% % Only the most commonly-used macros. Needed by everything else. % % Place the argument in matching left/right parntheses. \providecommand*{\of}[1]{ \left({#1}\right) } % Group terms using parentheses. \providecommand*{\qty}[1]{ \left({#1}\right) } % Group terms using square brackets. \providecommand*{\sqty}[1]{ \left[{#1}\right] } % Create a set from the given elements \providecommand*{\set}[1]{\left\lbrace{#1}\right\rbrace} % A set comprehension, where the ``such that...'' bar is added % automatically. The bar was chosen over a colon to avoid ambiguity % with the L : V -> V notation. We can't leverage \set here because \middle % needs \left and \right present. \providecommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace} % A pair of things. \providecommand*{\pair}[2]{ \left({#1},{#2}\right) } % The Cartesian product of two things. \providecommand*{\cartprod}[2]{ {#1}\times{#2} } % The Cartesian product of three things. \providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} } % % Product spaces % % All of the product spaces (for example, R^n) that follow default to % an exponent of ``n'', but that exponent can be changed by providing % it as an optional argument. If the exponent given is ``1'', then it % will be omitted entirely. % % The natural n-space, N x N x N x ... x N. \providecommand*{\Nn}[1][n]{ \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi } % The integral n-space, Z x Z x Z x ... x Z. \providecommand*{\Zn}[1][n]{ \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi } % The rational n-space, Q x Q x Q x ... x Q. \providecommand*{\Qn}[1][n]{ \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi } % The real n-space, R x R x R x ... x R. \providecommand*{\Rn}[1][n]{ \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi } % The complex n-space, C x C x C x ... x C. \providecommand*{\Cn}[1][n]{ \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi }