Add two- and three-argument commands for union and intersection.

[mjotex.git] / mjo-common.tex

diff --git a/mjo-common.tex b/mjo-common.tex
index 88bdc1d65b4a3f8f5962c697f075c0268f1735df..b269417749dcf12738b968645a0083c7aa033ed2 100644 (file)
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -3,34 +3,88 @@
 %
 
 % 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}^{{#1}} }
+\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}^{{#1}} }
+\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}^{{#1}} }
+\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}^{{#1}} }
+\providecommand*{\Cn}[1][n]{
+  \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\providecommand*{\union}[2]{ {#1} \cup {#2} }
+
+% A three-argument union.
+\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The intersection of its two arguments.
+\providecommand*{\intersect}[2]{ {#1} \cap {#2} }
+
+% A three-argument intersection.
+\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }