% A pair of things.
\providecommand*{\pair}[2]{ \left( {#1}, {#2} \right) }
+
+% The integral n-space, Z x Z x Z x ... x Z.
+\providecommand*{\Zn}[1][n]{ \mathbb{Z}^{{#1}} }
+
+% The rational n-space, Q x Q x Q x ... x Q.
+\providecommand*{\Qn}[1][n]{ \mathbb{Q}^{{#1}} }
+
+% The real n-space, R x R x R x ... x R.
+\providecommand*{\Rn}[1][n]{ \mathbb{R}^{{#1}} }
+
+% The complex n-space, C x C x C x ... x C.
+\providecommand*{\Cn}[1][n]{ \mathbb{C}^{{#1}} }
%
% The nonnegative orthant in the given number of dimensions.
-\newcommand*{\Rnplus}[1][n]{ \mathbb{R}^{{#1}}_{+} }
+\newcommand*{\Rnplus}[1][n]{ \Rn[#1]_{+} }
% The Lorentz ``ice-cream'' cone in the given number of dimensions.
\newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} }