\newcommand{\heading}[1]
{\vspace{1ex minus 1ex}  \color{red} 
\begin{center} {\large \bf #1}  \end{center}  \color{black}  }

\definecolor{cream}{rgb}{1, 1,.9}
%\input{macs} %macros for bi be color etc.
\newcommand{\bc}{\begin{center}}
\newcommand{\ec}{\end{center}}
\newcommand{\be}{\begin{enumerate}}
\newcommand{\ee}{\end{enumerate}}
\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}
\newcommand{\bsi}{\small \begin{itemize}}
\newcommand{\esi}{\end{itemize}}
\newcommand{\im}{\item}

\newcommand{\BF}[1]{{\bf #1:}\hspace{1em}\ignorespaces}
%\BF{Definition}
 
%color shortcuts
%\definecolor{Blue}{rgb}{0.,0.,1.}
%\definecolor{Pink}{rgb}{1.,0.75,0.8}
\definecolor{Gold}{rgb}{1.,0.84,0.}
\definecolor{cola}{rgb}{0.9,0.4,0.6}
\definecolor{colb}{rgb}{0.4,0.6,0.9}
\definecolor{colc}{rgb}{0.6,0.9,0.4}
 
\newcommand{\myred}[1]{\textcolor{red}{#1}}
\newcommand{\myblue}[1]{\textcolor{blue}{#1}}
\newcommand{\myorange}[1]{\textcolor{orange}{#1}}
\newcommand{\mycyan}[1]{\textcolor{cyan}{#1}}
\newcommand{\mymagenta}[1]{\textcolor{magenta}{#1}}
\newcommand{\mygreen}[1]{\textcolor{green}{#1}}
\newcommand{\myyellow}[1]{\textcolor{yellow}{#1}}
\newcommand{\mygold}[1]{\textcolor{Gold}{#1}}
\newcommand{\mycola}[1]{\textcolor{cola}{#1}}
\newcommand{\mycolb}[1]{\textcolor{colb}{#1}}
\newcommand{\mycolc}[1]{\textcolor{colc}{#1}}


  \definecolor{coxcolor}{rgb}{1,.937,.835}
 \definecolor{darkgreen}{rgb}{.0, .392, .0}
  \definecolor{fcolor}{rgb}{0,1,1}
 \definecolor{ghostwhite}{rgb}{.973, .973, 1}
  \definecolor{Gray}{rgb}{.895,.93,.916}
 \definecolor{honeydew}{rgb}{.941, 1, .941}
 \definecolor{khaki}{rgb}{.741, .718, .42}
 \definecolor{lavenderdark}{rgb}{.8, .8, .9529411}
 \definecolor{lavender}{rgb}{.902, .902, .980}
 \definecolor{lightblue}{rgb}{.8, .8, .95}
\definecolor{lightcyan}{rgb}{.895,.93,.916}
 \definecolor{lightsteelblue}{rgb}{.690, .769, .871}
 \definecolor{lightturquoise}{rgb}{.686, .933, .933}
  \definecolor{logobackground}{rgb}{.35,.73,.87}
  \definecolor{menucolor}{rgb}{1,.25,0}
 \definecolor{oldlace}{rgb}{.992, .96187, .902}
  \definecolor{olivedrab}{rgb}{.42,.557,.137}
  \definecolor{orange1}{rgb}{1,.5,0}
  \definecolor{orange}{rgb}{1,.549,0}
  \definecolor{paleblue}{rgb}{0,0,0.1}
  \definecolor{rcolor}{rgb}{.439,.502,.565}
 \definecolor{snow}{rgb}{1, .98, .98}
\definecolor{tabcolor}{rgb}{.973, .973, 1}
 \definecolor{vlightblue}{rgb}{.88, .85, .95}
 \definecolor{wheat}{rgb}{.96, .87, .70}
 \definecolor{yellowgreen}{rgb}{.604, .804, .196}

% Various combinations of one colour on another -- Michael Gordon.

\newcommand{\greenonred}[1]%
{\psset{fillcolor=red}\psframebox*[framearc=.3]{\green #1}}

\newcommand{\whiteonred}[1]%
{\psset{fillcolor=red}\psframebox*[framearc=.3]{\white #1}}

\newcommand{\yellowonmagenta}[1]%
{\psset{fillcolor=magenta}\psframebox*[framearc=.3]{\yellow #1}}

\newcommand{\whiteonblack}[1]%
{\psset{fillcolor=black}\psframebox*[framearc=.3]{\white #1}}

\newcommand{\blackonlightgray}[1]%
{\psset{fillcolor=lightgray}\psframebox*[framearc=.3]{\black #1}}

\newcommand{\blueonlightgray}[1]%
{\psset{fillcolor=lightgray}\psframebox*[framearc=.3]{\blue #1}}

\newcommand{\cyanonblack}[1]%
{\psset{fillcolor=black}\psframebox*[framearc=.3]{\cyan #1}}

\newcommand{\blueonyellow}[1]%
{\psset{fillcolor=yellow}\psframebox*[framearc=.3]{\blue #1}}

\newcommand{\redonyellow}[1]%
{\psset{fillcolor=yellow}\psframebox*[framearc=.3]{\red #1}}

%\newcommand{\heading}[1]%
%{\begin{center}\whiteonblack{\large\bf\blueonlightgray{#1}}\end{center}}

\newcommand{\emphatic}[1]{\blueonyellow{#1}}

\newcommand{\veryemphatic}[1]%
{\begin{center}{\emphatic{#1}}\end{center}}


% Colour bullets

%\def\labelitemi{{\black$\bullet$}}
%\def\labelitemii{{\black--}}
%\def\labelitemiii{{\black$\ast$}}
%\def\labelitemiv{{\black$\cdot$}}


\newenvironment{rset}{\[\begin{array}{rcl}}{\end{array}\]}
\newenvironment{eqset}{\[\begin{array}{rcl}}{\end{array}\]}
\newenvironment{crset}{\[\begin{array}{rcrcl}}{\end{array}\]}
\newenvironment{brset}{\[\begin{array}{|rcl|}\hline}{\\\hline\end{array}\]}
\newenvironment{beqset}{\[\begin{array}{|rcl|}\hline}{\\\hline\end{array}\]}
\newenvironment{bcrset}{\[\begin{array}{|rclcl|}\hline}{\\\hline\end{array}\]}
\newenvironment{bnset}{\[\begin{array}{|rrcrcl|}\hline}{\\\hline\end{array}\]}

\newcommand{\rr}[2]{#1 & \ \rightarrow \  & #2 }
\newcommand{\eq}[2]{#1 & \ = \ & #2 }

% for putting rules/eqns in a table 
\newcommand{\ucr}[2]{#1 & \ \rightarrow \ & #2 & \ & \  }
\newcommand{\crr}[3]{#1 & \ \rightarrow \ & #2 & if & #3 }
\newcommand{\uce}[2]{\ &\  & #1 & \ = \  & #2 }
\newcommand{\ceq}[3]{#1 & : & #2 & \ = \ & #3 }

% one more argument for Numbering rules and equations.
\newcommand{\nceq}[4]{#1. & #2 & : & #3 & \ = \ & #4 }
\newcommand{\nuce}[3]{#1. & \  &  & #2 & \ = \ & #3 }
\newcommand{\ncrr}[4]{#1. & #2 & : & #3 & \ \rightarrow \ & #4 }
\newcommand{\nucr}[3]{#1. & \  &  & #2 & \ \rightarrow \ & #3 }

\newcommand{\join}{\downarrow}
\newcommand{\cnn}{\ \wedge \ \cdots \ \wedge \ }
\newcommand{\cnds}{p_{1}\ =\ q_{1} \cnn \ p_{n}\ =\ q_{n}}
\newcommand{\gceq}{\[ \cnds \ :\ s\ =\ t\]}
\newcommand{\gncr}[1]{\[p_1 #1 q_1 \cnn p_n #1 q_n \ : \ l \ \rew \ r \]}
\newcommand{\gcre}{\gncr{=}}
\newcommand{\gcrj}{\gncr{\join}}
\newcommand{\gcrn}{\gncr{\join^{!}}}
\newcommand{\gcri}{\gncr{\join^{i}}}
\newcommand{\gcro}{\gncr{\join^{o}}}

\newcommand{\Grobner}{Gr\"{o}bner}
\newcommand{\Groebner}{Gr\"{o}bner}
\newcommand{\RRL}{{\sl RRL}}
\newcommand{\union}{\cup}
\newcommand{\itm}[1]{\/\mbox{\it #1\/}} % "itm" is "italicize in math context"
\newcommand{\cmt}[1]{\begin{quote}{\em #1}\end{quote}} 
\newcommand{\rl}[3]{#1 & #2 & \rightarrow & #3}
\newcommand{\eqn}[3]{#1 & #2 & = & #3}
\newcommand{\onerule}[3]{\[\begin{array}{rlcl}\rl {#1} {#2} {#3}\end{array}\]}
\newcommand{\myand}{\wedge}
\newcommand{\grt}{\mathop{\succ}}
%\newcommand{\rew}{\rightarrow}
\newenvironment{defset}{\[\begin{array}{lrl}}{\end{array}\]}
\newcommand{\df}[3] {#1 \ \ & #2 \ \ & #3 }
\newcommand{\mynot}{\neg}
\newcommand{\myor}{\vee}
\newcommand{\implies}{\Rightarrow}
\newcommand{\myequiv}{\Leftrightarrow}
\newcommand{\TT}{\cal T}
\newcommand{\ignore}[1]{}


% \newtheorem{theorem}{Theorem}[chapter]
% \newtheorem{proposition}{Proposition}[chapter]
% \newtheorem{lemma}{Lemma}[chapter]

\newcommand{\nar}{\leadsto}
\newcommand{\goal}{\join_{?}}
\newcommand{\rgoal}{\rightarrow^{?}}
\newcommand{\rew}{\rightarrow}
\newcommand{\rwn}{\stackrel{!}{\rightarrow}}
\newcommand{\der}{\rightarrow^{*}}
\newcommand{\bder}{\>{}^*\!\!\!\leftarrow}
\newcommand{\nru}[1]{\stackrel{#1}{\leadsto}}
\newcommand{\rwd}[1]{\displaystyle \mathop{\rightarrow}_{#1}}
\newcommand{\rwk}{\rwd{k}}

% \newcommand{\rwk}{\stackrel{\rightarrow}{k}}
% \newcommand{\rwd}[1]{\displaystyle \rew_{#1}}
% \newcommand{\rwd}[1]{\rightarrow\kern-1em\,_{\,_#1}\ }

\newcommand{\dpt}{\stackrel{!}{\rwd{m-1}}}

\newcommand{\pair}[2]{\langle #1 \ , \ #2 \rangle}

\newcommand{\pic}[3]{\begin{figure}\input{#1}
        \fbox{\box\graph} \caption{#2}\label{#3}\end{figure}}

\newcommand{\egoal}{\displaystyle \mathop{=}^{?}}
\newcommand{\cep}{\large{C}\normalsize{EP}\ \/}
%% \newcommand{\rrl}{\large{R}\normalsize{RL} \/}
\newcommand{\rrl}{RRL}

