%%
\RequirePackage{tikz}
\RequirePackage{etoolbox} % for \@ifclassloaded
%%
%% Make the default vertex size 6mm, except 4mm in Beamer
%%
\newlength{\Vsize}
\setlength{\Vsize}{6mm}
\@ifclassloaded{beamer}{%
  \setlength{\Vsize}{4mm}%
}{}
%%
%%
%% ESSENTIAL COLORS
%%
\definecolor{lightestgray}{rgb}{.925, .925, .925}
\definecolor{lightgray}{rgb}{.85, .85, .85}
\definecolor{midgray}{rgb}{.5,.5,.5}
\definecolor{darkgray}{rgb}{.3,.3,.3}
%%
%%---------------------------------------------------------------------------
%%
%% TEXT COLORS
%%
\definecolor{xRed}{rgb}{.9,0,0}      % 
\definecolor{xBlue}{rgb}{0,0,.9}     % 
\definecolor{xGreen}{HTML}{009000}   % Islamic green
%\definecolor{xPurple}{HTML}{d14fff}   %% too pink
%\definecolor{ePurple}{HTML}{D287FF}
%\colorlet{xPurple}{ePurple!90!black}
\definecolor{xPurple}{rgb}{0.66 0.17 1}
\definecolor{xOrange}{HTML}{F56600}  % Clemson orange 

\DeclareRobustCommand{\Alert}[1]{{\color{xRed}#1}}
\DeclareRobustCommand{\Balert}[1]{{\color{xBlue}#1}}
\DeclareRobustCommand{\Galert}[1]{{\color{xGreen}#1}}
\DeclareRobustCommand{\Oalert}[1]{{\color{xOrange}#1}}
\DeclareRobustCommand{\Palert}[1]{{\color{xPurple}#1}}
\DeclareRobustCommand{\Walert}[1]{{\color{white}#1}}

%%---------------------------------------------------------------------------
%%
%% CAYLEY GRAPH COLORS 
%%

%% Vertices 
%%
\tikzset{v/.style={circle, draw, fill=lightgray,inner sep=0pt, 
  minimum size=\Vsize}}
%%
\tikzstyle{v-r} = [circle, draw, fill=vRed,inner sep=0pt,
    minimum size=\Vsize]
\tikzstyle{v-g} = [circle, draw, fill=vGreen,inner sep=0pt,
    minimum size=\Vsize]
\tikzstyle{v-b} = [circle, draw, fill=vBlue,inner sep=0pt,
    minimum size=\Vsize]
\tikzstyle{v-p} = [circle, draw, fill=vPurple,inner sep=0pt, 
  minimum size=\Vsize]
  \tikzstyle{v-o} = [circle, draw, fill=vOrange,inner sep=0pt, 
  minimum size=\Vsize]
    \tikzstyle{v-y} = [circle, draw, fill=vYellow,inner sep=0pt, 
  minimum size=\Vsize]
\tikzstyle{v-gr} = [circle, draw, fill=midgray,inner sep=0pt, 
  minimum size=\Vsize]
  

%% Edges colors
%%
\definecolor{eRed}{rgb}{1,0,0}      % Cayley diagram edges
\definecolor{eBlue}{rgb}{0,0,1}     % Cayley diagram edges
\definecolor{eGreen}{HTML}{7EC636}  % Goodnotes
\definecolor{eGreen}{HTML}{3CAC13}  % I like this
\definecolor{ePurple}{HTML}{D287FF} % Close to goodnotes 
\colorlet{eOrange}{orange}
\definecolor{eGray}{rgb}{.65,.65,.65}      % gray edges in subgroup lattices

\tikzset{r/.style={draw, very thick, eRed, -stealth}}  % Red -->
\tikzset{rr/.style={draw, very thick, eRed}}           % Red ---
\tikzset{r2/.style={draw, very thick, eRed,stealth'-stealth'}} 
\tikzset{b/.style={draw, very thick, eBlue, -stealth}} % Blue -->
\tikzset{bb/.style={draw, very thick, eBlue}}          % Blue ---
\tikzset{b2/.style={draw, very thick, eBlue,stealth'-stealth'}} 
\tikzset{g/.style={draw, very thick, eGreen, -stealth}} % Green -->
\tikzset{gg/.style={draw, very thick, eGreen}}          % Green ---
\tikzset{g2/.style={draw, very thick, eGreen,stealth'-stealth'}} 
\tikzset{p/.style={draw, very thick, ePurple, -stealth}} % Purple -->
\tikzset{pp/.style={draw, very thick, ePurple}}           % Purple ---
\tikzset{p2/.style={draw, very thick, ePurple,stealth'-stealth'}} 
\tikzset{o/.style={draw, very thick, eOrange, -stealth}} % Purple -->
\tikzset{oo/.style={draw, very thick, eOrange}}           % Purple ---
%%
\tikzstyle{cy2} = [draw,very thick]           %% cycle graph edges

%%---------------------------------------------------------------------------
%%
%% CAYLEY GRAPH COLORS, FADED EDGES
%%

%% Faded Edges
%%
\definecolor{faded}{rgb}{.75,.75,.75}
\colorlet{fRed}{red!30!white}      
\colorlet{fBlue}{blue!30!white}
\definecolor{fGreen}{rgb}{.733, .843, .714}
\definecolor{fPurple}{rgb}{.84, .76, .95}
\colorlet{fOrange}{orange!40!white} 

\tikzstyle{f} = [faded]
\tikzset{rFaded/.style={draw, very thick, fRed, -stealth}}  % Red -->
\tikzset{rrFaded/.style={draw, very thick, fRed}}           % Red ---
\tikzset{bFaded/.style={draw, very thick, fBlue, -stealth}} % Blue -->
\tikzset{bbFaded/.style={draw, very thick, fBlue}}          % Blue ---
\tikzset{gFaded/.style={draw, very thick, fGreen, -stealth}} % Green -->
\tikzset{ggFaded/.style={draw, very thick, fGreen}}          % Green ---
\tikzset{pFaded/.style={draw, very thick, fPurple, -stealth}} % Purple -->
\tikzset{ppFaded/.style={draw, very thick, fPurple}}           % Purple ---
\tikzset{oFaded/.style={draw, very thick, fOrange, -stealth}} % Purple -->
\tikzset{ooFaded/.style={draw, very thick, fOrange}}           % Purple ---

%%---------------------------------------------------------------------------
%%
%% COLORS FOR VERTICES (e.g., cycle graphs)
%%
\colorlet{vRed}{red!50!white}
\definecolor{vBlue}{rgb}{.60, .75, 1}
\definecolor{vGreen}{rgb}{.733, .843, .714}
\definecolor{vPurple}{HTML}{E4B7FF}
\colorlet{vYellow}{yellow!30!white}
\definecolor{vOrange}{HTML}{FFD4B7}  % same as coOrange
\definecolor{vGray}{rgb}{.5,.5,.5}

%%---------------------------------------------------------------------------
%%
%% COLORS FOR CAYLEY TABLES  
%%
\colorlet{tRed}{red!70!white}
\colorlet{tBlue}{blue!60!white}     %(higher number is more faded)
\colorlet{tGreen}{green!75!black}   %(higher number is brighter)
\colorlet{tYellow}{yellow!60!white}
\colorlet{tLime}{green!80!white}
\colorlet{tPink}{pink}
\definecolor{tPurple}{rgb}{0.7 0.45 0.9} %% Formally lpurple
\colorlet{tOrange}{orange}

%%---------------------------------------------------------------------------
%%
%% COLORS FOR BOXES: COSET & CONJUGACY CLASS PARTITIONS
%%
%\colorlet{coRed}{red!30!white}         %% Cosets not in the normalizer
%\colorlet{coBlue}{blue!30!white}       %% Cosets in the normalizer
%\definecolor{coPurple}{HTML}{E4B7FF}   %% Central elements
%\definecolor{coOrange}{HTML}{FFD4B7}   %% Non-central elements

\colorlet{boxRed}{red!25!white}         %% Cosets not in the normalizer
\colorlet{boxBlue}{blue!25!white}       %% Cosets in the normalizer
\definecolor{boxPurple}{HTML}{E4B7FF}   %% Central elements
\definecolor{boxOrange}{HTML}{FFD4B7}   %% Non-central elements

%%---------------------------------------------------------------------------
%%
%% COLORS FOR COSET BUBBBLES
%%
\colorlet{cosetGray}{gray!15!white}
\colorlet{cosetBlue}{blue!15!white}
\colorlet{cosetRed}{red!15!white}
\definecolor{cosetPurple}{rgb}{.9 .84 .965}
\definecolor{cosetGreen}{rgb}{.863 .92 .855}

%%---------------------------------------------------------------------------
%%
%% COLORS FOR ACTIONS: "binary-squares" and Chapter 1 rectangle & triangles
%%
\colorlet{actRed}{red!50!white}             %% lred
\definecolor{actBlue}{rgb}{0.60, 0.75, 1}   %% lblue
\colorlet{actGreen}{green!40!white}         %% lgreen
\colorlet{actYellow}{yellow!30!white}       %% lyellow
\definecolor{actPurple}{rgb}{0.7 0.45 0.9}  %% Purple in "binary squares"
\colorlet{actOrange}{orange!50!white}       %% Orange in "binary squares"

%%---------------------------------------------------------------------------
%%
%% COLORS FOR SUBRING LATTICES
%%
\colorlet{Ideal}{xBlue}
\colorlet{Subring}{xRed}
\definecolor{Subgroup}{rgb}{.6,.6,.6}

%%---------------------------------------------------------------------------

%% Mac: CMD+Space --> Digital color meter

%%---------------------------------------------------------------------------
%%
%% USEFUL MATH MACROS
%%
%% Math formatting 
\def\ds{\displaystyle}
\def\bold{\bm}     % Change ``bm'' to ''mathbf'' for upright boldface.

%% Basic math commands
\newcommand{\ceil}[1] {\left\lceil #1 \right\rceil}
\newcommand{\floor}[1] {\left\lfloor #1 \right\rfloor}
\DeclareMathOperator\del{\nabla}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator\Lcm{lcm}
\newcommand{\rddots}{\rotatebox{90}{$\ddots$}}
\def\setmin{-}
\newcommand{\Pmod}[1]{\ (\textup{mod}\ #1)}
\newcommand{\Mod}[1]{\ \mathrm{mod}\ #1}
\def\lleq{\preccurlyeq}
\def\Cdots{\cdot\!\cdot\!\cdot}
\DeclareMathOperator\curl{curl}

%% Linear algebra
\DeclareMathOperator\Mat{Mat}
\DeclareMathOperator\Span{Span}
\DeclareMathOperator\Trace{tr}
\newcommand{\VV}[2]{\begin{bmatrix} #1 \\ #2 \end{bmatrix}}
\newcommand{\VVV}[3]{\begin{bmatrix} #1 \\ #2 \\ #3 \end{bmatrix}}
\newcommand{\VVVV}[4]{\begin{bmatrix} #1 \\ #2 \\ #3 \\ #4 \end{bmatrix}}
\newcommand{\VVVVV}[5]{\begin{bmatrix} #1 \\ #2 \\ #3 \\ #4 \\ #5 \end{bmatrix}}
\newcommand{\vv}[2]{\begin{bsmallmatrix} #1 \\ #2 \end{bsmallmatrix}}
\newcommand{\vvv}[3]{\begin{bsmallmatrix} #1 \\ #2 \\ #3 \end{bsmallmatrix}}
\newcommand{\vvvv}[4]{\begin{bsmallmatrix} #1 \\ #2 \\ #3 \\ #4 \end{bsmallmatrix}}
\newcommand{\vvvvv}[5]{\begin{bsmallmatrix} #1 \\ #2 \\ #3 \\ #4 \\ #5 \end{bsmallmatrix}}

%% Sums, products, union & intersections, limits
\def\Sum{\sum\limits}
\def\Prod{\prod\limits}
\def\Cap{\mathop\cap\limits}
\def\Cup{\mathop\cup\limits}
\def\Times{\mathop\times\limits}
\def\Oplus{\mathop\oplus\limits}
\def\Lim{\mathop\lim\limits}
\newcommand*{\medcap}{\mathbin{\scalebox{.75}{\ensuremath{\bigcap}}}}%
\newcommand{\freeprod}{\mathop{\Huge \mathlarger{\mathlarger{\ast}}}}

%% Boolean functions
\def\And{\wedge}
\def\Or{\vee}
\def\Not{\neg}

%% Maps
\def\longto{\longrightarrow}
\def\into{\hookrightarrow}
\def\longinto{\longhookrightarrow}
\def\onto{\twoheadrightarrow}
\DeclareRobustCommand\longonto{\relbar\joinrel\twoheadrightarrow}
\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator{\Id}{Id}
\DeclareMathOperator{\ev}{ev}

%% Sets and Rings
\def\A{\mathbb{A}}
\def\C{\mathbb{C}}
\def\E{\mathbb{E}}
\def\F{\mathbb{F}}
\def\HH{\mathbb{H}}
\def\N{\mathbb{N}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\Z{\mathbb{Z}}

%% Abstract algebra commands
\def\normal{\lhd}
\def\normaleq{\unlhd}
\def\nnormal{\ntriangleleft}
\def\nnormaleq{\ntrianglelefteq}
\def\subgroup{\leqslant}
\def\nsubgroup{\nleqslant}
\def\Dot{\bm{.}}
\def\<{\langle}
\def\>{\rangle}
%%
\makeatletter
\DeclareRobustCommand{\normalneq}{\mathrel{\text{$\m@th\proper@ideal$}}}
\newcommand{\proper@ideal}{%
  \ooalign{$\lneq$\cr\raise.22ex\hbox{$\lhd$}\cr}%
}
\makeatother

%% Filled in normal subgroup symbol for characteristic subgroups
\newcommand{\bleq}{\mathrel{\mathpalette\bleqinn\relax}}
\newcommand{\bleqinn}[2]{%
  \ooalign{%
    \raisebox{.2ex}{$#1\blacktriangleleft$}\cr
    $#1\leq$\cr
  }%
}
  
%% Basic algebra commands
\DeclareMathOperator\Aut{Aut}
\DeclareMathOperator\Char{char}
\DeclareMathOperator\cl{cl}
\DeclareMathOperator\Conj{Conj}
\DeclareMathOperator\core{core}
\DeclareMathOperator\Inn{Inn}
\DeclareMathOperator\Gal{Gal}
\DeclareMathOperator\Out{Out}
\DeclareMathOperator\orb{orb}
\DeclareMathOperator\Orb{Orb}
\DeclareMathOperator\Perm{Perm}
\DeclareMathOperator\stab{stab}
\DeclareMathOperator\Stab{Stab}
\DeclareMathOperator\fix{fix}
\DeclareMathOperator\Fix{Fix}
\DeclareMathOperator\Syl{Syl}
\DeclareMathOperator\Sym{Sym}
\DeclareMathOperator\soc{soc}
\DeclareMathOperator{\nil}{nil}
\DeclareMathOperator{\Nil}{Nil}
\DeclareMathOperator\jac{jac}
\DeclareMathOperator\Jac{Jac}
\DeclareMathOperator\rad{rad}
\DeclareMathOperator\Rad{Rad}
\DeclareMathOperator\Eq{Eq}
\DeclareMathOperator\Hol{Hol}
\DeclareMathOperator\Frac{Frac}

%% Special Groups
\DeclareMathOperator\GL{GL}
\DeclareMathOperator\SL{SL}
\DeclareMathOperator\So{SO}
\DeclareMathOperator\SU{SU}
\DeclareMathOperator\PGL{PGL}
\DeclareMathOperator\PSL{PSL}
\DeclareMathOperator\PSU{PSU}
\DeclareMathOperator\PSP{PsP}
\DeclareMathOperator\AGL{AGL}
\DeclareMathOperator\Heis{Heis}
\DeclareMathOperator\Dic{Dic}
\DeclareMathOperator\SA{SA}
\DeclareMathOperator\SD{SD}
\DeclareMathOperator\Fr{Fr}
\DeclareMathOperator\DQ{DQ}
\DeclareMathOperator\QD{QD}
\DeclareMathOperator\OD{OD}
\DeclareMathOperator\Cl{Cl}
\DeclareMathOperator\BinTet{2T}
\DeclareMathOperator\BinOct{2O}
\DeclareMathOperator\BinIcos{2I}
\DeclareMathOperator\Aff{Aff}
\DeclareMathOperator\BS{BS}

%% Categories
\DeclareMathOperator\Hom{Hom}
\DeclareMathOperator\Ob{Ob}
\newcommand{\catname}[1]{{\normalfont\textbf{#1}}}
\newcommand{\Ab}{\catname{Ab}}
\newcommand{\Field}{\catname{Field}}
\newcommand{\Set}{\catname{Set}}
\newcommand{\Grp}{\catname{Grp}}
\newcommand{\Semi}{\catname{Sgp}}
\newcommand{\Ring}{\catname{Ring}}
\newcommand{\Rng}{\catname{Rng}}
\newcommand{\Top}{\catname{Top}}
\newcommand{\Vect}{\catname{Vect}}
\newcommand{\Nilp}{\catname{Nil}}    
\newcommand{\Svl}{\catname{Svl}}
\newcommand\cat{\mathcal{C}}
\newcommand\dat{\mathcal{D}}
\newcommand\eat{\mathcal{E}}
\newcommand\fun{\mathcal{F}}
\DeclareMathOperator\ad{ad}
\def\0{\mathbf{0}}
\def\1{\mathbf{1}}
\def\e{\bm{e}}

%% Book-specific commands
\DeclareMathOperator\Frieze{\mathbf{Frz}}
\DeclareMathOperator\Braid{\mathbf{Braid}}
\DeclareMathOperator\Rect{\mathbf{Rect}}
\DeclareMathOperator\Tri{\mathbf{Tri}}
\DeclareMathOperator\Sq{\mathbf{Sq}}
\DeclareMathOperator\Hex{\mathbf{Hex}}
\DeclareMathOperator\Coin{\mathbf{Coin}}
\DeclareMathOperator\BOX{\mathbf{Box}}
\DeclareMathOperator\Light{\mathbf{Light}}
\DeclareMathOperator\Rubik{\mathbf{Rubik}}
\DeclareMathOperator\Spin{Spin}
\DeclareMathOperator{\Deg}{Deg}

%% Ideals
\newcommand{\MFa}{\mathfrak{a}}
\newcommand{\MFb}{\mathfrak{b}}
\newcommand{\MFc}{\mathfrak{c}}
\newcommand{\MFm}{\mathfrak{m}}
\newcommand{\MFp}{\mathfrak{p}}
\newcommand{\MFq}{\mathfrak{q}}
\newcommand{\MFr}{\mathfrak{r}}
\newcommand{\MFs}{\mathfrak{s}}