AmsMath Guide in Org

The amsmath package provides a number of additional displayed equation structures beyond the ones provided in basic latex. The augmented set includes align, alignat, equation , flalign, gather, multline, with asterisk alternative, and split without.

Although the standard eqnarray environment remains available, it is better to use align or equation & split instead. Within eqnarray, spacing around signs of relation is not the preferred mathematical spacing, and is inconsistent with that spacing as it appears in other environments. Long lines in this environment may result in misplaced or overprinted equation numbers. This environment also does not support the use of \qed or \qedhere as provided by theorem packages.

Except for split, each environment has both starred and unstarred forms, where the unstarred forms have automatic numbering using latex's equation counter. You can suppress the number on any particular line by putting \notag before the end of that line.

\notag should not be used outside a display environment as it will mess up the numbering.

You can also override a number with a tag of your own using \tag{label}, where label means arbitrary text such as $*$ or ii used to “number” the equation. A tag can reference a different tagged display by use of \tag{\ref{label}modifier} where modifier is optional. If you include hyperref, use \ref*{}; using the starred form of \ref{} prevents a reference to a modified tag containing a nested link from linking to the original display.

There is also a \tag*{} command that causes the text you supply to be typeset literally, without adding parentheses around it. \tag{} and \tag*{} can also be used within the unnumbered versions of all the amsmath alignment structures. Some examples of the use of \tag{} may be found in the sample files 📂 testmath.tex and 📂 subeqn.tex provided with the amsmath package.

The split environment is a special subordinate form that is used only inside one of the others. It cannot be used inside multline, however. split supports only one alignment column, i.e. only one & character; if more are needed, aligned or alignedat should be used. The width of a split structure is the full line width.

In the structures that do alignment, i.e., split, align, alignat, and flalign, relation symbols have an & before them but not after — unlike eqnarray. Putting the & after the relation symbol will interfere with the normal spacing; it has to go before.

In all multiline environments, lines are divided by \\.

The \\ should not be used to end the last line. Using it there will result in unwanted extra vertical space following the display.

In all math environments, no matter if inline or display, blank lines, or the equivalents to \par, are not permitted, and will result in an error. → See Section 4.9.

The equation environment is for a single equation with an automatically generated number. The equation* environment is the same except for omitting the number.

Basic latex doesn't provide an equation* environment, but rather a functionally equivalent environment named displaymath.

The wrapper \[ ... \] is equivalent to equation*.

The multline environment is a variation of the equation environment used for equations that don't fit on a single line. The first line of a multline will be at the left margin and the last line at the right margin, except for an indention on both sides in the amount of \multlinegap{}. Any additional lines in between will be centered independently within the display width, unless the fleqn option is in effect.

Like equation, multline has only a single equation number (thus, none of the individual lines should be marked with \notag). The equation number is placed on the last line (\opt{reqno} option) or first line (\opt{leqno} option); vertical centering as for split is not supported by multline.%

It's possible to force one of the middle lines to the left or right with commands \shoveleft{}, \shoveright{}. These commands take the entire line as an argument, up to but not including the final \\; for example \shoveright{+e-f}\\ would shift the line \(+e-f\) in Figure 2 to the right leaving a virtual gap for the number (3) below.

The value of \multlinegap{} can be changed with the latex core commands \setlength{}{} or \addtolength{}{}.

Like multline, the split environment is for single equations that are too long to fit on one line and hence must be split into multiple lines. Unlike multline, however, the split environment provides for alignment among the split lines, using & to mark alignment points. Unlike the other amsmath equation structures, the split environment provides no numbering, because it is intended to be used only inside some other displayed equation structure, usually an equation, align, or gather environment, which provides the numbering. Check the difference in Figure 2.

The split structure should constitute the entire body of the enclosing structure, apart from commands like \label{} that produce no visible material.

The gather environment is used for a group of consecutive equations when there is no alignment desired among them; each one is centered separately within the text width, see Figure 3.

Equations inside gather are separated by a \\ command. Any equation in a gather may mix with split environments, for example:

\begin{gather} 1st equation \\ 2nd equation \\
\begin{split} 3rd & two \\ & line eqn \end{split} \\
4th equation \\ 5th ... get the picture ... \end{gather}

The align environment is used for two or more equations when vertical alignment is desired; usually binary relations such as equal signs are aligned, like in Figure 4.

To have several equation columns side-by-side, use extra ampersands to separate the columns:

\begin{align}
x&=y       & X&=Y       & a&=b+c\\
x'&=y'     & X'&=Y'     & a'&=b\\
x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b
\end{align}

Line-by-line annotations on an equation can be done by judicious application of \text{} inside an align environment:

\begin{align}
x& = y_1-y_2+y_3-y_5+\dots && \text{by \eqref{eq:C}}\\
 & = y'\circ y^*           && \text{by \eqref{eq:D}}\\
 & = y(0) y'           && \text {by Axiom 1.}
\end{align}

A variant environment alignat allows the horizontal space between equations to be explicitly specified. This environment takes one argument, the number of “equation columns” (the number of pairs of right-left aligned columns; the argument is the number of pairs): count the maximum number of ampersands in any row, add 1 and divide by 2.

\begin{alignat}{2}
x& = y_1-y_2+y_3-y_5+\dots &\;& \text{by \eqref{eq:C}}\\
 & = y'\circ y^*             && \text{by \eqref{eq:D}}\\
 & = y(0) y'             && \text {by Axiom 1.}
\end{alignat}

The environment flalign, i.e., full length alignment, stretches the space between the equation columns to the maximum possible width, leaving only enough space at the margin for the equation number, if present.

Like equation, the multi-equation environments gather, align, and alignat are designed to produce a structure whose width is the full line width. This means, for example, that one cannot readily add parentheses around the entire structure. But the variants gathered, aligned, and alignedat are provided whose total width is the actual width of the contents; thus they can be used as a component in a containing expression. E.g.,

\begin{equation*}\left.\begin{aligned}
  \frac{\partial B}{\partial t}&=-\nabla\times E,\\
  \frac{\partial E}{\partial t}&=\nabla\times B - 4\pi j,
\end{aligned}\right\}\qquad 
\text{Maxwell's equations} \end{equation*}

Like the array environment, these -ed variants also take an optional [t] top, [b] bottom or the default [c] center option argument to specify vertical positioning.

For maximum interoperability, do not insert a space or line break before the option.

Certain equation environments wrap their contents in an unbreakable box, with the consequence that neither \displaybreak nor \allowdisplaybreaks will have any effect on them. These include split, aligned, gathered, and alignedat.

Case constructions like the following are common in mathematics:

and in the amsmath package there is a cases environment to make them easy to write:

P_{r-j}=\begin{cases}
    0&  \text{if $r-j$ is odd},\\
    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
  \end{cases}

Notice the use of \text{} – → see Section 6 – and the nested math formulas. The cases environment is set in \textstyle. If \displaystyle is wanted, it must be requested explicitly; mathtools provides a dcases environment for this purpose.

The -ed and cases environments must appear within an enclosing math environment, which can be either in text, between $...$, or in any of the display environments.

Placing equation numbers can be a rather complex problem in multiline displays. The environments of the amsmath package try hard to avoid overprinting an equation number on the equation contents, if necessary moving the number down or up to a separate line. Difficulties in accurately calculating the profile of an equation can occasionally result in number movement that doesn't look right.

A \raisetag{} command is provided to adjust the vertical position of the current equation number, if it has been shifted away from its normal position. To move a particular number up by six points, write \raisetag{6pt}.

At the end of a display, the \raisetag{} command also shifts up the text following the display.

A \raisetag{} adjustment is fine tuning like line breaks and page breaks, and should be left undone until your document is nearly finalized, or you may end up redoing the fine tuning several times to keep up with changing document contents.

You can use the \\[dimension] command to get extra vertical space between lines in all the amsmath displayed equation environments, as is usual in latex.

Do not type a space between the \\ and the following [; only for display environments defined by amsmath the space is interpreted to mean that the bracketed material is part of the document content.

When the amsmath package is in use between equation lines are normally disallowed; the philosophy is that page breaks in such material should receive individual attention from the author. To get an individual page break inside a particular displayed equation, a \displaybreak command is provided. \displaybreak is best placed immediately before the \\ where it is to take effect. Like latex's \pagebreak, \displaybreak takes an optional argument between 0 and 4 denoting the desirability of the pagebreak. \displaybreak[0] means “it is permissible to break here” without encouraging a break; \displaybreak with no optional argument is the same as \displaybreak[4] and forces a break.

If you prefer a strategy of letting page breaks fall where they may, even in the middle of a multiline equation, then you might put \allowdisplaybreaks[1] in the preamble of your document. An optional argument 1–4 can be used for finer control: [1] means allow page breaks, but avoid them as much as possible; values of 2,3,4 mean increasing permissiveness. When display breaks are enabled with \allowdisplaybreaks, the \\* command can be used to prohibit a pagebreak after a given line, as usual.

Certain equation environments wrap their contents in an unbreakable box, with the consequence that neither \displaybreak nor \allowdisplaybreaks will have any effect on them. These include split, aligned, gathered, and alignedat.

The command \intertext{} is used for a short interjection of one or two lines of text in the middle of a multiple-line display structure; → see also Section 6 The text command of the User’s Guide for the amsmath Package. Its salient feature is preservation of the alignment, which would not happen if you simply ended the display and then started it up again afterwards. \intertext{} may only appear right after a \\ or \\* command. Notice the position of the word “and” in the example depicted in Figure 6, produced by

\begin{align}
  A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\
  A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\
\intertext{and}
  A_3&=\mathcal{N}(\lambda;\omega).
\end{align}

The mathtools package provides a command \shortintertext{} that is intended for use when the interjected text is only a few words; it uses less vertical space than \intertext{}. This is most effective when equation numbers are on the right.

The amsmath package provides some environments for matrices beyond the basic array environment of latex. The pmatrix, bmatrix, Bmatrix, vmatrix and Vmatrix have, respectively, \((\,)\), \([\,]\), \(\lbrace\,\rbrace\), \(\lvert\,\rvert\), and \(\lVert\,\rVert\) delimiters built in. For naming consistency there is a matrix environment sans delimiters. This is not entirely redundant with the array environment; the matrix environments all use more economical horizontal spacing than the rather prodigal spacing of the array environment. Also, unlike the array environment, you don't have to give column specifications for any of the matrix environments; by default you can have up to 10 centered columns.

The maximum number of columns in a matrix is determined by the counter MaxMatrixCols, default value .. 10, which you can change if necessary using latex's \setcounter{}{} or \addtocounter{}{} commands.

If you need left or right alignment in a column or other special formats you may use the array environment, or the mathtools package which provides starred variants of these environments with an optional argument to specify left or right alignment.

To produce a small matrix suitable for use in text, there is a smallmatrix environment, e.g., \( \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) \), that comes closer to fitting within a single text line than a normal matrix. Delimiters must be provided. The mathtools package provides p, b, B, v, and V versions of smallmatrix, as well as * variants as described above. The above example was produced by

\bigl( \begin{smallmatrix}
  a&b\\ c&d
\end{smallmatrix} \bigr)

\hdotsfor[]{n} produces a row of dots in a matrix spanning the given number of columns. For example,

This construct doesn't work with mathjax. Even in latex there are reported interferences with colortbl, see stackoverflow entry Interaction between \hdotsfor and colortbl: Bug or Feature? Results of this interference are shown in Figure 7, right and Figure 8, right: the dots just spans a region without the marginal colums of the specified range. It is described as a conflict of \fill commands.

If the command works the spacing of the dots can be varied through use of a square-bracket option, for example, \hdotsfor[1.5]{3}. The number in square brackets will be used as a multiplier, i.e., the normal value is 1.0. Figure 8, left, shows the effect of spacing two. The matrix on the right shows the colortbl conflict, and a regular \dots solution produced by the code

\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
\hdotsfor[2]{4}\\ \dots&\dots&\dots&\dots\\
-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}

The amsmath package slightly extends the set of math spacing commands, as shown in Table 1. Both the spelled-out and abbreviated forms of these commands are robust, and they can also be used outside of math.

For the greatest possible control over math spacing, use \mspace{} and math units. One math unit, or mu, is equal to 1/18 em. Thus to get a negative \quad{} you could write \mspace{-18.0mu}.

For preferred placement of ellipsis dots, raised or on the base line, in various contexts there is no general consensus. It may therefore be considered a matter of taste. By using the semantically oriented commands

• \dotsc{} for “dots with commas”
• \dotsb{} for “dots with binary operators/relations”
• \dotsm{} for “multiplication dots”
• \dotsi{} for “dots with integrals”
• \dotso{} for “other dots” (none of the above)

instead of \ldots and \cdots, you make it possible for your document to be adapted to different conventions on the fly, in case (for example) you have to submit it to a publisher who insists on following house tradition in this respect. The default treatment for the various kinds follows American Mathematical Society conventions; see the example below, first the code and then its compilation, where the \dot variations are used in the order given by the itemlist above:

Then we have the series \(A_1, A_2, \dotsc\), the regional
sum \(A_1 +A_2 +\dotsb\), the orthogonal product
\(A_1 A_2 \dotsm\), and the infinite integral
\[\int_{A_1}\int_{A_2}\dotsi.\]

Then we have the series \(A_1,A_2,\dotsc\), the regional sum \(A_1+A_2+\dotsb\), the orthogonal product \(A_1A_2\dotsm\), and the infinite integral \[\int_{A_1}\int_{A_2}\dotsi.\]

For most situations, the undifferentiated \dots can be used, and amsmath will output the most suitable form based on the immediate context; if an inappropriate form results, it can be corrected after examining the output.

A command \nobreakdash is provided to suppress the possibility of a line break after the following hyphen or dash. For example, if you write “pages 1– 9” as pages 1\nobreakdash--9 then a line break will never occur between the dash and the 9. You can also use \nobreakdash to prevent undesirable hyphenations in combinations like $p$-adic. For frequent use, it's advisable to construct new macros, e.g.,

\newcommand{\p}{$p$\nobreakdash}% for "\p-adic"
\newcommand{\Ndash}{\nobreakdash--}% for "pages 1\Ndash 9"
%    For "\n dimensional" ("n-dimensional"):
\newcommand{\n}[1]{$n$\nobreakdash-\hspace{0pt}}

The last example shows how to prohibit a line break after the hyphen but allow normal hyphenation in the following word. To accomplish this it suffices to add a zero-width space after the hyphen.

In ordinary latex the placement of the second accent in doubled math accents is often poor. With the amsmath package you will get improved placement of the second accent, i.e., \hat{\hat{A}} compiles to \(\hat{\hat{A}}\) and triggers a customization of the line height.

The commands \dddot and \ddddot are available to produce triple and quadruple dot accents \(\dddot{a}\) and \(\ddddot{a}\) in addition to the \dot and \ddot accents \(\dot{a}\) and \(\ddot{a}\) already available in latex.

To get a superscripted hat or tilde character, load the amsxtra package and use \sphat or \sptilde. Usage is A\sphat. Note the absence of the superscript operator ^.

To place an arbitrary symbol in math accent position, or to get under accents, see the accents package by Javier Bezos. And make sure to load amsmath before accents.

Sometimes we might not be happy with the default latex placement of root indices, e.g., \sqrt[\beta]{k} looks like \(\sqrt[\beta]{k}\). In the amsmath package \leftroot{} and \uproot{} allow you to adjust the position of the root:

\sqrt[\leftroot{-2}\uproot{2}\beta]{k}

will move the beta up and to the right: \(\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\). The negative argument used with \leftroot{-2} moves the \(\beta\) to the right. The units are normalized to a small amount that is a useful size for such adjustments.

The command \boxed{} puts a box around its argument, like \fbox{} except that the contents are in math mode, e.g.

is the result of

\begin{equation}
\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
\end{equation}

Basic latex provides \overrightarrow{} and \overleftarrow{} commands. Some additional over and under arrow commands are provided by the amsmath package to extend to concepts shown in Table 2.

\xleftarrow{} and \xrightarrow{} produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts. These commands take one optional subscript argument and one superscript argument:

A\xleftarrow{\overrightarrow{n+\mu-1}}%
B\xrightarrow[T]{n\pm i-1}%
C\xrightarrow[?]{\overleftarrow{\mspace{36mu}}}%
D\xrightarrow[\text{sunrise}]{}E

Here mathjax provides only some idea of the concept, while the latex compilation seems to include more layout considerations.

latex provides \stackrel{} for placing a superscript above a binary relation. In the amsmath package there are somewhat more general commands, \overset{} and \underset{}, that can be used to place one symbol above or below another symbol, whether it's a relation or something else. The input \underset{*}{X} is compiled to \(\underset{*}{X}\) while \overset{} is the analog for adding a symbol above like \(\overset{*}{X}\). The command \overunderset{o}{u} is a combination of these, taking three arguments to place superscript sized expressions above and below the same base.

In the paragraph above we can see that these under- and overscripts both add some line height. So it's probably not a good idea to use these commands inline.