X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-common.tex;h=e74648416d8a02bb7128c7f50275daecb5e7d3a8;hp=408ca3310e7dbff8e498936e4bfefbe77e49c483;hb=a6c1d186ec5bbd8d02dfd2f057cd147afdfe900f;hpb=2b6f9aa58154ba0d7d25a94f7f74674139b5ac92

diff --git a/mjo-common.tex b/mjo-common.tex
index 408ca33..e746484 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -1,36 +1,56 @@
 %
 % Only the most commonly-used macros. Needed by everything else.
 %
+\ifx\havemjocommon\undefined
+\def\havemjocommon{1}
 
-% Place the argument in matching left/right parntheses.
-\providecommand*{\of}[1]{ \left({#1}\right) }
+
+\ifx\mathbb\undefined
+  \usepackage{amsfonts}
+\fi
+
+\ifx\bigtimes\undefined
+  \usepackage{mathtools}
+\fi
+
+% Place the argument in matching left/right parentheses.
+\newcommand*{\of}[1]{ \left({#1}\right) }
 
 % Group terms using parentheses.
-\providecommand*{\qty}[1]{ \left({#1}\right) }
+\newcommand*{\qty}[1]{ \left({#1}\right) }
 
 % Group terms using square brackets.
-\providecommand*{\sqty}[1]{ \left[{#1}\right] }
+\newcommand*{\sqty}[1]{ \left[{#1}\right] }
 
 % Create a set from the given elements
-\providecommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
+\newcommand*{\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}
+\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
 
 % A pair of things.
-\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
+
+% A triple of things.
+\newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
 
 % The Cartesian product of two things.
-\providecommand*{\cartprod}[2]{ {#1}\times{#2} }
+\newcommand*{\cartprod}[2]{ {#1}\times{#2} }
 
 % The Cartesian product of three things.
-\providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+\newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+
+% The direct sum of two things.
+\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The direct sum of three things.
+\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
 
 % The factorial operator.
-\providecommand*{\factorial}[1]{ {#1}! }
+\newcommand*{\factorial}[1]{ {#1}! }
 
 %
 % Product spaces
@@ -42,26 +62,139 @@
 %
 
 % The natural n-space, N x N x N x ... x N.
-\providecommand*{\Nn}[1][n]{
+\newcommand*{\Nn}[1][n]{
   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
 
+\ifdefined\newglossaryentry
+  \newglossaryentry{N}{
+    name={\ensuremath{\Nn[1]}},
+    description={the set of natural numbers},
+    sort=N
+  }
+\fi
+
 % The integral n-space, Z x Z x Z x ... x Z.
-\providecommand*{\Zn}[1][n]{
+\newcommand*{\Zn}[1][n]{
   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
 
+\ifdefined\newglossaryentry
+  \newglossaryentry{Z}{
+    name={\ensuremath{\Zn[1]}},
+    description={the ring of integers},
+    sort=Z
+  }
+\fi
+
 % The rational n-space, Q x Q x Q x ... x Q.
-\providecommand*{\Qn}[1][n]{
+\newcommand*{\Qn}[1][n]{
   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
 
+\ifdefined\newglossaryentry
+  \newglossaryentry{Q}{
+    name={\ensuremath{\Qn[1]}},
+    description={the field of rational numbers},
+    sort=Q
+  }
+\fi
+
 % The real n-space, R x R x R x ... x R.
-\providecommand*{\Rn}[1][n]{
+\newcommand*{\Rn}[1][n]{
   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
 
+\ifdefined\newglossaryentry
+  \newglossaryentry{R}{
+    name={\ensuremath{\Rn[1]}},
+    description={the field of real numbers},
+    sort=R
+  }
+\fi
+
+
 % The complex n-space, C x C x C x ... x C.
-\providecommand*{\Cn}[1][n]{
+\newcommand*{\Cn}[1][n]{
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{C}{
+    name={\ensuremath{\Cn[1]}},
+    description={the field of complex numbers},
+    sort=C
+  }
+\fi
+
+
+% The space of real symmetric n-by-n matrices.
+\newcommand*{\Sn}[1][n]{
+  \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{Sn}{
+    name={\ensuremath{\Sn}},
+    description={the set of $n$-by-$n$ real symmetric matrices},
+    sort=Sn
+  }
+\fi
+
+% The space of complex Hermitian n-by-n matrices.
+\newcommand*{\Hn}[1][n]{
+  \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
+}
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{Hn}{
+    name={\ensuremath{\Hn}},
+    description={the set of $n$-by-$n$ complex Hermitian matrices},
+    sort=Hn
+  }
+\fi
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\newcommand*{\union}[2]{ {#1}\cup{#2} }
+
+% A three-argument union.
+\newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The intersection of its two arguments.
+\newcommand*{\intersect}[2]{ {#1}\cap{#2} }
+
+% A three-argument intersection.
+\newcommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+
+% An indexed arbitrary binary operation such as the union or
+% intersection of an infinite number of sets. The first argument is
+% the operator symbol to use, such as \cup for a union. The second
+% argument is the lower index, for example k=1. The third argument is
+% the upper index, such as \infty. Finally the fourth argument should
+% contain the things (e.g. indexed sets) to be operated on.
+\newcommand*{\binopmany}[4]{
+  \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+             { {#1}_{#2}^{#3}{#4} }
+}
+
+\newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
+\newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
+\newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
+\newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
+
+% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
+% the real line.
+\newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+
+
+\fi