X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=efa10a26045d9f199bd3bdb1f8c9f5ec97c1cb19;hb=d84c704c13a2e30c232710801c5483059094dac3;hp=c2f9dd786da6f3a7d4c4e9b30f4af75693117978;hpb=11d72c97a8c945faac9f355379678a5b8212ca0a;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index c2f9dd7..efa10a2 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -3,22 +3,71 @@
 %
 
 % Place the argument in matching left/right parntheses.
-\providecommand*{\of}[1]{ \left( {#1} \right) }
+\providecommand*{\of}[1]{ \left({#1}\right) }
 
 % Group terms using parentheses.
-\providecommand*{\qty}[1]{ \left( {#1} \right) }
+\providecommand*{\qty}[1]{ \left({#1}\right) }
 
 % Group terms using square brackets.
-\providecommand*{\sqty}[1]{ \left[ {#1} \right] }
+\providecommand*{\sqty}[1]{ \left[{#1}\right] }
 
 % Create a set from the given elements
-\providecommand*{\set}[1]{ \left\lbrace {#1} \right\rbrace }
+\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 }
+\providecommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
 
 % A pair of things.
-\providecommand*{\pair}[2]{ \left( {#1}, {#2} \right) }
+\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+
+% A triple of things.
+\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\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}}} }
+
+% The direct sum of two things.
+\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The factorial operator.
+\providecommand*{\factorial}[1]{ {#1}! }
+
+%
+% 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
+}