From 1f48d16cba21dac3c3508f719e81d8f28eaedcb0 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Mon, 29 May 2023 16:23:54 +0100
Subject: [PATCH] Replace displayed formula for bgmlv3 to nicer alt form
---
main.tex | 17 ++++++++++++-----
1 file changed, 12 insertions(+), 5 deletions(-)
diff --git a/main.tex b/main.tex
index 9165a51..0847d0d 100644
--- a/main.tex
+++ b/main.tex
@@ -541,11 +541,6 @@ assert bgmlv3_d_ineq.lhs() == d
bgmlv3_d_upperbound = bgmlv3_d_ineq.rhs() # Keep hold of lower bound for d
\end{sagesilent}
-\begin{dmath}
- \label{eqn-bgmlv3_d_upperbound}
- \sage{bgmlv3_d_ineq}
-\end{dmath}
-
\begin{sagesilent}
# Seperate out the terms of the lower bound for d
@@ -615,6 +610,18 @@ assert bgmlv3_d_upperbound_exp_term == (
)
\end{sagesilent}
+\bgroup
+\def\psi{\chern_1^{\beta}(F)}
+\def\phi{\chern_2^{\beta}(F)}
+\begin{dmath}
+ \label{eqn-bgmlv3_d_upperbound}
+ d \leq
+ \sage{bgmlv3_d_upperbound_linear_term}
+ + \sage{bgmlv3_d_upperbound_const_term_alt}
+ + \sage{bgmlv3_d_upperbound_exp_term_alt2}
+\end{dmath}
+\egroup
+
\noindent
Viewing equation \ref{eqn-bgmlv3_d_upperbound} as an upper bound for $d$ give:
--
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