-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathlattices.tex
125 lines (97 loc) · 3.46 KB
/
lattices.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
% Copyright 2013 Nicolai Hähnle <nhaehnle@gmail.com>
%
% This work is licensed under the Creative Commons Attribution-ShareAlike 3.0
% Unported License, see http://creativecommons.org/licenses/by-sa/3.0/
%
% Among other things, this means that yes, you may take e.g. illustrations from
% the book and use them in your own work. However, (a) you must give proper
% attribution by naming me as its original author and (b) you must make your
% derivative work available under the same or similar license terms.
%
% See the Creative Commons website for the exact licensing terms.
\documentclass[a4paper,10pt]{scrbook}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{clrscode}
\usepackage{multirow}
\usepackage{enumerate}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usetikzlibrary{arrows}
\usetikzlibrary{decorations.pathmorphing}
\newcommand{\E}{\mathbb{E}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\cA}{\mathcal{A}}
\newcommand{\cD}{\mathcal{D}}
\newcommand{\cI}{\mathcal{I}}
\newcommand{\cP}{\mathcal{P}}
\newcommand{\cV}{\mathcal{V}}
\providecommand{\one}{\mathbf{1}}
\DeclareMathOperator{\vol}{vol}
\DeclareMathOperator{\cone}{cone}
\DeclareMathOperator{\tcone}{tcone}
\DeclareMathOperator{\conv}{conv}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\poly}{poly}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\Id}{id}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\relint}{relint}
\DeclareMathOperator{\sgn}{sgn}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{conjecture}{Conjecture}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{example}[theorem]{Example}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{problem}[theorem]{Problem}
\usepackage[colorlinks]{hyperref}
%opening
\title{Lattices and Convex Bodies}
\author{Nicolai Hähnle}
%\includeonly{chapter05-lattice-programming}
\begin{document}
\maketitle
\tableofcontents
\chapter*{Preface}
These notes are being prepared as part of a lecture ``Lattices and Convex Bodies''
given by Nicolai Hähnle at the University of Bonn in Fall 2013.
The most recent version can be found at \url{https://github.com/nhaehnle/lattices}
in the form of a Git repository of the \LaTeX{} sources.
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0
Unported License (CC BY-SA 3.0). See \url{http://creativecommons.org/licenses/by-sa/3.0/}
for detailed information about what this means.
Contributions of spotted errors, improved proofs, and so on are welcome,
and will be added with proper attribution.
See the Github site linked above for more information.
\section*{Contributions}
Typos and other corrections have been contributed by:
\begin{quote}
Anna Hermann\\
Rasmus Schroeder\\
\end{quote}
\include{chapter01-basics}
\include{chapter02-basis-reduction}
\include{chapter03-voronoi}
\include{chapter04-dual-fourier}
\include{chapter05-lattice-programming}
\include{chapter06-lattice-enumeration}
\include{chapter07-generating-functions}
\bibliographystyle{alpha}
\bibliography{literature}
\end{document}