X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=26e761bda919ae79d587a16e8b435f49cd019694;hb=90f73298ec65ab89af5131ec8473f9c5909d333c;hp=c2f9dd786da6f3a7d4c4e9b30f4af75693117978;hpb=11d72c97a8c945faac9f355379678a5b8212ca0a;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index c2f9dd7..26e761b 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -22,3 +22,43 @@
 
 % 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
+}