From eef9ef89b09ef120be58935927844116cb57a471 Mon Sep 17 00:00:00 2001
From: Bokuan Li <bokuan.li@mail.mcgill.ca>
Date: Thu, 28 May 2026 13:03:41 -0400
Subject: [PATCH] Added some notations.

---
 src/cat/notation/index.tex | 4 +++-
 src/dg/notation.tex        | 5 ++++-
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/src/cat/notation/index.tex b/src/cat/notation/index.tex
index 20c91a1..dd484d6 100644
--- a/src/cat/notation/index.tex
+++ b/src/cat/notation/index.tex
@@ -14,6 +14,8 @@
     $\mathbb{D}_n$, $\mathbb{D}$ & Dyadic rationals of level $n$; all dyadic rationals. & \autoref{definition:dyadic} \\
     $\mathrm{rk}(q)$ & Dyadic rank of $q \in \mathbb{D}$. & \autoref{definition:dyadic-rank} \\
     $M(x)$ & Unique $M(x) \subset \mathbb{N}^+ \cap [1, \mathrm{rk}(x)]$ such that $x = \sum_{n \in M(x)} 2^{-n}$. & \autoref{proposition:dyadic-subset} \\
-    $[n]$ & $\bracs{1, \cdots, n}$ & N/A
+    $[n]$ & $\bracs{1, \cdots, n}$ & N/A \\
+    $R[x]$ & Ring of polynomials over $R$. & N/A \\
+    $F(x)$ & Field of fractions over $F$. & N/A \\ 
 \end{tabular}
 
diff --git a/src/dg/notation.tex b/src/dg/notation.tex
index 48129cc..adca4e4 100644
--- a/src/dg/notation.tex
+++ b/src/dg/notation.tex
@@ -17,5 +17,8 @@ Differential geometry is the study of things invariant under change of notation.
     $\tilde C_\sigma^n(U; F)$ & $n$-fold continuously $\tilde \sigma$-differentiable functions. & \autoref{definition:continuously-differentiable-space} \\
     $L^{(n)}_\sigma(E; F)$ & Codomain of derivatives. $L^{(0)}_\sigma(E; F) = F$, $L^{(n)}_\sigma(E; F) = L(E; L_\sigma^{(n-1)}(E; F))$, equipped with the $\sigma$-uniform topology. & \autoref{definition:higher-derivatives-codomain} \\
     $x^{(k)}$ & Tuple of $x$ repeated $k$ times. & \autoref{theorem:taylor-peano} \\
-    $D^+f(x)$ & Right derivative of $f$ at $x$. & \autoref{definition:right-differentiable-mvt}
+    $D^+f(x)$ & Right derivative of $f$ at $x$. & \autoref{definition:right-differentiable-mvt} \\
+    $\omega_{z, r}$ & Standard path of winding number 1. & \autoref{definition:winding-number-1} \\
+    $H(U; E)$ & Space of $E$-valued holomorphic functions on $U$. & \autoref{definition:holomorphic-function-space} \\
+    $H(A; E)$ & Space of $E$-valued holomorphic functions near $A$. & \autoref{definition:holomorphic-function-space-near} 
 \end{tabular}