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2 % Only the most commonly-used macros. Needed by everything else.
5 % Place the argument in matching left/right parntheses.
6 \providecommand*
{\of}[1]{ \left(
{#1}\right)
}
8 % Group terms using parentheses.
9 \providecommand*
{\qty}[1]{ \left(
{#1}\right)
}
11 % Group terms using square brackets.
12 \providecommand*
{\sqty}[1]{ \left[{#1}\right] }
14 % Create a set from the given elements
15 \providecommand*
{\set}[1]{\left\lbrace{#1}\right\rbrace}
17 % A set comprehension, where the ``such that...'' bar is added
18 % automatically. The bar was chosen over a colon to avoid ambiguity
19 % with the L : V -> V notation. We can't leverage \set here because \middle
20 % needs \left and \right present.
21 \providecommand*
{\setc}[2]{\left\lbrace{#1}\
\middle|\
{#2} \right\rbrace}
24 \providecommand*
{\pair}[2]{ \left(
{#1},
{#2}\right)
}
26 % The Cartesian product of two things.
27 \providecommand*
{\cartprod}[2]{ {#1}\times{#2} }
29 % The Cartesian product of three things.
30 \providecommand*
{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
32 % The direct sum of two things.
33 \providecommand*
{\directsum}[2]{ {#1}\oplus{#2} }
35 % The factorial operator.
36 \providecommand*
{\factorial}[1]{ {#1}!
}
41 % All of the product spaces (for example, R^n) that follow default to
42 % an exponent of ``n'', but that exponent can be changed by providing
43 % it as an optional argument. If the exponent given is ``1'', then it
44 % will be omitted entirely.
47 % The natural n-space, N x N x N x ... x N.
48 \providecommand*
{\Nn}[1][n
]{
49 \mathbb{N
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
52 % The integral n-space, Z x Z x Z x ... x Z.
53 \providecommand*
{\Zn}[1][n
]{
54 \mathbb{Z
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
57 % The rational n-space, Q x Q x Q x ... x Q.
58 \providecommand*
{\Qn}[1][n
]{
59 \mathbb{Q
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
62 % The real n-space, R x R x R x ... x R.
63 \providecommand*
{\Rn}[1][n
]{
64 \mathbb{R
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
67 % The complex n-space, C x C x C x ... x C.
68 \providecommand*
{\Cn}[1][n
]{
69 \mathbb{C
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi