Guide to LaTeX (4th Edition) (Tools and Techniques

136 Chapter 5. Mathematical Formulas
is given by the expression
±
l1 m1
l2 m2
x1 − x2 y1 − y2 z1 − z2
l1 m1 n1
l2 m2 n2
2
+
m1 n1
m2 n2
2
+
n1 l1
n2 l2
If the numerator is zero, the two lines meet somewhere.
Note: we do not recommend using {|cc|} in the formatting argument of
the three determinants in the denominator under the root sign. Here the
\left|. . . \right| pair should be applied. Try out both possibilities for yourself
and compare the results.
Exercise 5.15: Laurent expansion: using cn = 1
−n−1 (ζ −a) f (ζ) dζ, for every
2πi
function f (z) the following representation is valid (n = 0, ±1, ±2, . . . )
+∞
f (x) = cn(z − a)
n=−∞
n ⎧
⎪⎨ c0 + c1(z − a) + c2(z − a)
=
⎪⎩
2 + · · · + cn(z − a) n + · · ·
+ c−1(z − a) −1 + c−2(z − a) −2 + · · ·
+ c−n(z − a) −n + · · ·
Tip: the right-hand side of the equation can be created with an array environment
consisting of only one column. What is its formatting argument?
5.4.4 Lines above and below formulas
The commands
\overline{sub form} and \underline{sub form}
can be used to draw lines over or under a formula or sub-formula. They
may be nested to any level:
a 2 + xy + z
\[ \overline{\overline{a}ˆ2 + \underline{xy}
+ \overline{\overline{z}}} \]
The command \underline may also be employed in normal text mode
to underline text, whereas \overline is allowed only in math mode.
Exactly analogous to these are the two commands
\overbrace{sub form} and \underbrace{sub form}
which put horizontal curly braces above or below the sub-formula.
a + b
+ c
+d
\overbrace{a + \underbrace{b+c} + d}
In displayed formulas, these commands may have exponents or indices
attached to them. The (raised) exponent is set above the overbrace while
the (lowered) index is placed below the underbrace.
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