From 94a5531eb4c07fbda90e2f14beea568b7c9aedc5 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 11 Dec 2020 13:43:11 +0100
Subject: Tweaked some spacing since fonts have changed.

---
 bezout.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 896e705..6d4b145 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -2,7 +2,7 @@
 
 \usepackage[utf8]{inputenc} % why not type "Bézout" with unicode?
 \usepackage[T1]{fontenc} % vector fonts plz
-\usepackage{newtxtext,newtxmath}
+\usepackage{newtxtext,newtxmath} % Times for PR
 \usepackage[
   colorlinks=true,
   urlcolor=purple,
@@ -126,9 +126,9 @@ of $2N$ real variables. Its number of saddle-points is given by the usual
 Kac--Rice formula:
 \begin{equation} \label{eq:real.kac-rice}
   \begin{aligned}
-    \mathcal N_J(\kappa,\epsilon)
-      &= \int dx\,dy\,\delta(\partial_x\operatorname{Re}H)\delta(\partial_y\operatorname{Re}H) \\
-      &\qquad\times\left|\det\begin{bmatrix}
+    \mathcal N_J&(\kappa,\epsilon)
+      = \int dx\,dy\,\delta(\partial_x\operatorname{Re}H)\delta(\partial_y\operatorname{Re}H) \\
+      &\hspace{6pc}\times\left|\det\begin{bmatrix}
           \partial_x\partial_x\operatorname{Re}H & \partial_x\partial_y\operatorname{Re}H \\
           \partial_y\partial_x\operatorname{Re}H & \partial_y\partial_y\operatorname{Re}H
         \end{bmatrix}\right|.
@@ -141,9 +141,9 @@ $\partial_y\operatorname{Re}H=-\operatorname{Im}\partial H$. Carrying these
 transformations through, we have
 \begin{equation} \label{eq:complex.kac-rice}
   \begin{aligned}
-    &\mathcal N_J(\kappa,\epsilon)
+    \mathcal N_J&(\kappa,\epsilon)
       = \int dx\,dy\,\delta(\operatorname{Re}\partial H)\delta(\operatorname{Im}\partial H) \\
-        &\qquad\qquad\qquad\times\left|\det\begin{bmatrix}
+                &\hspace{6pc}\times\left|\det\begin{bmatrix}
             \operatorname{Re}\partial\partial H & -\operatorname{Im}\partial\partial H \\
             -\operatorname{Im}\partial\partial H & -\operatorname{Re}\partial\partial H
           \end{bmatrix}\right| \\
-- 
cgit v1.2.3-54-g00ecf

