1 \documentclass{article}
11 To have several equation columns side-by-side, use extra ampersands
12 to separate the columns:
14 x&=y & X&=Y & a&=b+c\\
15 x'&=y' & X'&=Y' & a'&=b\\
16 x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b
19 Line-by-line annotations on an equation can be done by judicious
20 application of text inside an align environment:
22 x& = y_1-y_2+y_3-y_5+y_8-\dots
24 & = y'\circ y^* && \text{by (2)}\\
25 & = y(0) y' && \text {by Axiom 1.}
29 alignat: count the maximum number of \verb'&'s
30 in any row, add 1 and divide by 2.
32 x& = y_1-y_2+y_3-y_5+y_8-\dots
33 &\quad& \text{by (1)}\\
34 & = y'\circ y^* && \text{by (2)}\\
35 & = y(0) y' && \text {by Axiom 1.}