1091 lines
24 KiB
ReStructuredText
1091 lines
24 KiB
ReStructuredText
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.. _TeX-support:
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*****************************
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MathJax TeX and LaTeX Support
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*****************************
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The support for TeX and LaTeX in MathJax consists of two parts: the
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`tex2jax` preprocessor, and the TeX input processor. The first of
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these looks for mathematics within your web page (indicated by math
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delimiters like ``$$...$$``) and marks the mathematics for later
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processing by MathJax. The TeX input processor is what converts the
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TeX notation into MathJax's internal format, where on of MathJax's
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output processors then displays is in the web page.
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The `tex2jax` preprocessor can be configured to look for whatever
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markers you want to use for your math delimiters. See the
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:ref:`tex2jax configuration options <configure-tex2jax>` section for
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details on how to customize the action of `tex2jax`.
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The TeX input processor handles conversion of your mathematical
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notation into MathJax's internal format (which is essentially MathML),
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and so acts as a TeX to MathML converter. The TeX input processor has
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few configuration options (see the :ref:`TeX options
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<configure-TeX>` section for details), but it can also be customized
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through the use of extensions that define additional functionality
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(see the :ref:`TeX and LaTeX extensions <tex-extensions>` below).
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Note that the TeX input processor implements **only** the math-mode
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macros of TeX and LaTeX, not the text-mode macros. MathJax expects
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that you will use standard HTML tags to handle formatting the text of
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your page; it only handles the mathematics. So, for example, MathJax
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does not implement ``\emph`` or
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``\begin{enumerate}...\end{enumerate}`` or other text-mode macros or
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environments. You must use HTML to handle such formatting tasks. If
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you need a LaTeX-to-HTML converter, you should consider `other options
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<http://www.google.com/search?q=latex+to+html+converter>`_.
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TeX and LaTeX in HTML documents
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===============================
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Keep in mind that your mathematics is part of an HTML document, so you
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need to be aware of the special characters used by HTML as part of its
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markup. There can not be HTML tags within the math delimiters (other
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than ``<BR>``) as TeX-formatted math does not include HTML tags.
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Also, since the mathematics is initially given as text on the page,
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you need to be careful that your mathematics doesn't look like HTML
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tags to the browser (which parses the page before MathJax gets to see
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it). In particular, that means that you have to be careful about
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things like less-than and greater-than signs (``<``and ``>``), and
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ampersands (``&``), which have special meaning to the browsers. For
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example,
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.. code-block:: latex
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... when $x<y$ we have ...
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will cause a problem, because the brower will think ``<y`` is the
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beginning of a tag named ``y`` (even though there is no such tag in
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HTML). When this happens, the browser will think the tag continues up
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to the next ``>`` in the document (typically the end of the next
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actual tag in the HTML file), and you may notice that you are missing
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part of the text of the document. In the example above, the `` we
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have ...`` will not be displayed because the browsers thinks it is
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part of the tag starting at ``<y``. This is one indication you can
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use to spot this prooblem; it is a common error and should be avoided.
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Usually, it is sufficient to simply put spaces around these symbols to
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cause the browser to avoid them, so
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.. code-block:: latex
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... when $x < y$ we have ...
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should work. Alternatively, you can use the HTML entities ``<``,
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``>`` and ``&`` to encode these characters so that the browser
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will not interpret them, but MathJax will. E.g.,
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.. code-block:: latex
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... when $x < y$ we have ...
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Finally, there are ``\lt`` and ``\gt`` macros defined to make it
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easier to enter ``<`` and ``>`` using TeX-like syntax:
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.. code-block:: latex
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... when $x \lt y$ we have ...
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Keep in mind that the browser interprets your text before MathJax
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does.
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.. _tex-extensions:
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TeX and LaTeX extensions
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========================
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While MathJax includes nearly all of the Plain TeX math macros, and
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many of the LaTeX macros and environments, note everything is
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implemented in the core TeX input processor. Some less-used commands
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are defined in extensions to the TeX processor. MathJax will load
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some extensions automatically when you first use the commands they
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implement (for example, the ``\def`` and ``\newcommand`` macros are
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implemented in the ``TeX/newcommand.js`` extension, but MathJax loads
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this extension itself when you use those macros). Not all extensions
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are set up to load automatically, however, so you may need to request
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some extensions explicitly yourself.
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To enable any of the TeX extensions, simply add the appropriate string
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(e.g., `"TeX/AMSmath.js"`) to your config's `extensions` array. The
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main extensions are described below.
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AMSmath and AMSsymbol
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---------------------
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The `AMSmath` extension implements AMS math environments and macros,
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and the `AMSsymbol` extension implements macros for accessing the AMS
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symbol fonts. To use these extensions, add them to your `extensions` array.
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.. code-block:: javascript
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extensions: ["TeX/AMSmath.js", "TeX/AMSsymbol.js", ...]
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See the list of commands at the end of this document for details about
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what commands are implemented in these extensions.
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The `AMSmath` extension will be loaded automatically when you first
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use one of the math environments it defines, but you will have to load
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it explicitly if you want to use the other macros that it defines.
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The `AMSsymbols` extension is not loaded automatically, so you must
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include it explicitly if you want to use the macros it defines.
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Autobold
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--------
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The `autobold` extension adds ``\boldsymbol{...}`` around mathematics that
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appears in a section of an HTML page that is in bold.
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.. code-block:: javascript
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extensions: ["TeX/autobold.js"]
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noErrors
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--------
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The `noErrors` extension prevents TeX error messages from being
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displayed and shows the original TeX code instead. You can configure
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whether the dollar signs are shown or not for in-line math, and
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whether to put all the TeX on one line or use multiple lines (if the
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original text contained line breaks).
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To enable the `noErrors` extension and configure it, use
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.. code-block:: javascript
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extensions: ["TeX/noErrors.js", ...],
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TeX: {
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noErrors: {
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inlineDelimiters: ["",""], // or ["$","$"] or ["\\(","\\)"]
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multiLine: true, // false for TeX on all one line
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style: {
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"font-family": "serif",
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"font-size": "80%",
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"color": "black",
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"border": "1px solid"
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// add any additional CSS styles that you want
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// (be sure there is no extra comma at the end of the last item)
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}
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}
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}
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Display-style math is always shown in multi-line format, and without
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delimiters, as it will already be set off in its own centered
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paragraph, like standard display mathematics.
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The default settings place the invalid TeX in a multi-line box with a
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black border. If you want it to look as though the TeX is just part of
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the paragraph, use
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.. code-block:: javascript
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TeX: {
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noErrors: {
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inlineDelimiters: ["$","$"], // or ["",""] or ["\\(","\\)"]
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multiLine: false,
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style: {
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"font-size": "normal",
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"border": ""
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}
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}
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}
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You may also wish to set the font family, as the default is "serif"
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noUndefined
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-----------
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The `noUndefined` extension causes undefined control sequences to be
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shown as their macro names rather than produce an error message. So
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$X_{\xxx}$ would display as an "X" with a subscript consiting of the
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text ``\xxx`` in red.
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To enable and configure this extension, use for example
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.. code-block:: javascript
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extensions: ["TeX/noUndefined.js", ...],
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TeX: {
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noUndefined: {
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attributes: {
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mathcolor: "red",
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mathbackground: "#FFEEEE",
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mathsize: "90%"
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}
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}
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}
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The ``attributes`` setting specifies attributes to apply to the
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``mtext`` element that encodes the name of the undefined macro. The
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default settings set ``mathcolor`` to ``"red"``, but do not set any
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other attributes. This example sets the background to a light pink,
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and reduces the font size slightly.
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Unicode support
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---------------
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The `unicode` extension implements a ``\unicode{}`` extension to TeX
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that allows arbitrary unicode code points to be entered in your
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mathematics. You can specify the height and depth of the character
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(the width is determined by the browser), and the default font from
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which to take the character.
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Examples:
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.. code-block:: latex
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\unicode{65} % the character 'A'
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\unicode{x41} % the character 'A'
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\unicode[.55,0.05]{x22D6} % less-than with dot, with height .55em and depth 0.05em
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\unicode[.55,0.05][Geramond]{x22D6} % same taken from Geramond font
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\unicode[Garamond]{x22D6} % same, but with default height, depth of .8em,.2em
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Once a size and font are provided for a given unicode point, they need
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not be specified again in subsequent ``\unicode{}`` calls for that
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character.
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The result of ``\unicode{...}`` will have TeX class `ORD` (i.e., it
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will act like a variable). Use ``\mathbin{...}``, ``\mathrel{...}``,
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etc., to specify a different class.
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Note that a font list can be given in the ``\unicode{}`` macro, but
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Internet Explorer has a buggy implementation of the ``font-family``
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CSS attribute where it only looks in the first font in the list that
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is actually installed on the system, and if the required glyph is not
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in that font, it does not look at later fonts, but goes directly to
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the default font as set in the `Internet-Options/Font` panel. For
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this reason, the default font list for the ``\unicode{}`` macro is
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``STIXGeneral, 'Arial Unicode MS'``, so if the user has :term:`STIX`
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fonts, the symbol will be taken from that (almost all the symbols are
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in `STIXGeneral`), otherwise MathJax tries `Arial Unicode MS`.
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The `unicode` extension is loaded automatically when you first use the
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``\unicode{}`` macro, so you do not need to add it to the `extensions`
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array. You can configure the extension as follows:
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.. code-block:: javascript
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TeX: {
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unicode: {
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fonts: "STIXGeneral, 'Arial Unicode MS'"
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}
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}
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.. _tex-commands:
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Supported LaTeX commands
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========================
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This is a long list of the TeX macros supported by MathJax. If the
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macro is defined in an extension, the name of the extension follows
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the macro name.
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.. code-block:: latex
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#
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( )
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.
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/
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[ ]
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\!
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\#
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\$
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\%
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\&
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\:
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\;
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\\
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\_
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\{ \}
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\|
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A
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\above
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\abovewithdelims
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\acute
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\aleph
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\alpha
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\amalg
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\And
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\angle
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\approx
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\approxeq AMSsymbols
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\arccos
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\arcsin
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\arctan
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\arg
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\array
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\Arrowvert
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\arrowvert
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\ast
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\asymp
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\atop
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\atopwithdelims
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B
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\backepsilon AMSsymbols
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\backprime AMSsymbols
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\backsim AMSsymbols
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\backsimeq AMSsymbols
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\backslash
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\backslash
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\bar
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\barwedge AMSsymbols
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\Bbb
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\Bbbk AMSsymbols
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\bbFont
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\because AMSsymbols
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\begin ... \end
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\begin{align*} ... \end{align*}
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\begin{alignat*} ... \end{alignat*}
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\begin{alignat} ... \end{alignat}
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\begin{alignedat} ... \end{alignedat}
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\begin{aligned} ... \end{aligned}
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\begin{align} ... \end{align}
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\begin{array} ... \end{array}
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\begin{Bmatrix} ... \end{Bmatrix}
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\begin{bmatrix} ... \end{bmatrix}
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\begin{cases} ... \end{cases}
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\begin{eqnarray*} ... \end{eqnarray*}
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\begin{eqnarray} ... \end{eqnarray}
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\begin{equation*} ... \end{equation*}
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\begin{equation} ... \end{equation}
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\begin{gather*} ... \end{gather*}
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\begin{gathered} ... \end{gathered}
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\begin{gather} ... \end{gather}
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\begin{matrix} ... \end{matrix}
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\begin{multline*} ... \end{multline*}
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\begin{multline} ... \end{multline}
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\begin{pmatrix} ... \end{pmatrix}
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\begin{smallmatrix} ... \end{smallmatrix} AMSmath
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\begin{split} ... \end{split}
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\begin{subarray} ... \end{subarray} AMSmath
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\begin{Vmatrix} ... \end{Vmatrix}
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\begin{vmatrix} ... \end{vmatrix}
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\beta
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\beth AMSsymbols
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\between AMSsymbols
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\bf
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\Big
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\big
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\bigcap
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\bigcirc
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\bigcup
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\Bigg
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\bigg
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\Biggl
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\biggl
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\Biggm
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\biggm
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\Biggr
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\biggr
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\Bigl
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\bigl
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\Bigm
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\bigm
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\bigodot
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\bigoplus
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\bigotimes
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\Bigr
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\bigr
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\bigsqcup
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\bigstar AMSsymbols
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\bigtriangledown
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\bigtriangleup
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\biguplus
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\bigvee
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\bigwedge
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\binom AMSmath
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\blacklozenge AMSsymbols
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\blacksquare AMSsymbols
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\blacktriangle AMSsymbols
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\blacktriangledown AMSsymbols
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\blacktriangleleft AMSsymbols
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\blacktriangleright AMSsymbols
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||
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\bmod
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||
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\boldsymbol
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||
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\bot
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||
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\bowtie
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\Box AMSsymbols
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||
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\boxdot AMSsymbols
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||
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\boxed AMSmath
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||
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\boxminus AMSsymbols
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||
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\boxplus AMSsymbols
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||
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\boxtimes AMSsymbols
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||
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\brace
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||
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\bracevert
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\brack
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||
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\breve
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||
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\buildrel
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||
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\bullet
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||
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\Bumpeq AMSsymbols
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||
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\bumpeq AMSsymbols
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|
C
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||
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\cal
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||
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\Cap AMSsymbols
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||
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\cap
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||
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\cases
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||
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\cdot
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||
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\cdotp
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||
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\cdots
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||
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\centerdot AMSsymbols
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||
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\cfrac AMSmath
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||
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\check
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\checkmark AMSsymbols
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||
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\chi
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||
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\choose
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||
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\circ
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||
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\circeq AMSsymbols
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||
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\circlearrowleft AMSsymbols
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||
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\circlearrowright AMSsymbols
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||
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\circledast AMSsymbols
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||
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\circledcirc AMSsymbols
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||
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\circleddash AMSsymbols
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||
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\circledR AMSsymbols
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||
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\circledS AMSsymbols
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||
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\clubsuit
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||
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\colon
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||
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\color
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||
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\complement AMSsymbols
|
||
|
\cong
|
||
|
\coprod
|
||
|
\cos
|
||
|
\cosh
|
||
|
\cot
|
||
|
\coth
|
||
|
\cr
|
||
|
\csc
|
||
|
\Cup AMSsymbols
|
||
|
\cup
|
||
|
\curlyeqprec AMSsymbols
|
||
|
\curlyeqsucc AMSsymbols
|
||
|
\curlyvee AMSsymbols
|
||
|
\curlywedge AMSsymbols
|
||
|
\curvearrowleft AMSsymbols
|
||
|
\curvearrowright AMSsymbols
|
||
|
|
||
|
D
|
||
|
\dagger
|
||
|
\daleth AMSsymbols
|
||
|
\dashleftarrow AMSsymbols
|
||
|
\dashrightarrow AMSsymbols
|
||
|
\dashv
|
||
|
\dbinom AMSmath
|
||
|
\ddagger
|
||
|
\ddddot AMSmath
|
||
|
\dddot AMSmath
|
||
|
\ddot
|
||
|
\ddots
|
||
|
\DeclareMathOperator AMSmath
|
||
|
\def
|
||
|
\deg
|
||
|
\Delta
|
||
|
\delta
|
||
|
\det
|
||
|
\dfrac AMSmath
|
||
|
\diagdown AMSsymbols
|
||
|
\diagup AMSsymbols
|
||
|
\Diamond AMSsymbols
|
||
|
\diamond
|
||
|
\diamondsuit
|
||
|
\digamma AMSsymbols
|
||
|
\dim
|
||
|
\displaylines
|
||
|
\displaystyle
|
||
|
\div
|
||
|
\divideontimes AMSsymbols
|
||
|
\dot
|
||
|
\Doteq AMSsymbols
|
||
|
\doteq
|
||
|
\doteqdot AMSsymbols
|
||
|
\dotplus AMSsymbols
|
||
|
\dots
|
||
|
\dotsb
|
||
|
\dotsc
|
||
|
\dotsi
|
||
|
\dotsm
|
||
|
\dotso
|
||
|
\doublebarwedge AMSsymbols
|
||
|
\doublecap AMSsymbols
|
||
|
\doublecup AMSsymbols
|
||
|
\Downarrow
|
||
|
\downarrow
|
||
|
\downdownarrows AMSsymbols
|
||
|
\downharpoonleft AMSsymbols
|
||
|
\downharpoonright AMSsymbols
|
||
|
|
||
|
E
|
||
|
\ell
|
||
|
\emptyset
|
||
|
\enspace
|
||
|
\epsilon
|
||
|
\eqalign
|
||
|
\eqalignno
|
||
|
\eqcirc AMSsymbols
|
||
|
\eqsim AMSsymbols
|
||
|
\eqslantgtr AMSsymbols
|
||
|
\eqslantless AMSsymbols
|
||
|
\equiv
|
||
|
\eta
|
||
|
\eth AMSsymbols
|
||
|
\exists
|
||
|
\exp
|
||
|
|
||
|
F
|
||
|
\fallingdotseq AMSsymbols
|
||
|
\fbox
|
||
|
\Finv AMSsymbols
|
||
|
\flat
|
||
|
\forall
|
||
|
\frac
|
||
|
\frac AMSmath
|
||
|
\frak
|
||
|
\frown
|
||
|
|
||
|
G
|
||
|
\Game AMSsymbols
|
||
|
\Gamma
|
||
|
\gamma
|
||
|
\gcd
|
||
|
\ge
|
||
|
\genfrac AMSmath
|
||
|
\geq
|
||
|
\geqq AMSsymbols
|
||
|
\geqslant AMSsymbols
|
||
|
\gets
|
||
|
\gg
|
||
|
\ggg AMSsymbols
|
||
|
\gggtr AMSsymbols
|
||
|
\gimel AMSsymbols
|
||
|
\gnapprox AMSsymbols
|
||
|
\gneq AMSsymbols
|
||
|
\gneqq AMSsymbols
|
||
|
\gnsim AMSsymbols
|
||
|
\grave
|
||
|
\gt
|
||
|
\gt
|
||
|
\gtrapprox AMSsymbols
|
||
|
\gtrdot AMSsymbols
|
||
|
\gtreqless AMSsymbols
|
||
|
\gtreqqless AMSsymbols
|
||
|
\gtrless AMSsymbols
|
||
|
\gtrsim AMSsymbols
|
||
|
\gvertneqq AMSsymbols
|
||
|
|
||
|
H
|
||
|
\hat
|
||
|
\hbar
|
||
|
\hbox
|
||
|
\heartsuit
|
||
|
\hom
|
||
|
\hookleftarrow
|
||
|
\hookrightarrow
|
||
|
\hphantom
|
||
|
\hskip
|
||
|
\hslash AMSsymbols
|
||
|
\hspace
|
||
|
\Huge
|
||
|
\huge
|
||
|
|
||
|
I
|
||
|
\idotsint AMSmath
|
||
|
\iff
|
||
|
\iiiint AMSmath
|
||
|
\iiint
|
||
|
\iint
|
||
|
\Im
|
||
|
\imath
|
||
|
\impliedby AMSsymbols
|
||
|
\implies AMSsymbols
|
||
|
\in
|
||
|
\inf
|
||
|
\infty
|
||
|
\injlim AMSmath
|
||
|
\int
|
||
|
\intercal AMSsymbols
|
||
|
\intop
|
||
|
\iota
|
||
|
\it
|
||
|
|
||
|
J
|
||
|
\jmath
|
||
|
\Join AMSsymbols
|
||
|
|
||
|
K
|
||
|
\kappa
|
||
|
\ker
|
||
|
\kern
|
||
|
|
||
|
L
|
||
|
\label
|
||
|
\Lambda
|
||
|
\lambda
|
||
|
\land
|
||
|
\langle
|
||
|
\LARGE
|
||
|
\Large
|
||
|
\large
|
||
|
\LaTeX
|
||
|
\lbrace
|
||
|
\lbrack
|
||
|
\lceil
|
||
|
\ldotp
|
||
|
\ldots
|
||
|
\le
|
||
|
\leadsto AMSsymbols
|
||
|
\left
|
||
|
\Leftarrow
|
||
|
\leftarrow
|
||
|
\leftarrowtail AMSsymbols
|
||
|
\leftharpoondown
|
||
|
\leftharpoonup
|
||
|
\leftleftarrows AMSsymbols
|
||
|
\Leftrightarrow
|
||
|
\leftrightarrow
|
||
|
\leftrightarrows AMSsymbols
|
||
|
\leftrightharpoons AMSsymbols
|
||
|
\leftrightsquigarrow AMSsymbols
|
||
|
\leftroot
|
||
|
\leftthreetimes AMSsymbols
|
||
|
\leq
|
||
|
\leqalignno
|
||
|
\leqq AMSsymbols
|
||
|
\leqslant AMSsymbols
|
||
|
\lessapprox AMSsymbols
|
||
|
\lessdot AMSsymbols
|
||
|
\lesseqgtr AMSsymbols
|
||
|
\lesseqqgtr AMSsymbols
|
||
|
\lessgtr AMSsymbols
|
||
|
\lesssim AMSsymbols
|
||
|
\lfloor
|
||
|
\lg
|
||
|
\lgroup
|
||
|
\lhd AMSsymbols
|
||
|
\lim
|
||
|
\liminf
|
||
|
\limits
|
||
|
\limsup
|
||
|
\ll
|
||
|
\llap
|
||
|
\llcorner AMSsymbols
|
||
|
\Lleftarrow AMSsymbols
|
||
|
\lll AMSsymbols
|
||
|
\llless AMSsymbols
|
||
|
\lmoustache
|
||
|
\ln
|
||
|
\lnapprox AMSsymbols
|
||
|
\lneq AMSsymbols
|
||
|
\lneqq AMSsymbols
|
||
|
\lnot
|
||
|
\lnsim AMSsymbols
|
||
|
\log
|
||
|
\Longleftarrow
|
||
|
\longleftarrow
|
||
|
\Longleftrightarrow
|
||
|
\longleftrightarrow
|
||
|
\longmapsto
|
||
|
\Longrightarrow
|
||
|
\longrightarrow
|
||
|
\looparrowleft AMSsymbols
|
||
|
\looparrowright AMSsymbols
|
||
|
\lor
|
||
|
\lower
|
||
|
\lozenge AMSsymbols
|
||
|
\lrcorner AMSsymbols
|
||
|
\Lsh AMSsymbols
|
||
|
\lt
|
||
|
\ltimes AMSsymbols
|
||
|
\lVert AMSmath
|
||
|
\lvert AMSmath
|
||
|
\lvertneqq AMSsymbols
|
||
|
|
||
|
M
|
||
|
\maltese AMSsymbols
|
||
|
\mapsto
|
||
|
\mathbb
|
||
|
\mathbf
|
||
|
\mathbin
|
||
|
\mathcal
|
||
|
\mathchoice
|
||
|
\mathclose
|
||
|
\mathfrak
|
||
|
\mathinner
|
||
|
\mathit
|
||
|
\mathop
|
||
|
\mathopen
|
||
|
\mathord
|
||
|
\mathpunct
|
||
|
\mathrel
|
||
|
\mathring AMSmath
|
||
|
\mathrm
|
||
|
\mathscr
|
||
|
\mathsf
|
||
|
\mathstrut
|
||
|
\mathtt
|
||
|
\matrix
|
||
|
\max
|
||
|
\mbox
|
||
|
\measuredangle AMSsymbols
|
||
|
\mho AMSsymbols
|
||
|
\mid
|
||
|
\min
|
||
|
\mit
|
||
|
\mkern
|
||
|
\mod
|
||
|
\models
|
||
|
\moveleft
|
||
|
\moveright
|
||
|
\mp
|
||
|
\mskip
|
||
|
\mspace
|
||
|
\mu
|
||
|
\multimap AMSsymbols
|
||
|
|
||
|
N
|
||
|
\nabla
|
||
|
\natural
|
||
|
\ncong AMSsymbols
|
||
|
\ne
|
||
|
\nearrow
|
||
|
\neg
|
||
|
\negmedspace AMSmath
|
||
|
\negthickspace AMSmath
|
||
|
\negthinspace
|
||
|
\neq
|
||
|
\newcommand
|
||
|
\newenvironment
|
||
|
\newline
|
||
|
\nexists AMSsymbols
|
||
|
\ngeq AMSsymbols
|
||
|
\ngeqq AMSsymbols
|
||
|
\ngeqslant AMSsymbols
|
||
|
\ngtr AMSsymbols
|
||
|
\ni
|
||
|
\nLeftarrow AMSsymbols
|
||
|
\nleftarrow AMSsymbols
|
||
|
\nLeftrightarrow AMSsymbols
|
||
|
\nleftrightarrow AMSsymbols
|
||
|
\nleq AMSsymbols
|
||
|
\nleqq AMSsymbols
|
||
|
\nleqslant AMSsymbols
|
||
|
\nless AMSsymbols
|
||
|
\nmid AMSsymbols
|
||
|
\nobreakspace AMSmath
|
||
|
\nolimits
|
||
|
\nonumber
|
||
|
\normalsize
|
||
|
\not
|
||
|
\notag
|
||
|
\notin
|
||
|
\nparallel AMSsymbols
|
||
|
\nprec AMSsymbols
|
||
|
\npreceq AMSsymbols
|
||
|
\nRightarrow AMSsymbols
|
||
|
\nrightarrow AMSsymbols
|
||
|
\nshortmid AMSsymbols
|
||
|
\nshortparallel AMSsymbols
|
||
|
\nsim AMSsymbols
|
||
|
\nsucc AMSsymbols
|
||
|
\nsucceq AMSsymbols
|
||
|
\ntriangleleft AMSsymbols
|
||
|
\ntrianglelefteq AMSsymbols
|
||
|
\ntriangleright AMSsymbols
|
||
|
\ntrianglerighteq AMSsymbols
|
||
|
\nu
|
||
|
\nVDash AMSsymbols
|
||
|
\nVdash AMSsymbols
|
||
|
\nvDash AMSsymbols
|
||
|
\nvdash AMSsymbols
|
||
|
\nwarrow
|
||
|
|
||
|
O
|
||
|
\odot
|
||
|
\oint
|
||
|
\oldstyle
|
||
|
\Omega
|
||
|
\omega
|
||
|
\omicron
|
||
|
\ominus
|
||
|
\operatorname AMSmath
|
||
|
\oplus
|
||
|
\oslash
|
||
|
\otimes
|
||
|
\over
|
||
|
\overbrace
|
||
|
\overleftarrow
|
||
|
\overleftrightarrow
|
||
|
\overline
|
||
|
\overrightarrow
|
||
|
\overset
|
||
|
\overwithdelims
|
||
|
\owns
|
||
|
|
||
|
P
|
||
|
\parallel
|
||
|
\partial
|
||
|
\perp
|
||
|
\phantom
|
||
|
\Phi
|
||
|
\phi
|
||
|
\Pi
|
||
|
\pi
|
||
|
\pitchfork AMSsymbols
|
||
|
\pm
|
||
|
\pmatrix
|
||
|
\pmb
|
||
|
\pmod
|
||
|
\pod
|
||
|
\Pr
|
||
|
\prec
|
||
|
\precapprox AMSsymbols
|
||
|
\preccurlyeq AMSsymbols
|
||
|
\preceq
|
||
|
\precnapprox AMSsymbols
|
||
|
\precneqq AMSsymbols
|
||
|
\precnsim AMSsymbols
|
||
|
\precsim AMSsymbols
|
||
|
\prime
|
||
|
\prod
|
||
|
\projlim AMSmath
|
||
|
\propto
|
||
|
\Psi
|
||
|
\psi
|
||
|
|
||
|
Q
|
||
|
\qquad
|
||
|
\quad
|
||
|
|
||
|
R
|
||
|
\raise
|
||
|
\rangle
|
||
|
\rbrace
|
||
|
\rbrack
|
||
|
\rceil
|
||
|
\Re
|
||
|
\require
|
||
|
\restriction AMSsymbols
|
||
|
\rfloor
|
||
|
\rgroup
|
||
|
\rhd AMSsymbols
|
||
|
\rho
|
||
|
\right
|
||
|
\Rightarrow
|
||
|
\rightarrow
|
||
|
\rightarrowtail AMSsymbols
|
||
|
\rightharpoondown
|
||
|
\rightharpoonup
|
||
|
\rightleftarrows AMSsymbols
|
||
|
\rightleftharpoons
|
||
|
\rightleftharpoons AMSsymbols
|
||
|
\rightrightarrows AMSsymbols
|
||
|
\rightsquigarrow AMSsymbols
|
||
|
\rightthreetimes AMSsymbols
|
||
|
\risingdotseq AMSsymbols
|
||
|
\rlap
|
||
|
\rm
|
||
|
\rmoustache
|
||
|
\root
|
||
|
\Rrightarrow AMSsymbols
|
||
|
\Rsh AMSsymbols
|
||
|
\rtimes AMSsymbols
|
||
|
\Rule
|
||
|
\rVert AMSmath
|
||
|
\rvert AMSmath
|
||
|
|
||
|
S
|
||
|
\S
|
||
|
\scr
|
||
|
\scriptscriptstyle
|
||
|
\scriptsize
|
||
|
\scriptstyle
|
||
|
\searrow
|
||
|
\sec
|
||
|
\setminus
|
||
|
\sf
|
||
|
\sharp
|
||
|
\shortmid AMSsymbols
|
||
|
\shortparallel AMSsymbols
|
||
|
\shoveleft AMSmath
|
||
|
\shoveright AMSmath
|
||
|
\sideset AMSmath
|
||
|
\Sigma
|
||
|
\sigma
|
||
|
\sim
|
||
|
\simeq
|
||
|
\sin
|
||
|
\sinh
|
||
|
\skew
|
||
|
\small
|
||
|
\smallfrown AMSsymbols
|
||
|
\smallint
|
||
|
\smallsetminus AMSsymbols
|
||
|
\smallsmile AMSsymbols
|
||
|
\smash
|
||
|
\smile
|
||
|
\Space
|
||
|
\space
|
||
|
\spadesuit
|
||
|
\sphericalangle AMSsymbols
|
||
|
\sqcap
|
||
|
\sqcup
|
||
|
\sqrt
|
||
|
\sqsubset AMSsymbols
|
||
|
\sqsubseteq
|
||
|
\sqsupset AMSsymbols
|
||
|
\sqsupseteq
|
||
|
\square AMSsymbols
|
||
|
\stackrel
|
||
|
\star
|
||
|
\strut
|
||
|
\Subset AMSsymbols
|
||
|
\subset
|
||
|
\subseteq
|
||
|
\subseteqq AMSsymbols
|
||
|
\substack AMSmath
|
||
|
\succ
|
||
|
\succapprox AMSsymbols
|
||
|
\succcurlyeq AMSsymbols
|
||
|
\succeq
|
||
|
\succnapprox AMSsymbols
|
||
|
\succneqq AMSsymbols
|
||
|
\succnsim AMSsymbols
|
||
|
\succsim AMSsymbols
|
||
|
\sum
|
||
|
\sup
|
||
|
\Supset AMSsymbols
|
||
|
\supset
|
||
|
\supseteq
|
||
|
\supseteqq AMSsymbols
|
||
|
\surd
|
||
|
\swarrow
|
||
|
|
||
|
T
|
||
|
\tag
|
||
|
\tan
|
||
|
\tanh
|
||
|
\tau
|
||
|
\tbinom AMSmath
|
||
|
\TeX
|
||
|
\text
|
||
|
\textbf
|
||
|
\textit
|
||
|
\textrm
|
||
|
\textstyle
|
||
|
\tfrac AMSmath
|
||
|
\therefore AMSsymbols
|
||
|
\Theta
|
||
|
\theta
|
||
|
\thickapprox AMSsymbols
|
||
|
\thicksim AMSsymbols
|
||
|
\thinspace
|
||
|
\tilde
|
||
|
\times
|
||
|
\Tiny
|
||
|
\tiny
|
||
|
\to
|
||
|
\top
|
||
|
\triangle
|
||
|
\triangledown AMSsymbols
|
||
|
\triangleleft
|
||
|
\trianglelefteq AMSsymbols
|
||
|
\triangleq AMSsymbols
|
||
|
\triangleright
|
||
|
\trianglerighteq AMSsymbols
|
||
|
\tt
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\twoheadleftarrow AMSsymbols
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\twoheadrightarrow AMSsymbols
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U
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\ulcorner AMSsymbols
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\underbrace
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\underleftarrow
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\underleftrightarrow
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\underline
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\underrightarrow
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\underset
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\unicode
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\unlhd AMSsymbols
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\unrhd AMSsymbols
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\Uparrow
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\uparrow
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\Updownarrow
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\updownarrow
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\upharpoonleft AMSsymbols
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\upharpoonright AMSsymbols
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\uplus
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\uproot
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\Upsilon
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\upsilon
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\upuparrows AMSsymbols
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\urcorner AMSsymbols
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V
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\varDelta AMSsymbols
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\varepsilon
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\varGamma AMSsymbols
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\varinjlim AMSmath
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\varkappa AMSsymbols
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\varLambda AMSsymbols
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||
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\varliminf AMSmath
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\varlimsup AMSmath
|
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\varnothing AMSsymbols
|
||
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\varOmega AMSsymbols
|
||
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\varPhi AMSsymbols
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||
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\varphi
|
||
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\varPi AMSsymbols
|
||
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\varpi
|
||
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\varprojlim AMSmath
|
||
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\varpropto AMSsymbols
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||
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\varPsi AMSsymbols
|
||
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\varrho
|
||
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\varSigma AMSsymbols
|
||
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\varsigma
|
||
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\varTheta AMSsymbols
|
||
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\vartheta
|
||
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\vartriangle AMSsymbols
|
||
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\vartriangleleft AMSsymbols
|
||
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\vartriangleright AMSsymbols
|
||
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\varUpsilon AMSsymbols
|
||
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\varXi AMSsymbols
|
||
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\vcenter
|
||
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\Vdash AMSsymbols
|
||
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\vDash AMSsymbols
|
||
|
\vdash
|
||
|
\vdots
|
||
|
\vec
|
||
|
\vee
|
||
|
\veebar AMSsymbols
|
||
|
\verb
|
||
|
\Vert
|
||
|
\vert
|
||
|
\vphantom
|
||
|
\Vvdash AMSsymbols
|
||
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|
||
|
W
|
||
|
\wedge
|
||
|
\widehat
|
||
|
\widetilde
|
||
|
\wp
|
||
|
\wr
|
||
|
|
||
|
X
|
||
|
\Xi
|
||
|
\xi
|
||
|
\xleftarrow AMSmath
|
||
|
\xrightarrow AMSmath
|
||
|
|
||
|
Y
|
||
|
\yen AMSsymbols
|
||
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||
|
Z
|
||
|
\zeta
|
||
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