From: Michael Orlitzky <michael@orlitzky.com>
Date: Sat, 13 Apr 2024 21:10:40 +0000 (-0400)
Subject: mjo-algebra.tex,examples.tex: add the \variety command
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=fc43a7cd831de2042a728269e791ab82b65962ba;p=mjotex.git

mjo-algebra.tex,examples.tex: add the \variety command
---

diff --git a/examples.tex b/examples.tex
index 6b60b00..383cef2 100644
--- a/examples.tex
+++ b/examples.tex
@@ -41,6 +41,9 @@
     then that element is denoted by $\unit{R}$. Its additive identity
     element is $\zero{R}$. The stabilizer (or isotropy)
     subgroup of $G$ that fixes $x$ is $\Stab{G}{x}$.
+
+    If $I$ is an ideal, then $\variety{I}$ is the variety that
+    corresponds to it.
   \end{section}
 
   \begin{section}{Algorithm}
diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 1ab8880..42ab2aa 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -94,4 +94,17 @@
 % given by its second argument.
 \newcommand*{\Stab}[2]{ #1_{#2} }
 
+
+% The affine algebraic variety consisting of the common solutions to
+% every polynomial in its argument, which should be a subset of some
+% polynomial ring.
+\newcommand*{\variety}[1]{ \mathcal{V}\of{{#1}} }
+\ifdefined\newglossaryentry
+  \newglossaryentry{variety}{
+    name={\ensuremath{\variety{I}}},
+    description={variety corresponding to the ideal $I$},
+    sort=p
+  }
+\fi
+
 \fi