From b2db786b9d7794a3d95143e37ffcbf9163429c71 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 26 Apr 2023 23:47:58 +0100
Subject: [PATCH] Add extra expressions which match exp term of d bound
---
main.tex | 10 ++++++++++
1 file changed, 10 insertions(+)
diff --git a/main.tex b/main.tex
index aa20ca5..71c9681 100644
--- a/main.tex
+++ b/main.tex
@@ -246,6 +246,15 @@ This can be rearranged to express a bound on $d$ as follows:
+ C*q
- q^2
).expand()/(R-2*r)
+ foo = (
+ - 2*D*R + (C^2)/4
+ - ((C - 4*R*beta_min)/2 - q)^2
+ ).expand()/(R-2*r)
+ foo = (
+ (2*R*beta_min + q)
+ *(2*R*beta_min + q - C)
+ + 2*D*R
+ ).expand()/(2*r - R)
\end{sagesilent}
\begin{equation}
@@ -322,6 +331,7 @@ This can be rearranged to express a bound on $d$ as follows:
\section{Conclusion}
+\newpage
\section{Appendix - SageMath code}
\definecolor{codegreen}{rgb}{0,0.6,0}
--
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