%% ----------------------------------------------------------------
\definecolor{lightred}{rgb}{1.0,0.7,0.7}
\definecolor{blue1}{rgb}{0.0,0.2,0.7}
\definecolor{blue2}{rgb}{0,0,0.7}
\definecolor{darkred}{rgb}{0.5,0,0}
\definecolor{lightgreen}{rgb}{0.7,1.0,0.7}
\definecolor{lightblue}{rgb}{0.7,0.85,1}
\definecolor{darkblue}{rgb}{0.125,0,0.508}
\definecolor{darkerblue}{rgb}{0.2,0,0.5}
\definecolor{backgroundColor}{rgb}{1,1,1}
\definecolor{textColor}{rgb}{0,0,0}
\definecolor{shaded}{rgb}{0.8,0.8,0.8}
\definecolor{formulaColor}{rgb}{0,0.2,0.6}
\definecolor{formulaExtraColor}{rgb}{1,0,0}
\definecolor{beamerstructure}{rgb}{0,0.5,0.1}
\definecolor{structure}{rgb}{0,0,0}
\newcommand{\fcl}{\color{formulaColor}}
\newcommand{\tcl}{\color{textColor}}
\newcommand{\excol}{\color{formulaExtraColor}}
\newcommand{\emcol}{\color{darkred}}
\newcommand{\ff}[1]{\fcl \ensuremath{#1} \tcl}

%% ----------------------------------------------------------------
%\newcommand{\comment}[1]{}
\newcommand{\comment}[1]{\marginpar{\tiny #1}}
\newcommand{\nn}{\nonumber}

\DeclareMathSymbol{\leqslant}{\mathalpha}{AMSa}{"36}
\DeclareMathSymbol{\geqslant}{\mathalpha}{AMSa}{"3E}
\DeclareMathSymbol{\doteqdot}{\mathalpha}{AMSa}{"2B}
\DeclareMathSymbol{\circlearrowright}{\mathalpha}{AMSa}{"08}
\DeclareMathSymbol{\subsetneq}{\mathalpha}{AMSb}{"28}
\DeclareMathSymbol{\supsetneq}{\mathalpha}{AMSb}{"29}
\renewcommand{\leq}{\;\leqslant\;}
\renewcommand{\geq}{\;\geqslant\;}
\newcommand{\isdefby}{\;\doteqdot\;}
%\newcommand{\isdefby}{\; := \;}
\newcommand{\bydefis}{\; =: \;}
\newcommand{\strictinc}{\;\subsetneq\;}
%\newcommand{\dd}{{\rm d}}
%\newcommand{\e}[1]{\,{\rm e}^{#1}\,}
\newcommand{\ii}{{\rm i}}
\newcommand{\sumtwo}[2]{\sum_{\substack{#1 \\ #2}}}
\newcommand{\sumthree}[3]{\sum_{\substack{#1 \\ #2 \\ #3}}}
\newcommand{\uniontwo}[2]{\union_{\substack{#1 \\ #2}}}
\newcommand{\inttwo}[2]{\int_{\substack{#1 \\ #2}}}
\newcommand{\intthree}[3]{\int_{\substack{#1 \\ #2 \\ #3}}}
\newcommand{\prodtwo}[2]{\prod_{\substack{#1 \\ #2}}}
\newcommand{\maxtwo}[2]{\max_{\substack{#1 \\ #2}}}
\DeclareMathOperator*{\union}{\text{\large$\cup$}}
\DeclareMathOperator*{\Union}{\text{\Large$\cup$}}
\newcommand{\Uniontwo}[2]{\Union_{\substack{#1 \\ #2}}}
\DeclareMathOperator*{\inter}{\text{\large$\cap$}}
\DeclareMathOperator*{\Inter}{\text{\Large$\cap$}}
\newcommand{\Biggerint}[1]{\lceil #1 \rceil}
\DeclareMathOperator*{\supp}{\text{supp}}

% Use a bullet for itemized lists:
\setbeamertemplate{itemize item}{$\bullet$}
% Make it darkred, not the default blue:
\setbeamercolor{item}{fg=darkred}
% Theorems, propositions, etc.:
\setbeamercolor{structure}{fg=darkred}

%% ----------------------------------------------------------------
% figures
\makeatletter
%\renewcommand\captionfont@{\footnotesize}
\makeatother
\def\writefig#1 #2 #3 {\rlap{\kern #1 truecm \raise #2 truecm
\hbox{#3}}}
\def\figtext#1{\smash{\hbox{#1}} \vspace{-5mm}}
