%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%
% LaTeX COMMANDS
%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%

% Miscellaneous Special Capitals
\newcommand{\zz}{\mathbb{Z}}
\newcommand{\nn}{\mathbb{N}}
\newcommand{\pp}{\mathbb{P}}
\newcommand{\qq}{\mathbb{Q}}
\newcommand{\rr}{\mathbb{R}}
\newcommand{\cc}{\mathbb{C}}
\newcommand{\kk}{\bm{k}}
\newcommand{\xx}{\bm{x}}
\newcommand{\bfa}{\bm{a}}
\newcommand{\bfb}{\bm{b}}
\newcommand{\sm}{\mathscr{M}}
\newcommand{\sg}{\mathscr{S}}
\newcommand{\LL}{\mathscr{L}}
\newcommand{\rD}{\widetilde{\Delta}}
\newcommand{\rL}{\widetilde{\LL}}
\newcommand{\rV}{\widetilde{V}}
\newcommand{\GG}{\bm{G}}
\newcommand{\HH}{\bm{H}}
\newcommand{\bfs}{\bm{s}}

%Miscellaneous symbols
\newcommand{\di}{\"}
\newcommand{\la}{\langle}
\newcommand{\ra}{\rangle}
\newcommand{\os}{\overset}
\newcommand{\us}{\underset}
\newcommand{\perpp}{\mbox{$\perp\!\!\!\perp$}}
\newcommand{\Times}{\!\times\!}
\newcommand{\lra}{\longrightarrow} 
\newcommand{\Lra}{\Longrightarrow}
\newcommand{\lto}{\longleftarrow}
\newcommand{\lf}{\left}
\newcommand{\rt}{\right}
\newcommand{\bv}{\, \big\vert \,}
\newcommand{\wt}{\widetilde}
\providecommand{\abs}[1]{\lvert#1\rvert}
\providecommand{\norm}[1]{\lVert#1\rVert}

%Miscellaneous Greek letters
\newcommand{\eps}{\ensuremath{\epsilon}}
\newcommand{\ga}{\ensuremath{\gamma}}

%Miscellaneous operators
\DeclareMathOperator{\coker}{Coker}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\codim}{codim}
\DeclareMathOperator{\smax}{\sigma_{\mathrm{max}}}
\DeclareMathOperator{\tail}{tail}
\DeclareMathOperator{\head}{head}
\DeclareMathOperator{\outdeg}{outdeg}
\DeclareMathOperator{\indeg}{indeg}
\DeclareMathOperator{\supp}{supp}

% Displaystyle in $$ mode
\newcommand{\ds}{\displaystyle}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EXTRA COMMANDS 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\sxy}[2]{\sum_{i=#1}^{#2}}
\newcommand{\res}[3]{$ 0 \leftarrow S^{#1} \leftarrow S^{#2} \leftarrow S^{#3} \leftarrow 0$}
%  Blank box placeholder for figures 
% To reserve space that later will be used for a table or figure.
\newcommand{\blankbox}[2]{%
  \parbox{\columnwidth}{\centering
%    Set fboxsep to 0 so that the actual size of the box will match the
%    given measurements more closely.
    \setlength{\fboxsep}{0pt}%
    \fbox{\raisebox{0pt}[#2]{\hspace{#1}}}%
  }%
}
%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%

\endinput

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% End of commands.tex
%-----------------------------------------------------------------------
