preamble.tex

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\newtheorem{alg}{\hspace{1.3in} Algorithm}
\newtheorem{thrm}{Theorem}
\newtheorem{lemm}[thrm]{Lemma}
\newtheorem{conj}[thrm]{Conjecture}
%\newtheorem{claim}[thrm]{Claim}
\newtheorem{prop}[thrm]{Proposition}
\newtheorem{defn}[thrm]{Definition}
\newtheorem{obs}[thrm]{Observation}

\hyphenation{Chris-to-dou-lak-is}
\def\proof{\bigbreak\noindent {\sl Proof.\/}\enspace}
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% \def\B{\tt{B}}
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\def\CP{\tt{CP}}
\def\MNC{\tt{MNC}}
\def\PR{\tt{PR}}
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\def\CPR{\tt{CPR}}
% \def\POS{\tt{POS}}
\def\LEN{\tt{LEN}}
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\newif\ifShow
\Showfalse
% MATH -----------------------------------------------------------
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\newcommand{\Real}{\mathbb R}
\newcommand{\eps}{\varepsilon}
\newcommand{\To}{\longrightarrow}
\newcommand{\BX}{\mathbf{B}(X)}
\newcommand{\A}{\mathcal{A}}
% Algorithm ------------------------------------------------------

\algnewcommand{\LineComment}[1]{\State \(\triangleright\) \normalfont{\sl #1}}
\algtext*{EndWhile}% l
\algtext*{EndIf}% Remove "end if" text
\algtext*{EndFor}% Remove "end for" text
\algtext*{EndFor}% Remove "end for" text
\algtext*{EndProcedure}% Remove "end procedure" text

% manifold
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\newcommand{\scL}{{\EuScript L}}
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% \newcommand{\CP}{\C\PP}
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\newcommand{\chone} {\CH^1}
%\newcommand{\mean}{{\mathcal m}}
\newcommand{\mean}{{\mathbf m}}
%\def\({\left (}
\def\({\left(}
%\def\){\right )}
\def\){\right)}
\def\<{\langle}
\def\>{\rangle}
\def\a {\alpha}
\def\b {\beta}
\def\l {\lambda}

% Pfaffian systems
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\newcommand{\I}{{\mathcal I}}
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\newcommand{\K}{{\mathcal K}}
\newcommand{\Khat}{\widehat{\K}}
\newcommand{\M}{{\mathcal M}}
\newcommand{\V}{\mathcal V}
\newcommand{\calS}{\mathcal S}

% differential forms
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\newcommand{\kh}{\hat\kappa}
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% \newcommand{\alg}{{\operatorname{alg}}}

%maps
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%open sets
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% vectors
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\newcommand{\bn}{\mathbf n}
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% complex variables
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% operators
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5pt depth 0pt %
         \vrule height 3pt width .5pt depth 0pt}}}}
\newcommand{\hook}{\intprod}
\def\&{\wedge}
% \def\s{\sigma}
\def\a{\alpha}
\def\b{\beta}
\def\n{\nabla}