As mentioned in the overview,
Section 3.6, we use
LaTeX syntax for mathematics. In order to allow for quality display in
HTML, and other electronic formats, this limits us to the subset of
LaTeX supported by the very capable
MathJax Javascript library. Generally this looks like the
amsmath package maintained by the American Mathematical Society at their
AMS-LaTeX page. For a complete and precise list of what MathJax supports, see MathJax’s
Supported TeX/LaTeX commands. Once you have digested this more general section, be sure to also consult
Section 4.10 for some very specific suggestions.
Subsection 4.9.3 Multi-line Display Mathematics
We begin with the
<md> element, but now used as a container. Within the container, content, on a per-line basis, goes into a
<mrow> element. You can think of
<mrow> as being very similar to a one-line
<md> that does not have additional structure. In a
LaTeX align environment, the
\\ marks the end of a displayed line. In PreTeXt each
<mrow> delimits a displayed line, and there are no
\\s. Use
\amp to mark the alignment point.
On any given
<mrow> you can place the
@number attribute, with allowable values of
yes and
no. These will typically be used to override the behavior you might place on the
<md> container, via an overall
@number attribute, but there is no harm if they are redundant. A given line of the display may be the target of a cross-reference (
<xref>) via an
@xml:id attribute, though the numbering flexibility means you can try (and fail) to target an unnumbered equation.
An <mrow> may have a @tag attribute in place of a @number attribute. This will create a “number” on the equation which is just a symbol. This is meant for situations where you do not want to use numbers, and the resulting cross-reference is “local.” In other words, the <xref> and its target are not far apart, such as maybe within the same <example> or the same <proof>. Allowable values for the attribute are:
star, dstar, tstar,
dagger, ddagger, tdagger,
daggerdbl, ddaggerdbl, tdaggerdbl,
hash, dhash, thash,
maltese, dmaltese, tmaltese
These are the names of symbols, with prefixes where the prefix
d means “double”, and the prefix
t means “triple”. Cross-references to these tagged equations happens in the usual way and should behave as expected. See
Section 3.4 and
Section 4.5 for more on cross-references.
Finally, the default is to not number displayed expressions. If you want every displayed expression numbered, or you find yourself electing to number the majority of the displayed expressions, then there is a global default. In your
<docinfo> element, put a
@equations attribute on the
<numbering> element, and set its value to
yes, rather than the default
no.
Subsection 4.9.5 Text in Mathematics
Once in a while, you need a little bit of “regular” text within an expression and you do not want it to look like a product of a bunch of one-letter variables. Use the \text{} macro for these. Only. Other ways of switching out of math-mode and into some sort of “regular” text will appear inferior, and can raise errors in certain conversions.
-
Do place surrounding spaces inside the \text{} macro.
-
Do not place any mathematics inside the \text{} macro.
-
Do not use the \mbox{} macro as a substitute.
-
Do not use font-changing commands (e.g. \rm) as a substitute.
For example,
<me>f(x) = \begin{cases} x^2 \amp \text{if } x\gt 0\\
-7 \amp \text{otherwise} \end{cases}</me>
produces
\begin{equation*}
f(x) = \begin{cases}x^2\amp\text{if }x\gt 0\\-7\amp\text{otherwise}\end{cases}\text{.}
\end{equation*}
This example amply illustrates the use of macros for XML exceptional characters (twice), appropriate use of the \text{} macro (twice), spaces in the \text{} macro (once), sentence-ending punctuation (see the source, the period is not inside the <md> element) and yes, we did think twice about the \\ (an exception to the rule).
Subsection 4.9.8 Alignment in Display Mathematics
Displayed mathematics is implemented with the AMS-
LaTeX align environment. Ampersands are used to control this, so use the
\amp macro for these. The first ampersand in a line or row is an alignment point, typically a symbol, like an equality. The next ampersand is a column separator, then the next is an alignment point, then a column separator, then… The moral of the story is you should have
\(n\) alignment points, with
\(n-1\) column separators, for a total of
\(2n-1\) ampersands—always an odd number.
For example,
<md>
<mrow>A \amp = B \amp D \amp = E \amp \amp \text{Because}</mrow>
<mrow> \amp = C \amp \amp = F \amp \amp <xref ref="txo" /></mrow>
</md>
produces
\begin{align*}
A \amp = B \amp D \amp = E \amp \amp\text{Because}\\
\amp = C \amp \amp = F \amp \amp\knowl{./knowl/xref/txo.html}{\text{Table 4.5.3}}\text{.}
\end{align*}
Sometimes you want several short equations on one line. Do not use the bare
<md>. Instead use a single
<mrow> inside an
<md>, and use alignment to spread them out evenly.
For multi-line display mathematics with no ampersands present, each line will be centered. This is implemented with the AMS-
LaTeX gather environment.
You can fool the alignment behavior by hiding all your ampersands in macro definitions, so there is the optional
@alignment attribute for the
<md> element, in order to force the right kind of alignment. Allowable values are
gather,
align, and
alignat. The latter is similar to
align, but no space is automatically provided between columns. You can leave it that way, or explicitly add your own. For example, this allows you to precisely arrange individual terms of a system of linear equations, especially when terms with zero coefficients are omitted. When using the
alignat option PreTeXt tries to count ampersands to see how many columns you intend, since
LaTeX needs this number (we are not sure why). This detection can be fooled too, especially if you have something like a matrix with lots of ampersands for other purposes. So set the
@alignat-columns attribute to the
number of intended columns, if necessary.
If you have many aligned equation in a single
<md>, but want to add a short sentence or two somewhere in the middle, place it in an
<intertext> element, and keep it simple. Just some words and punctuation, plus maybe some elements like
<em> or
<q>, but nothing like a list. In
PDF output constructed via
LaTeX the alignment will be preserved across the break for the intertext (since this feature is inspired by
LaTeX’s
\intertext{} macro). Unfortunately, this is too complicated in other (electronic) output formats, so we just do the best we can to preserve your intent. Perhaps some day, MathJax will be more capable, and we can make your source do better.
Subsection 4.9.9 Commutative Diagrams
Commutative diagrams may be authored using the
AMS LaTeX amscd package. While restricted in some ways, such as the lack of sloped or curved arrows, it has one important advantage over more general drawing tools. Support for
HTML output comes from MathJax, and hence has accessible versions included in the output.
Typical use would be within an
<md> element, so starting with
\begin{CD}. Despite this being multi-line output, we have not chosen to integrate it within the more general
md/mrow structure, but that decision can be revisited.
Subsection 4.9.12 Your Macros
These go in the
<docinfo> section, wrapped in a
<macros> element. Keep them simple—one or two arguments, and one-line definitions. This is not the place to be fancy, and not the place to try to end-run the structural aspects of PreTeXt. The idea is to define something like
\adjoint{A} for the matrix
A to be a superscript asterisk, and later you can change your mind and use a superscript dagger instead. Keep in the spirit of PreTeXt and use readable, semantic macros. For example, do not use
\a{A} for the adjoint of
A. Repeating: keep your
LaTeX macros simmple, and to a single line.
PreTeXt will use your macros correctly for print and for
HTML, after erasing whitespace from the left margin, and stripping
LaTeX comments.
The name of your macros also cannot contain any numbers, otherwise MathJax will “silently” fail and may not read any subsequent macros you might have. This is important because PreTeXt will place custom macros for you at the end of your own, defined at
Subsection 4.9.4, to be used. Those would fail to be processed by MathJax if your own macros caused it to stop reading.
Subsection 4.9.14 Punctuation After Display Math
If a chunk of displayed math concludes a sentence, then the sentence-ending punctuation should appear at the conclusion of the display. (And certainly not at the start of the first line after the display!) But do not author the punctuation within the mathematics element, put it afterwards, where it logically belongs.
More specifically, place a sentence-ending period (say)
immediately after the closing of an
<md> element. PreTeXt will place the period in your output in the right place and in the right way. (By using
LaTeX’s
\text{} macro, if you are curious to know the details.) Here is an example. The
XML source
<md>
<mrow>(a+b)^2</mrow>
</md>. Now...
will render as
\begin{gather*}
(a+b)^2\text{.}
\end{gather*}
Now…
This all applies more generally to clause-ending punctuation, such as a comma. Take notice of the requirement that the punctuation must be
immediately after the closing tag of the math element, otherwise it will not migrate properly. For example, do not interrupt the flow with whitespace, or an
XML comment, or anything else.
For inline mathematics (the
<m> element) the same authoring principle holds, though you would likely do this naturally. Author the punctuation
outside the element, where it will remain.
Here is a technical subtlety that will demonstrate some of the inner machinery of PreTeXt and our conversions. In your work, locate a theorem that has some numbered display mathematics (
md) which is at the end of a sentence, and which you have authored as described above. In
HTML output, test a cross-reference (
xref) to the theorem and you will see the period for the end of the sentence at the end of the display, where it should be. Now test a cross-reference (
xref) to one of the numbered equations. First, the knowl will contain the entire display, to provide context, but it also will not contain the period, since the rest of the sentence is not in the knowl and so the period is not necessary.
Subsection 4.9.15 Lists of Mathematical Expressions
It is common to make lists of expressions, equations, or identities. Think of the definitions of trigonometric functions, a collection of antiderivatives, or a compendium of generating functions.
In these situations, author a list item,
<li>, within an
<ol> or
<ul>, by using
only the necessary
<m> element. Do not use an intervening
<p>, and do not include any adjacent text. Whitespace is OK. Then PreTeXt will add
LaTeX’s
\displaystyle command to improve the visual appearance of the mathematics, and so you do not need to.
If you prefer to not have this behavior, insert an intervening
<p>, and output will be identical, but without the
\displaystyle.
Note that
any text, other than whitespace, outside the
<m> tag will disable this feature,
including punctuation. However, according to the
Chicago Manual of Style [1, 6.127], “Items carry no closing punctuation unless they consist of complete sentences.” So that comma at the end of your equation probably doesn’t belong there anyway.
Subsection 4.9.16 LaTeX Packages, MathJax Extensions
LaTeX, which we use as the syntax for mathematics, allows extensive customization through
packages, which are enabled through a
\usepackage{} macro. Packages also provide extensive customization or control over the document structure. Thus, PreTeXt provides support for additional packages
to enhance mathematical content, but does not have any facility beyond this (e.g. to influence or support document structure).
We use
LaTeX to create
PDF and print output. For most other electronic formats, we use MathJax to embed mathematics onto a web page or to make images of mathematics used in EPUB, and so on. MathJax has
extensions, which mimic certain
LaTeX packages. For a list of supported extensions see MathJax’s
TeX/LaTeX Extension List. Note that some of these extensions are technical (not supporting mathematical syntax) and some we load already as part of setting up MathJax, so carefully evaluate how a given package is selected to support certain macros.
Suppose there is a
LaTeX math-mode macro you would like to use. We will illustrate with the
\cancelto macro that is part of the fairly standard
cancel package. It will draw an arrow through a mathematical formula, with a replacement value. Conveniently, MathJax has a
cancel extension, and this extension
also defines the
\cancelto macro. You need to check this, as a
LaTeX package and a MathJax extension are not guaranteed to define the same collection of macros. Nor are the two guaranteed to have the same name (though this is best practice).
To make the \cancelto macro available and active in your mathematical elements (<m> or <md>) add the following to your <docinfo> element:
<math-package latex-name="cancel" mathjax-name="cancel"/>
Now you may freely use the \cancelto macro in your mathematics, confident that it will render correctly in all output formats.
Note that both attributes
@latex-name and
@mathjax-name must be present. They may be identical (as above, and typical) or they may be different (rare). There are situations where one might be empty. Of course, you can use these macros in other definitions of mathematics macros you might make (
Subsection 4.9.12). However, we do not guarantee the absence of conflicts with other packages in use, even if employed by PreTeXt. Nor do we support debugging such conflicts.
If there are
LaTeX macros you desire, but without a MathJax implementation, then there is not much we can do, short of suggesting you write your own extension (not recommended, see
A Custom Extension). There are some workarounds which we may document shortly.
