From eb4bb1e940b223d9c508733aaa3700701f51e986 Mon Sep 17 00:00:00 2001
From: Christian Grothoff <christian@grothoff.org>
Date: Thu, 13 Sep 2018 17:44:03 +0200
Subject: fix build

---
 coinselection/ilp.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'coinselection')

diff --git a/coinselection/ilp.tex b/coinselection/ilp.tex
index b182000..5d65ae5 100644
--- a/coinselection/ilp.tex
+++ b/coinselection/ilp.tex
@@ -59,7 +59,7 @@ Simple model:
      - \sum_{c \in {\cal C}} n_c \cdot \alpha \\
   \texttt{such that} \quad
   \bigwedge_{c \in {\cal C}} n_c \cdot (d_c + f^{withdraw}_c) &\le w \label{eq:sound} \\ 
-       n_c &\in {\mathbb N_0} \label{eq:nc} 
+       n_c &\in {\mathbb N}_0 \label{eq:nc} 
 \end{align}
 
 Explanations:
@@ -112,7 +112,7 @@ and then study the affect on larger simulations of many transactions.
 
 \begin{align}
   \min &M \cdot \tau + \sum_{c \in {\cal C}} s_c 
-                     + \sum_{c \in {\cal C}} n_c \cdot \alpha)
+                     + \sum_{c \in {\cal C}} n_c \cdot \alpha
                      + \sum_{c \in {\cal C}} r_c \cdot \beta \\
   \texttt{such that} \quad
   \bigwedge_{c \in {\cal C}} n_c \cdot d_c &\ge s_c  \label{eq:coinnum} \\ 
@@ -121,10 +121,10 @@ and then study the affect on larger simulations of many transactions.
        \sum_{c \in {\cal C}} (s_c - f^{deposit}_c \cdot n_c) + f &\ge p \label{eq:fees} \\
        \sum_{c \in {\cal C}} s_c - \tau p &\le p \label{eq:tau} \\
        \tau &\in \{0,1\} \label{eq:bin} \\
-       n_c &\in {\mathbb N_0} \label{eq:nc} \\
-       s_c &\in {\mathbb R^+_0} \label{eq:r} \\
-       r_c \cdot d_c + sc_c \ge  n_c \cdot d_c \label{eq:refresh} \\
-       r_c &\in \{0,1\}_ \label{eq:rc}        
+       n_c &\in {\mathbb N}_0 \label{eq:nc} \\
+       s_c &\in {\mathbb R}^+_0 \label{eq:r} \\
+       r_c \cdot d_c + s_c &\ge  n_c \cdot d_c \label{eq:refresh} \\
+       r_c &\in \{0,1\} \label{eq:rc}        
 \end{align}
 
 Explanations:
-- 
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