X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-common.tex;h=041a1eb604a1bb753ba5b8415098d4f310fecc4d;hb=7dfe6fdee9d819258393544917c871f6b85a3eb8;hp=0fcc2aa64817a4705059d35bb79f5d0373e5e7b7;hpb=4febc3ad82bc8ac73e660c484e105835feb1ed84;p=mjotex.git

diff --git a/mjo-common.tex b/mjo-common.tex
index 0fcc2aa..041a1eb 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -8,6 +8,10 @@
   \usepackage{amsfonts}
 \fi
 
+\ifx\restriction\undefined
+  \usepackage{amssymb}
+\fi
+
 % Place the argument in matching left/right parentheses.
 \newcommand*{\of}[1]{ \left({#1}\right) }
 
@@ -17,15 +21,6 @@
 % Group terms using square brackets.
 \newcommand*{\sqty}[1]{ \left[{#1}\right] }
 
-% Create a set from the given elements
-\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.
-\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
-
 % A pair of things.
 \newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
 
@@ -44,15 +39,34 @@
 % A seven-tuple of things.
 \newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
 
-% 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 "least common multiple of" function. Takes a nonempty set of
+% things that can be multiplied and ordered as its argument. Name
+% chosen for synergy with \gcd, which *does* exist already.
+\newcommand*{\lcm}[1]{ \operatorname{lcm}\of{{#1}} }
+\ifdefined\newglossaryentry
+  \newglossaryentry{lcm}{
+    name={\ensuremath{\lcm{X}}},
+    description={the least common multiple of the elements of $X$},
+    sort=l
+  }
+\fi
 
 % The factorial operator.
 \newcommand*{\factorial}[1]{ {#1}! }
 
+% Restrict the first argument (a function) to the second argument (a
+% subset of that functions domain). Abused for polynomials to specify
+% an associated function with a particular domain (also its codomain,
+% in the case of univariate polynomials).
+\newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{restriction}{
+    name={\ensuremath{\restrict{f}{X}}},
+    description={the restriction of $f$ to $X$},
+    sort=r
+  }
+\fi
+
 %
 % Product spaces
 %
@@ -143,9 +157,6 @@
 }
 
 
-\newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#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