Aligned subsidiary environment

Aligned subsidiary environment

i (mod Θ)

split one column, aligned

Figure 9.1: The Visual Guide for multiline math formulas.

9.1 Visual Guide 209

9.1.1 Columns

Multiline math formulas are displayed in columns. The columns are either adjusted, that is, centered, or set flush left or right, or aligned, that is, an alignment point is des- ignated for each column and for each line. Moreover, the columns are either separated by the intercolumn space or adjacent with no separation.

One column As in Chapter 3, we start with a simple align:

r 2 =s 2 +t 2 , 2u + 1 = v + w α

This is a single column, aligned at the = signs, and coded with the align environment (see Section 3.4.2).

Two columns The annotated align, coded with the align environment,

x=x ∧ (y ∨ z) (by distributivity) = (x ∧ y) ∨ (x ∧ z)

(by condition (M)) =y ∨z

has two columns. The first column is aligned like our example of simple align, but the second column is aligned flush left. There is a sizeable intercolumn space.

9.1.2 Subsidiary math environments

The cases example in Chapter 3:

introduces a new concept. The part of the formula to the right of = is a multiline construct. This is an example of a subsidiary math environment that can only be used inside another math environment . It creates a “large math symbol”, in this case

 −x ,

if x < 0; α + x, if 0 ≤ x ≤ 1;

otherwise.

210 Chapter 9 Multiline math displays

So the cases example:

f (x) = large math symbol

is a single line displayed formula, where “large math symbol” is replaced by the cases construct.

9.1.3 Adjusted columns

An adjusted column is either set centered, or flush left, or flush right. This may happen by default, built into the environment, or so specified in the code.

For instance, in the displayed formula

x x +x 2 1 2 1 x 2 2 +x 3 , x 1 x 3 +x 2 1 x 2 3 +x 2

typeset with the gather environment, by default all the lines are centered.

On the other hand, in

coded with the array subsidiary math environment, the first column is flush left, the second centered, the third flush right.

9.1.4 Aligned columns

Aligned columns, on the other hand, are only of one kind, aligned by you. For instance,

f (x) = x + yz

g(x) = x + y + z

k(x) = (x + y)(x + z)(y + z) is coded with the alignat environment. It has two aligned columns, both aligned at

h(x) = xy + xz + yz

the = sign.

9.1.5 Touring the Visual Guide

Figure 9.1, the Visual Guide, shows thumbnail pictures of the various kinds of multiline math environments and subsidiary math environments.

The first part of the Visual Guide illustrates gather and multline. The gather environment is a one-column, centered math environment—discussed in Section 9.2— which is used to display a number of formulas collected into one multiline formula. In contrast, multline—discussed in Section 9.3—displays one long formula in a num- ber of lines. The first line is set flush left, the last line set flush right, and the rest (if any) of the lines are centered.

The third part of the Visual Guide illustrates the align environment and two of its variants, alignat and flalign, discussed in Section 9.5.

9.2 Gathering formulas 211

Three adjusted subsidiary math environments—matrix, cases, and array—are illustrated in second part of the Visual Guide and presented in Section 9.7.

The aligned subsidiary math environments aligned and gathered look just like the align and gather environments, so they are not illustrated in the Visual Guide. The aligned and gathered environments—along with \itemref—are discussed in Section 9.6, along with the split subsidiary math environment; this last one is illus- trated in the last part of the Visual Guide.