheses and brackets
around fractions.  Doing things the obvious way produces brackets that are too
small::

    r'$(\frac{5 - \frac{1}{x}}{4})$'

.. math ::

    (\frac{5 - \frac{1}{x}}{4})

The solution is to precede the bracket with ``\left`` and ``\right`` to inform
the parser that those brackets encompass the entire object.::

    r'$\left(\frac{5 - \frac{1}{x}}{4}\right)$'

.. math ::

    \left(\frac{5 - \frac{1}{x}}{4}\right)

Radicals
--------

Radicals can be produced with the ``\sqrt[]{}`` command.  For example::

    r'$\sqrt{2}$'

.. math ::

    \sqrt{2}

Any base can (optionally) be provided inside square brackets.  Note that the
base must be a simple expression, and can not contain layout commands such as
fractions or sub/superscripts::

    r'$\sqrt[3]{x}$'

.. math ::

    \sqrt[3]{x}

.. _mathtext-fonts:

Fonts
-----

The default font is *italics* for mathematical symbols.

.. note::

   This default can be changed using the ``mathtext.default`` rcParam.  This is
   useful, for example, to use the same font as regular non-math text for math
   text, by setting it to ``regular``.

To change fonts, e.g., to write "sin" in a Roman font, enclose the text in a
font command::

    r'$s(t) = \mathcal{A}\mathrm{sin}(2 \omega t)$'

.. math::

    s(t) = \mathcal{A}\mathrm{sin}(2 \omega t)

More conveniently, many commonly used function names that are typeset in
a Roman font have shortcuts.  So the expression above could be written as
follows::

    r'$s(t) = \mathcal{A}\sin(2 \omega t)$'

.. math::

    s(t) = \mathcal{A}\sin(2 \omega t)

Here "s" and "t" are variable in italics font (default), "sin" is in Roman
font, and the amplitude "A" is in calligraphy font.  Note in the example above
the calligraphy ``A`` is squished into the ``sin``.  You can use a spacing
command to add a little whitespace between them::

    r's(t) = \mathcal{A}\/\sin(2 \omega t)'

.. Here we cheat a bit: for HTML math rendering, Sphinx relies on MathJax which
   doesn't actually support the italic correction (\/); instead, use a thin
   space (\,) which is supported.

.. math::

    s(t) = \mathcal{A}\,\sin(2 \omega t)

The choices available with all fonts are:

    ========================= ================================
    Command                   Result
    ========================= ================================
    ``\mathrm{Roman}``        :mathmpl:`\mathrm{Roman}`
    ``\mathit{Italic}``       :mathmpl:`\mathit{Italic}`
    ``\mathtt{Typewriter}``   :mathmpl:`\mathtt{Typewriter}`
    ``\mathcal{CALLIGRAPHY}`` :mathmpl:`\mathcal{CALLIGRAPHY}`
    ========================= ================================

.. role:: math-stix(mathmpl)
   :fontset: stix

When using the `STIX <http://www.stixfonts.org/>`_ fonts, you also have the
choice of:

    ================================ =========================================
    Command                          Result
    ================================ =========================================
    ``\mathbb{blackboard}``          :math-stix:`\mathbb{blackboard}`
    ``\mathrm{\mathbb{blackboard}}`` :math-stix:`\mathrm{\mathbb{blackboard}}`
    ``\mathfrak{Fraktur}``           :math-stix:`\mathfrak{Fraktur}`
    ``\mathsf{sansserif}``           :math-stix:`\mathsf{sansserif}`
    ``\mathrm{\mathsf{sansserif}}``  :math-stix:`\mathrm{\mathsf{sansserif}}`
    ================================ =========================================

There are also three global "font sets" to choose from, which are
selected using the ``mathtext.fontset`` parameter in :ref:`matplotlibrc
<matplotlibrc-sample>`.

``cm``: **Computer Modern (TeX)**

.. image:: ../../_static/cm_fontset.png

``stix``: **STIX** (designed to blend well with Times)

.. image:: ../../_static/stix_fontset.png

``stixsans``: **STIX sans-serif**

.. image:: ../../_static/stixsans_fontset.png

Additionally, you can use ``\mathdefault{...}`` or its alias
``\mathregular{...}`` to use the font used for regular text outside of
mathtext.  There are a number of limitations to this approach, most notably
that far fewer symbols will be available, but it can be useful to make math
expressions blend well with other text in the plot.

Custom fonts
~~~~~~~~~~~~

mathtext also provides a way to use custom fonts for math.  This method is
fairly tricky to use, and should be considered an experimental feature for
patient users only.  By setting the rcParam ``mathtext.fontset`` to ``custom``,
you can then set the following parameters, which control which font file to use
for a particular set of math characters.

    ============================== =================================
    Parameter                      Corresponds to
    ============================== =================================
    ``mathtext.it``                ``\mathit{}`` or default italic
    ``mathtext.rm``                ``\mathrm{}`` Roman (upright)
    ``mathtext.tt``                ``\mathtt{}`` Typewriter (monospace)
    ``mathtext.bf``                ``\mathbf{}`` bold italic
    ``mathtext.cal``               ``\mathcal{}`` calligraphic
    ``mathtext.sf``                ``\mathsf{}`` sans-serif
    ============================== =================================

Each parameter should be set to a fontconfig font descriptor (as defined in the
yet-to-be-written font chapter).

.. TODO: Link to font chapter

The fonts used should have a Unicode mapping in order to find any
non-Latin characters, such as Greek.  If you want to use a math symbol
that is not contained in your custom fonts, you can set the rcParam
``mathtext.fallback_to_cm`` to ``True`` which will cause the mathtext system
to use characters from the default Computer Modern fonts whenever a particular
character can not be found in the custom font.

Note that the math glyphs specified in Unicode have evolved over time, and many
fonts may not have glyphs in the correct place for mathtext.

Accents
-------

An accent command may precede any symbol to add an accent above it.  There are
long and short forms for some of them.

    ============================== =================================
    Command                        Result
    ============================== =================================
    ``\acute a`` or ``\'a``        :mathmpl:`\acute a`
    ``\bar a``                     :mathmpl:`\bar a`
    ``\breve a``                   :mathmpl:`\breve a`
    ``\ddot a`` or ``\''a``        :mathmpl:`\ddot a`
    ``\dot a`` or ``\.a``          :mathmpl:`\dot a`
    ``\grave a`` or ``\`a``        :mathmpl:`\grave a`
    ``\hat a`` or ``\^a``          :mathmpl:`\hat a`
    ``\tilde a`` or ``\~a``        :mathmpl:`\tilde a`
    ``\vec a``                     :mathmpl:`\vec a`
    ``\overline{abc}``             :mathmpl:`\overline{abc}`
    ============================== =================================

In addition, there are two special accents that automatically adjust to the
width of the symbols below:

    ============================== =================================
    Command                        Result
    ============================== =================================
    ``\widehat{xyz}``              :mathmpl:`\widehat{xyz}`
    ``\widetilde{xyz}``            :mathmpl:`\widetilde{xyz}`
    ============================== =================================

Care should be taken when putting accents on lower-case i's and j's.  Note that
in the following ``\imath`` is used to avoid the extra dot over the i::

    r"$\hat i\ \ \hat \imath$"

.. math::

    \hat i\ \ \hat \imath

Symbols
-------

You can also use a large number of the TeX symbols, as in ``\infty``,
``\leftarrow``, ``\sum``, ``\int``.

.. math_symbol_table::

If a particular symbol does not have a name (as is true of many of the more
obscure symbols in the STIX fonts), Unicode characters can also be used::

   r'$\u23ce$'

Example
-------

Here is an example illustrating many of these features in context.

.. figure:: ../../gallery/pyplots/images/sphx_glr_pyplot_mathtext_001.png
   :target: ../../gallery/pyplots/pyplot_mathtext.html
   :align: center
   :scale: 50

   Pyplot Mathtext
"""
