new package cool (25sep06)

git-svn-id: svn://tug.org/texlive/trunk@2199 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 5827 insertions, 0 deletions

diff --git a/Master/texmf-dist/source/latex/cool/cool.dtx b/Master/texmf-dist/source/latex/cool/cool.dtx
new file mode 100644
index 00000000000..0312fb8fee0
--- /dev/null
+++ b/Master/texmf-dist/source/latex/cool/cool.dtx
@@ -0,0 +1,5787 @@
+% \iffalse
+%
+%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+%<package>\ProvidesPackage{cool}
+%<package> [2006/09/17 v1.2 COntent Oriented LaTeX]
+%<package>\RequirePackage{ifthen}
+%<package>\RequirePackage{coollist}
+%<package>\RequirePackage{coolstr}
+%<package>\RequirePackage{forloop}
+%<package>\RequirePackage{amsmath}
+%<package>\RequirePackage{amssymb}
+%
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{cool}
+\usepackage{url}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\begin{document}
+\DocInput{cool.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \iffalse meta-comment
+% remove this comment to get a checksum
+% \CheckSum{0}
+% \fi
+%
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+%
+% \changes{v0}{2005/07/20}{pre-Initial version [tenative edition]}
+% \changes{v1.0}{2005/08/27}{Initial Release}
+% \changes{v1.1}{2006/03/19}{Added listlenstore to package to allow storing of the list length}
+% \changes{v1.2}{2006/09/17}{Split off the list, string, and forloop parts to separate packages}
+%
+% \GetFileInfo{cool.sty}
+%
+% \DoNotIndex{\#,\$,\%,\&,\@,\\,\{,\},\^,\_,\~,\ ,\!,\(,\),\,}
+% \DoNotIndex{\@ne,\expandafter}
+% \DoNotIndex{\advance,\begingroup,\catcode,\closein}
+% \DoNotIndex{\newcommand,\renewcommand,\providecommand}
+% \DoNotIndex{\closeout,\day,\def,\edef,\gdef,\let,\empty,\endgroup}
+% \DoNotIndex{\newcounter,\providecounter,\addtocounter,\setcounter,\stepcounter,\value,\arabic}
+% \DoNotIndex{\if,\fi,\ifthenelse,\else,\setboolean,\boolean,\newboolean,\provideboolean,\equal,\AND,\OR,\NOT,\whiledo}
+% \DoNotIndex{\ifcase,\ifcat,\or,\else}
+% \DoNotIndex{\par,\parbox,\mbox,\hbox,\begin,\end,\nabla,\partial}
+% \DoNotIndex{\overline,\bar,\small,\tiny,\mathchoice,\scriptsize,\textrm,\texttt}
+% \DoNotIndex{\alpha,\beta,\gamma,\epsilon,\varepsilon,\delta,\zeta,\eta,\theta,\vartheta,\iota,\kappa,\lambda,\mu,\nu}
+% \DoNotIndex{\xi,\omicron,\pi,\varpi,\rho,\varrho,\sigma,\tau,\upsilon,\phi,\varphi,\chi,\psi,\omega}
+% \DoNotIndex{\Delta,\Gamma,\Theta,\Lambda,\Xi,\Pi,\Sigma,\Phi,\Psi,\Omega}
+% \DoNotIndex{\digamma,\lceil,\rceil,\lfloor,\rfloor,\left,\right,\inp,\inb,\inbr,\inap,\nop}
+% \DoNotIndex{\sum,\prod,\int,\log,\ln,\exp,\sin,\cos,\tan,\csc,\sec,\cot,\arcsin,\arccos,\arctan,\det}
+% \DoNotIndex{\sinh,\cosh,\tanh,\csch,\sech,\coth,\arcsinh,\arccosh,\arctanh}
+% \DoNotIndex{\mod,\max,\min,\gcd,\lcm,\wp,\arg,\dots,\infty,}
+% \DoNotIndex{\frac,\binom,\braket,\@@atop}
+% \DoNotIndex{\cdot,\ldots,\tilde,\times,\dagger,\relax}
+% \DoNotIndex{\mathbb,\roman,\bf,\mathord,\cal,\DeclareMathOperator,\PackageError,\PackageWarning}
+% \DoNotIndex{\csname,\endcsname,\ifx,\ifnum}
+% \DoNotIndex{\COOL@Hypergeometric@pq,\COOL@Hypergeometric@pq@ab@value,\hideOnSF,\COOL@decide@paren}
+% \DoNotIndex{\COOL@decide@indicies}
+% \DoNotIndex{\mod,\bmod,\pmod,\pod,\operatorname}
+% \DoNotIndex{\forLoop}
+% \DoNotIndex{
+% \COOL@notation@AiryAiParen,
+% \COOL@notation@AiryBiParen,
+% \COOL@notation@AppellFOneParen,
+% \COOL@notation@ArcCoshParen,
+% \COOL@notation@ArcCosParen,
+% \COOL@notation@ArcCothParen,
+% \COOL@notation@ArcCotParen,
+% \COOL@notation@ArcCschParen,
+% \COOL@notation@ArcCscParen,
+% \COOL@notation@ArcSechParen,
+% \COOL@notation@ArcSecParen,
+% \COOL@notation@ArcSinhParen,
+% \COOL@notation@ArcSinParen,
+% \COOL@notation@ArcTanhParen,
+% \COOL@notation@ArcTanParen,
+% \COOL@notation@ArithGeoMeanParen,
+% \COOL@notation@AssocLegendrePParen,
+% \COOL@notation@AssocLegendreQParen,
+% \COOL@notation@BernoulliParen,
+% \COOL@notation@BernoulliBParen,
+% \COOL@notation@BesselIParen,
+% \COOL@notation@BesselJParen,
+% \COOL@notation@BesselKParen,
+% \COOL@notation@BesselYParen,
+% \COOL@notation@BetaParen,
+% \COOL@notation@BetaRegularizedParen,
+% \COOL@notation@CarmichaelLambdaParen,
+% \COOL@notation@ChebyshevTParen,
+% \COOL@notation@ChebyshevUParen,
+% \COOL@notation@ConjugateParen,
+% \COOL@notation@CoshIntParen,
+% \COOL@notation@CoshParen,
+% \COOL@notation@CosIntParen,
+% \COOL@notation@CosParen,
+% \COOL@notation@CothParen,
+% \COOL@notation@CotParen,
+% \COOL@notation@CschParen,
+% \COOL@notation@CscParen,
+% \COOL@notation@CyclotomicCParen,
+% \COOL@notation@DaggerParen,
+% \COOL@notation@DedekindEtaParen,
+% \COOL@notation@DetParen,
+% \COOL@notation@DiGammaParen,
+% \COOL@notation@DiracDeltaParen,
+% \COOL@notation@DivisorsParen,
+% \COOL@notation@DivisorSigmaParen,
+% \COOL@notation@DiscreteDeltaParen,
+% \COOL@notation@EllipticEParen,
+% \COOL@notation@EllipticExpParen,
+% \COOL@notation@EllipticFParen,
+% \COOL@notation@EllipticKParen,
+% \COOL@notation@EllipticLogParen,
+% \COOL@notation@EllipticNomeQInvParen,
+% \COOL@notation@EllipticNomeQParen,
+% \COOL@notation@EllipticPiParen,
+% \COOL@notation@EllipticThetaParen,
+% \COOL@notation@ErfcInvParen,
+% \COOL@notation@ErfcParen,
+% \COOL@notation@ErfInvParen,
+% \COOL@notation@ErfiParen,
+% \COOL@notation@ErfParen,
+% \COOL@notation@EulerParen,
+% \COOL@notation@EulerEParen,
+% \COOL@notation@EulerPhiParen,
+% \COOL@notation@ExpIntEiParen,
+% \COOL@notation@ExpIntEParen,
+% \COOL@notation@ExpParen,
+% \COOL@notation@ExtendedGCDParen,
+% \COOL@notation@FactorIntegerParen,
+% \COOL@notation@FibonacciParen,
+% \COOL@notation@FibonacciFParen,
+% \COOL@notation@FractionalPartParen,
+% \COOL@notation@FresnelCParen,
+% \COOL@notation@FresnelSParen,
+% \COOL@notation@GammaFuncParen,
+% \COOL@notation@GammaRegularizedParen,
+% \COOL@notation@GCDParen,
+% \COOL@notation@GegenbauerCParen,
+% \COOL@notation@HeavisideStepParen,
+% \COOL@notation@HermiteHParen,
+% \COOL@notation@HypergeometricParen,
+% \COOL@notation@IdentityMatrixParen,
+% \COOL@notation@ImagParen,
+% \COOL@notation@IntegerPartParen,
+% \COOL@notation@InverseBetaRegularizedParen,
+% \COOL@notation@InverseGammaRegularizedParen,
+% \COOL@notation@JacobiAmplitudeParen,
+% \COOL@notation@JacobiCDInvParen,
+% \COOL@notation@JacobiCDParen,
+% \COOL@notation@JacobiCNInvParen,
+% \COOL@notation@JacobiCNParen,
+% \COOL@notation@JacobiCSInvParen,
+% \COOL@notation@JacobiCSParen,
+% \COOL@notation@JacobiDCInvParen,
+% \COOL@notation@JacobiDCParen,
+% \COOL@notation@JacobiDNInvParen,
+% \COOL@notation@JacobiDNParen,
+% \COOL@notation@JacobiDSInvParen,
+% \COOL@notation@JacobiDSParen,
+% \COOL@notation@JacobiNCInvParen,
+% \COOL@notation@JacobiNCParen,
+% \COOL@notation@JacobiNDInvParen,
+% \COOL@notation@JacobiNDParen,
+% \COOL@notation@JacobiNSInvParen,
+% \COOL@notation@JacobiNSParen,
+% \COOL@notation@JacobiPParen,
+% \COOL@notation@JacobiSCInvParen,
+% \COOL@notation@JacobiSCParen,
+% \COOL@notation@JacobiSDInvParen,
+% \COOL@notation@JacobiSDParen,
+% \COOL@notation@JacobiSNInvParen,
+% \COOL@notation@JacobiSNParen,
+% \COOL@notation@JacobiZetaParen,
+% \COOL@notation@KleinInvariantJParen,
+% \COOL@notation@LaugerreLParen,
+% \COOL@notation@LCMParen,
+% \COOL@notation@LegendrePParen,
+% \COOL@notation@LegendreQParen,
+% \COOL@notation@LerchPhiParen,
+% \COOL@notation@LogGammaParen,
+% \COOL@notation@LogIntParen,
+% \COOL@notation@LogParen,
+% \COOL@notation@MathieuCharacteristicAParen,
+% \COOL@notation@MathieuCharacteristicBParen,
+% \COOL@notation@MathieuCharacteristicExponentParen,
+% \COOL@notation@MathieuSParen,
+% \COOL@notation@MathieuCParen,
+% \COOL@notation@MoebiusMuParen,
+% \COOL@notation@MaxParen,
+% \COOL@notation@MinParen,
+% \COOL@notation@ModularLambdaParen,
+% \COOL@notation@NevilleThetaCParen,
+% \COOL@notation@NevilleThetaDParen,
+% \COOL@notation@NevilleThetaNParen,
+% \COOL@notation@NevilleThetaSParen,
+% \COOL@notation@NielsenPolyLogParen,
+% \COOL@notation@PartitionsPParen,
+% \COOL@notation@PartitionsQParen,
+% \COOL@notation@PolyGammaParen,
+% \COOL@notation@PolyLogParen,
+% \COOL@notation@PrimeParen,
+% \COOL@notation@PrimePiParen,
+% \COOL@notation@ProductLogParen,
+% \COOL@notation@QuotientParen,
+% \COOL@notation@RealParen,
+% \COOL@notation@RegHypergeometricParen,
+% \COOL@notation@RiemannSiegelThetaParen,
+% \COOL@notation@RiemannSiegelZParen,
+% \COOL@notation@SechParen,
+% \COOL@notation@SecParen,
+% \COOL@notation@SignParen,
+% \COOL@notation@SinhIntParen,
+% \COOL@notation@SinhParen,
+% \COOL@notation@SinIntParen,
+% \COOL@notation@SinParen,
+% \COOL@notation@SphericalHarmonicYParen,
+% \COOL@notation@StruveHParen,
+% \COOL@notation@StruveLParen,
+% \COOL@notation@TanhParen,
+% \COOL@notation@TanParen,
+% \COOL@notation@TransposeParen,
+% \COOL@notation@TrParen,
+% \COOL@notation@WeierstrassPInvParen,
+% \COOL@notation@WeierstrassPParen,
+% \COOL@notation@WeierstrassZetaParen,
+% \COOL@notation@ZetaParen}
+% \DoNotIndex{\COOL@notation@KroneckerDeltaIndicies,\COOL@notation@LeviCivitaIndicies}
+% \DoNotIndex{\COOL@notation@SphericalHarmonicParen,\COOL@notation@SphericalHarmonicSymb}
+% \DoNotIndex{\COOL@notation@WeierstrassPHalfPeriodValuesDisplay,\COOL@notation@WeierstrassZetaHalfPeriodValuesDisplay}
+% \DoNotIndex{
+% \COOL@Beta@arg@i,
+% \COOL@Beta@arg@ii,
+% \COOL@Beta@arg@iii,
+% \COOL@Beta@arg@iv,
+% \COOL@BetaRegularized@arg@i,
+% \COOL@BetaRegularized@arg@ii,
+% \COOL@BetaRegularized@arg@iii,
+% \COOL@BetaRegularized@arg@iv,
+% \COOL@EllipticE@arg@i,
+% \COOL@EllipticE@arg@ii,
+% \COOL@EllipticF@arg@i,
+% \COOL@EllipticF@arg@ii,
+% \COOL@EllipticPi@arg@i,
+% \COOL@EllipticPi@arg@ii,
+% \COOL@EllipticPi@arg@iii,
+% \COOL@Euler@arg@i,
+% \COOL@Euler@arg@ii,
+% \COOL@Fibonacci@arg@i,
+% \COOL@Fibonacci@arg@ii,
+% \COOL@InverseBetaRegularized@arg@i,
+% \COOL@InverseBetaRegularized@arg@ii,
+% \COOL@InverseBetaRegularized@arg@iii,
+% \COOL@InverseBetaRegularized@arg@iv,
+% \COOL@LegendreP@arg@i,
+% \COOL@LegendreP@arg@ii,
+% \COOL@LegendreP@arg@iii,
+% \COOL@LegendreP@arg@iv,
+% \COOL@LegendreQ@arg@i,
+% \COOL@LegendreQ@arg@ii,
+% \COOL@LegendreQ@arg@iii,
+% \COOL@LegendreQ@arg@iv,
+% \COOL@PolyLog@arg@i,
+% \COOL@PolyLog@arg@ii,
+% \COOL@PolyLog@arg@iii,
+% \COOL@WeiSigma@arg@z@i,
+% \COOL@WeiSigma@arg@z@ii,
+% \COOL@Zeta@arg@i,
+% \COOL@Zeta@arg@ii}
+% \DoNotIndex{
+% \COOL@notation@AssocLegendrePSymb,
+% \COOL@notation@AssocLegendreQSymb,
+% \COOL@notation@BesselISymb,
+% \COOL@notation@BesselJSymb,
+% \COOL@notation@BesselKSymb,
+% \COOL@notation@BesselYSymb,
+% \COOL@notation@ChebyshevTSymb,
+% \COOL@notation@ChebyshevUSymb,
+% \COOL@notation@EllipticESymb,
+% \COOL@notation@EllipticFSymb,
+% \COOL@notation@EllipticKSymb,
+% \COOL@notation@EllipticPiSymb,
+% \COOL@notation@GegenbauerCSymb,
+% \COOL@notation@HermiteHSymb,
+% \COOL@notation@HypergeometricSymb,
+% \COOL@notation@HypergeometricUSymb,
+% \COOL@notation@JacobiPSymb,
+% \COOL@notation@JacobiZetaSymb,
+% \COOL@notation@LaugerreLSymb,
+% \COOL@notation@LegendrePSymb,
+% \COOL@notation@LegendreQSymb,
+% \COOL@notation@LogBaseESymb,
+% \COOL@notation@MeijerGSymb,
+% \COOL@notation@RegHypergeometricSymb,
+% \COOL@notation@SphericalHarmonicYSymb}
+% \DoNotIndex{\COOL@wrt@temp,\COOL@temp@D@top@power,\COOL@temp@D@top,\COOL@temp@D@result,\COOL@temp@D@bot}
+% \DoNotIndex{\COOL@power@temp}
+% \DoNotIndex{\listval,\liststore,\isint,\isnumeric}
+% \DoNotIndex{
+% \COOL@list@temp@i,
+% \COOL@list@temp@ii,
+% \COOL@list@temp@iii}
+% \DoNotIndex{
+% \COOL@MeijerG@sniffer,
+% \COOL@MeijerG@sniffer@end}
+% \DoNotIndex{\COOL@Multinomial@tempa}
+% \DoNotIndex{
+% \COOL@notation@ArcTrig,
+% \COOL@notation@Conjugate,
+% \COOL@notation@DShorten,
+% \COOL@notation@LogShowBase}
+% \DoNotIndex{
+% \COOL@notation@DDisplayFunc,
+% \COOL@notation@DetDisplay,
+% \COOL@notation@IntegrateDisplayFunc,
+% \COOL@notation@ModDisplay}
+% \DoNotIndex{
+% \COOL@notation@KroneckerDeltaUseComma,
+% \COOL@notation@LeviCivitaUseComma}
+%
+% \title{The \textsf{cool} package\thanks{This document
+% corresponds to \textsf{cool}~\fileversion,
+% dated~\filedate.}}
+% \author{nsetzer}
+%
+% \maketitle
+%
+% \setcounter{IndexColumns}{2}
+% \StopEventually{\PrintChanges\PrintIndex}
+%
+%
+% This is the \textsf{cool} package: a COntent Oriented \LaTeX{} package.  That is, it is designed to give \LaTeX{} 
+% commands the ability to contain the mathematical meaning while retaining the typesetting versatility.
+%
+% This package requires the following, non-standard \LaTeX{} packages (all of which are available on \url{www.ctan.org}):
+% \textsf{coolstr},
+% \textsf{coollist},
+% \textsf{forloop}
+%
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\section{Implementation}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%    \begin{macrocode}
+\newcounter{COOL@ct} %just a general counter
+\newcounter{COOL@ct@}%just a general counter
+%    \end{macrocode}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+%\subsection{Parenthesis}
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%    \begin{macrocode}
+\newcommand{\inp}[2][0cm]{\left(#2\parbox[h][#1]{0cm}{}\right)}
+        % in parentheses ()
+\newcommand{\inb}[2][0cm]{\left[#2\parbox[h][#1]{0cm}{}\right]}
+        % in brackets []
+\newcommand{\inbr}[2][0cm]{\left\{#2\parbox[h][#1]{0cm}{}\right\}}
+	% in braces {}
+\newcommand{\inap}[2][0cm]{\left<{#2}\parbox[h][#1]{0cm}{}\right>}
+	% in angular parentheses <>
+\newcommand{\nop}[1]{\left.{#1}\right.}
+	% no parentheses
+%    \end{macrocode}
+%
+%
+% \begin{macro}{\COOL@decide@paren}
+% |\COOL@decide@paren[|\meta{parenthesis type}|]{|\meta{function name}|}{|\meta{contained text}|}|.
+%
+% \noindent Since the handling of parentheses is something that will be common to many elements this 
+% function will take care of it.  
+%
+% If the optional argument is given, |\COOL@notation@|\meta{function name}|Paren| is ignored and 
+% \meta{parenthesis type} is used
+%
+% \meta{parenthesis type} and |\COOL@notation@|\meta{function name}|Paren| must be one of |none|, |p| for |()|, |b| for |[]|, |br| for |{}|, |ap| for \meta{}, |inv| for |\left.\right.|
+%    \begin{macrocode}
+\let\COOL@decide@paren@no@type=\relax
+\newcommand{\COOL@decide@paren}[3][\COOL@decide@paren@no@type]{%
+\ifthenelse{ \equal{#1}{\COOL@decide@paren@no@type} }%
+	{%
+	\def\COOL@decide@paren@type{\csname COOL@notation@#2Paren\endcsname}%
+	}%
+% Else
+	{%
+	\def\COOL@decide@paren@type{#1}%
+	}%
+\ifthenelse{ \equal{\COOL@decide@paren@type}{none} }%
+	{%
+	#3%
+	}%
+% Else
+	{%
+	\ifthenelse{ \equal{\COOL@decide@paren@type}{p} }%
+		{%
+		\inp{#3}%
+		}%
+	% Else
+		{%
+		\ifthenelse{ \equal{\COOL@decide@paren@type}{b} }%
+			{%
+			\inb{#3}%
+			}%
+		% Else
+			{%
+			\ifthenelse{ \equal{\COOL@decide@paren@type}{br} }%
+				{%
+				\inbr{#3}%
+				}%
+			% Else
+				{%
+				\ifthenelse{ \equal{\COOL@decide@paren@type}{ap} }%
+					{%
+					\inap{#3}%
+					}%
+				% Else
+					{%
+					\ifthenelse{ \equal{\COOL@decide@paren@type}{inv} }%
+						{%
+						\nop{#3}%
+						}%
+					% Else
+						{%
+						\PackageError{cool}{Invalid Parenthesis Option}%
+							{*Paren can only be `none', `p', `b', `br', `ap', `inv'}%
+						}%
+					}%
+				}%
+			}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+%\subsection{Indicies}
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\COOL@decide@indicies}
+% |\COOL@decide@indicies|\marg{function name}\marg{local indication}\marg{indicies}
+%
+% \noindent Since up or down indicies can be as common as the parenthesis decision, this macro is the solution.
+%
+% \meta{local indication} must be either |u| or |d| 
+%
+% \meta{indicies} is very likely to be required to be a comma separated list in the near future
+%
+% the options for indicies are
+%
+% \begin{tabular}{ll}
+% |local| 	& allow the indicies to be decided by an optional argument to  		\\
+%		& the function (such as |\LeviCivita[u]{i j}|)				\\
+% |up|		& force the indicies to appear as superscript				\\
+% |down|	& force the indicies to appear as subscript				\\
+% \end{tabular}
+%
+%    \begin{macrocode}
+\newcommand{\COOL@decide@indicies}[3]{%
+\def\COOL@decide@indicies@placement%
+	{\csname COOL@notation@#1Indicies\endcsname}%
+\ifthenelse{\equal{\COOL@decide@indicies@placement}{local}}%
+	{%
+	\ifthenelse{\equal{#2}{u}}%
+		{^{#3}}%
+		{_{#3}}%
+	}%
+% Else
+	{%
+	\ifthenelse{\equal{\COOL@decide@indicies@placement}{up}}%
+		{%
+		{^{#3}}%
+		}%
+	% Else
+		{%
+		\ifthenelse{\equal{\COOL@decide@indicies@placement}{down}}%
+			{%
+			{_{#3}}%
+			}%
+		% else
+			{%
+			\PackageError{cool}{Invalid Option Sent}%
+				{#1Indices can only be 'up', 'down', or 'local'}%
+			}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+%\subsection{COntent Oriented LaTeX (COOL)}
+% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Style}
+% |\Style{|\meta{options}|}| sets the style of the output (how to notate particular functions).
+% \meta{options} is a comma delimited list of the form \meta{key}|=|\meta{value}, where \meta{key} is the \emph{long}
+% form of the command name without the preceeding backslash (i.e. |Integrate| and not |Int| or |\Int|).
+% The list can be in any order and need only contain the styles that the user desires to set.
+%
+% There can be multiple |\Style| commands within any document---the styled output of the command depends on the
+% last |\Style| command to have specified its style.
+%
+% For a list of styling options for a command, see the code where the command is defined
+%
+%    \begin{macrocode}
+\newcommand{\Style}[1]{%
+\COOL@keyeater#1,\COOL@keystop\COOL@keyend%
+}
+\newcommand{\COOL@keystop}{@@@}%
+\def\COOL@keyeater#1=#2,#3\COOL@keyend{%
+\ifx#3\COOL@keystop%
+	\expandafter\gdef\csname COOL@notation@#1\endcsname{#2}%
+\else%
+	\expandafter\gdef\csname COOL@notation@#1\endcsname{#2}%
+	\COOL@keyeater#3\COOL@keyend%
+\fi%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\UseStyleFile}
+% Since notational style should be kept consistent and will likely need to span several documents, use this command
+% to input a notation style file that has previously been prepared. (to be implemented in a future release)
+%    \begin{macrocode}
+\newcommand{\UseStyleFile}[1]{}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Fundamental Constants}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% see \url{http://functions.wolfram.com/} for the definitions
+% \begin{macro}{\I}
+% The square root of minus 1 ($\sqrt{-1}$), $\I$.
+%    \begin{macrocode}
+\newcommand{\I}{i}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\E}
+% Euler's constant and the base of the natural logarithm, $\E$.
+%    \begin{macrocode}
+\newcommand{\E}{e}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\PI}
+% Pi---the ratio of the circumference of a circle to its diameter, $\PI$.
+%    \begin{macrocode}
+\newcommand{\PI}{\pi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GoldenRatio}
+% The Golden Ratio, $\GoldenRatio$
+%    \begin{macrocode}
+\newcommand{\GoldenRatio}{\varphi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\EulerGamma}
+% Euler's Gamma constant, $\EulerGamma$
+%    \begin{macrocode}
+\newcommand{\EulerGamma}{\gamma}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Catalan}
+% Catalan constant, $\Catalan$
+%    \begin{macrocode}
+\newcommand{\Catalan}{C}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Glaisher}
+% Glaisher constant, $\Glaisher$
+%    \begin{macrocode}
+\newcommand{\Glaisher}{\mathord{\operatorname{Glaisher}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Khinchin}
+% Khinchin constant, $\Khinchin$
+%    \begin{macrocode}
+\newcommand{\Khinchin}{\mathord{\operatorname{Khinchin}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Symbols}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Infinity}
+% Infinity, $\Infinity$
+%    \begin{macrocode}
+\newcommand{\Infinity}{\infty}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Indeterminant}
+% An indeterminant quantity
+%    \begin{macrocode}
+\newcommand{\Indeterminant}{%
+	\mathchoice%
+		{\mbox{\textrm>}}%
+		{\mbox{\small>}}%
+		{\mbox{\scriptsize>}}%
+		{\mbox{\tiny>}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DirectedInfinity}
+% \begin{macro}{\DirInfty}
+% Directed Infinity |\DirectedInfinity{|\meta{complex number}|}| or |\DirInfty{|\meta{complex number}|}|
+%    \begin{macrocode}
+\newcommand{\DirectedInfinity}[1]{#1 \, \infty}
+\newcommand{\DirInfty}[1]{\DirectedInfinity{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\ComplexInfinity}
+% \begin{macro}{\CInfty}
+% Complex infinity, $\CInfty$
+%    \begin{macrocode}
+\newcommand{\ComplexInfinity}{\tilde{\infty}}
+\newcommand{\CInfty}{\ComplexInfinity}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Exponential Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Exp}
+% Exponential---for use when $\E^x$ won't suffice, $\Exp{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ExpParen}{p}
+\newcommand{\Exp}[1]
+{%
+\exp\COOL@decide@paren{Exp}{#1}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Log}
+% Logarithm, |\Log{x}|.  This function has several options to be set.  The usual parentheses, then some
+% about the notation to be used for displaying the symbol.
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LogParen}{none}
+%    \end{macrocode}
+% The following set the symbols:
+%
+% |LogBaseESymb| can be |ln| or |log|, indicating what symbol should be used for the natural logarithm.  If set to
+% |log| then logarithms of base 10 are displayed as $\log_{10}$.
+%
+% |LogShowBase| can be either |at will| or |always| and decides whether or not one should show the base, as in
+% |log_b x|.  If this option is set to |always| then |LogBaseESymb| is ignored.
+%
+% \begin{tabular}{lll}
+% |\Log{5}|				& $\Log{5}$		& $\displaystyle \Log{5}$		\\
+% |\Log[10]{5}| 			& $\Log[10]{5}$		& $\displaystyle \Log[10]{5}$		\\
+% |\Log[4]{5}|				& $\Log[4]{5}$		& $\displaystyle \Log[4]{5}$		\\
+% |\Style{LogBaseESymb=log}|%
+% \Style{LogBaseESymb=log}										\\
+% |\Log{5}|				& $\Log{5}$		& $\displaystyle \Log{5}$		\\
+% |\Log[10]{5}| 			& $\Log[10]{5}$		& $\displaystyle \Log[10]{5}$		\\
+% |\Log[4]{5}|				& $\Log[4]{5}$		& $\displaystyle \Log[4]{5}$		\\
+% |\Style{LogShowBase=always}|%
+% \Style{LogBaseESymb=ln}%
+% \Style{LogShowBase=always}										\\
+% |\Log{5}|				& $\Log{5}$		& $\displaystyle \Log{5}$		\\
+% |\Log[10]{5}| 			& $\Log[10]{5}$		& $\displaystyle \Log[10]{5}$		\\
+% |\Log[4]{5}|				& $\Log[4]{5}$		& $\displaystyle \Log[4]{5}$		\\
+% |\Style{LogShowBase=at will}|%
+% \Style{LogShowBase=at will}										\\
+% |\Log{5}|				& $\Log{5}$		& $\displaystyle \Log{5}$		\\
+% |\Log[10]{5}| 			& $\Log[10]{5}$		& $\displaystyle \Log[10]{5}$		\\
+% |\Log[4]{5}|				& $\Log[4]{5}$		& $\displaystyle \Log[4]{5}$		\\
+% |\Style{LogParen=p}|%
+% \Style{LogParen=p}											\\
+% |\Log[4]{5}|				& $\Log[4]{5}$		& $\displaystyle \Log[4]{5}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LogBaseESymb}{ln}% 'ln', 'log'
+	\newcommand{\COOL@notation@LogShowBase}{at will}% 'at will', 'always'
+\newcommand{\Log}[2][\E]
+{%
+\ifthenelse{ \equal{\COOL@notation@LogShowBase}{at will} }%
+	{%
+	\ifthenelse{ \equal{#1}{\E} }%
+		{%
+		\ifthenelse{ \equal{\COOL@notation@LogBaseESymb}{ln} }%
+			{%
+			\ln \COOL@decide@paren{Log}{#2}%
+			}%
+		% Else
+			{%
+			\ifthenelse{ \equal{\COOL@notation@LogBaseESymb}{log} }%
+				{%
+				\log \COOL@decide@paren{Log}{#2}%
+				}%
+			% Else
+				{%
+				\PackageError{cool}{Invalid Option Sent}%
+					{LogBaseESymb can only be `ln' or `log'}%
+				}%
+			}%
+		}%
+	% Else
+		{%
+		\ifthenelse{	\equal{#1}{10} \AND 
+				\NOT \equal{\COOL@notation@LogBaseESymb}{log}	 }%
+			{%
+			\log \COOL@decide@paren{Log}{#2}%
+			}%
+		% Else
+			{%
+			\log_{#1} \COOL@decide@paren{Log}{#2}%
+			}%
+		}%
+	}%
+% Else
+	{%
+	\ifthenelse{ \equal{\COOL@notation@LogShowBase}{always} }%
+		{%
+		\log_{#1}\COOL@decide@paren{Log}{#2}%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Option Sent}%
+			{LogShowBase can only be 'at will' or 'always'}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Trigonometric Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Sin}
+% The sine function, |\Sin{x}|, $\Sin{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SinParen}{p}
+\newcommand{\Sin}[1]{\sin\COOL@decide@paren{Sin}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Cos}
+% The cosine function, |\Cos{x}|, $\Cos{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CosParen}{p}
+\newcommand{\Cos}[1]{\cos\COOL@decide@paren{Cos}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Tan}
+% The tangent function, |\Tan{x}|, $\Tan{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@TanParen}{p}
+\newcommand{\Tan}[1]{\tan\COOL@decide@paren{Tan}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Csc}
+% The cosecant function, |\Csc{x}|, $\Csc{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CscParen}{p}
+\newcommand{\Csc}[1]{\csc\COOL@decide@paren{Csc}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Sec}
+% The secant function, |\Sec{x}|, $\Sec{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SecParen}{p}
+\newcommand{\Sec}[1]{\sec\COOL@decide@paren{Sec}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Cot}
+% The cotangent function, |\Cot{x}|, $\Cot{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CotParen}{p}
+\newcommand{\Cot}[1]{\cot\COOL@decide@paren{Cot}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Inverse Trigonometric Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\COOL@notation@ArcTrig}
+% The inverse trigoneometric functions style is governed by this global key.  It's options are
+%
+% |inverse| (default), this displays as $\sin^{-1}$
+%
+% |arc|, this displays as $\arcsin$
+%    \begin{macrocode}
+	\def\COOL@notation@ArcTrig{inverse}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcSin}
+% The inverse of the sine function, |\ArcSin{x}|, $\ArcSin{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcSinParen}{p}
+\newcommand{\ArcSin}[1]{%
+\ifthenelse{ \equal{\COOL@notation@ArcTrig}{inverse} }%
+	{%
+	\sin^{-1}\COOL@decide@paren{ArcSin}{#1}%
+	}
+% else
+	{
+	\ifthenelse{\equal{\COOL@notation@ArcTrig}{arc}}%
+		{%
+		\arcsin\COOL@decide@paren{ArcSin}{#1}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{Invalid option sent}{}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCos}
+% the inverse of the cosine function, |\ArcCos{x}|, $\ArcCos{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCosParen}{p}
+\newcommand{\ArcCos}[1]{%
+\ifthenelse{ \equal{\COOL@notation@ArcTrig}{inverse} }%
+	{%
+	\cos^{-1}\COOL@decide@paren{ArcCos}{#1}%
+	}%
+% else
+	{%
+	\ifthenelse{\equal{\COOL@notation@ArcTrig}{arc}}%
+		{%
+		\arccos\COOL@decide@paren{ArcCos}{#1}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{Invalid option sent}{}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcTan}
+% The inverse of the tangent function, |\ArcTan{x}|, $\ArcTan{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcTanParen}{p}
+\newcommand{\ArcTan}[1]{%
+\ifthenelse{ \equal{\COOL@notation@ArcTrig}{inverse} }%
+	{%
+	\tan^{-1}\COOL@decide@paren{ArcTan}{#1}%
+	}%
+% else
+	{%
+	\ifthenelse{\equal{\COOL@notation@ArcTrig}{arc}}%
+		{%
+		\arctan\COOL@decide@paren{ArcTan}{#1}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{Invalid option sent}{}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCsc}
+% The Inverse Cosecant function, |\ArcCsc{x}|, $\ArcCsc{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCscParen}{p}
+\newcommand{\ArcCsc}[1]{\csc^{-1}\COOL@decide@paren{ArcCsc}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcSec}
+% The inverse secant function, |\ArcSec{x}|, $\ArcSec{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcSecParen}{p}
+\newcommand{\ArcSec}[1]{\sec^{-1}\COOL@decide@paren{ArcSec}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCot}
+% The inverse cotangent function, |\ArcCot{x}|, $\ArcCot{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCotParen}{p}
+\newcommand{\ArcCot}[1]{\cot^{-1}\COOL@decide@paren{ArcCot}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Hyperbolic Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Sinh}
+% Hyperbolic sine, |\Sinh{x}|, $\Sinh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SinhParen}{p}
+\newcommand{\Sinh}[1]{\sinh\COOL@decide@paren{Sinh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Cosh}
+% Hyperbolic cosine, |\Cosh{x}|, $\Cosh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CoshParen}{p}
+\newcommand{\Cosh}[1]{\cosh\COOL@decide@paren{Cosh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Tanh}
+% Hyperbolic Tangent, |\Tanh{x}|, $\Tanh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@TanhParen}{p}
+\newcommand{\Tanh}[1]{\tanh\COOL@decide@paren{Tanh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Csch}
+% Hyperbolic cosecant |\Csch{x}|, $\Csch{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CschParen}{p}
+	\DeclareMathOperator{\csch}{csch}
+\newcommand{\Csch}[1]{\csch\COOL@decide@paren{Csch}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Sech}
+% Hyperbolic secant, |\Sech{x}|, $\Sech{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SechParen}{p}
+	\DeclareMathOperator{\sech}{sech}
+\newcommand{\Sech}[1]{\sech\COOL@decide@paren{Sech}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Coth}
+% Hyperbolic Cotangent, |\Coth{x}|, $\Coth{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CothParen}{p}
+\newcommand{\Coth}[1]{\coth\COOL@decide@paren{Coth}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Inverse Hyperbolic Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\ArcSinh}
+% Inverse hyperbolic sine, |\ArcSinh{x}|, $\ArcSinh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcSinhParen}{p}
+\newcommand{\ArcSinh}[1]{\sinh^{-1}\COOL@decide@paren{ArcSinh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCosh}
+% Inverse hyperbolic cosine, |\ArcCosh{x}|, $\ArcCosh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCoshParen}{p}
+\newcommand{\ArcCosh}[1]{\cosh^{-1}\COOL@decide@paren{ArcCosh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcTanh}
+% Inverse hyperbolic tangent, |\ArcTanh{x}|, $\ArcTanh{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcTanhParen}{p}
+\newcommand{\ArcTanh}[1]{\tanh^{-1}\COOL@decide@paren{ArcTanh}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCsch}
+% Inverse hyperbolic cosecant, |\ArcCsch{x}|, $\ArcCsch{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCschParen}{p}
+\newcommand{\ArcCsch}[1]{\csch^{-1}\COOL@decide@paren{ArcCsch}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcSech}
+% Inverse hyperbolic secant, |\ArcSech{x}|, $\ArcSech{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcSechParen}{p}
+\newcommand{\ArcSech}[1]{\sech^{-1}\COOL@decide@paren{ArcSech}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ArcCoth}
+% Inverse hyperbolic cotangent, |\ArcCoth{x}|, $\ArcCoth{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArcCothParen}{p}
+\newcommand{\ArcCoth}[1]{\coth^{-1}\COOL@decide@paren{ArcCoth}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Product Logarithms}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+% \begin{macro}{\LambertW}
+% Lambert Function. |\LambertW| is an alias for |\ProductLog| and its properties are therefore set using that function
+%    \begin{macrocode}
+\newcommand{\LambertW}[1]{\ProductLog{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ProductLog}
+% Generalized Lambert Function |\ProductLog{|[\meta{index}|,|]\meta{variable}|}|.
+%
+% \begin{tabular}{lll}
+% Lambert Function		& |\ProductLog{x}|	& $\ProductLog{x}$		\\
+% Generalized Lambert Function	& |\ProductLog{k,x}|	& $\ProductLog{k,x}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ProductLogParen}{p}
+\newcommand{\ProductLog}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer}=1}%
+	{%
+	W\!\COOL@decide@paren{ProductLog}{#1}%
+	}%
+% else
+	{%
+	\ifthenelse{\value{COOL@listpointer}=2}%
+		{%
+		W_{\listval{#1}{1}}\!\COOL@decide@paren{ProductLog}{\listval{#1}{2}}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{`ProductLog' Invaid Argument}%
+			{Must have a comma separated list of length 1 or 2}
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Max and Min}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Max}
+% the maximum function, |\Max{x,y,z}|, $\Max{x,y,z}$ 
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MaxParen}{p}
+\newcommand{\Max}[1]{\max\COOL@decide@paren{Max}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Min}
+% the minimum function, |\Min{x,y,z}|, $\Min{x,y,z}$ 
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MinParen}{p}
+\newcommand{\Min}[1]{\min\COOL@decide@paren{Min}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Bessel Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\BesselJ}
+% Bessel Function of the first kind, |\BesselJ{\nu}{x}|, $\BesselJ{\nu}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BesselJSymb}{J}
+	\newcommand{\COOL@notation@BesselJParen}{p}
+\newcommand{\BesselJ}[2]%
+{\COOL@notation@BesselJSymb_{#1}\!\COOL@decide@paren{BesselJ}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\BesselY}
+% Bessel Function of the second kind, |\BesselY{\nu}{x}|, $\BesselY{\nu}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BesselYSymb}{Y}
+	\newcommand{\COOL@notation@BesselYParen}{p}
+\newcommand{\BesselY}[2]%
+{\COOL@notation@BesselYSymb_{#1}\!\COOL@decide@paren{BesselY}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\BesselI}
+% Modified Bessel Function of the first kind, |\BesselI{\nu}{x}|, $\BesselI{\nu}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BesselISymb}{I}
+	\newcommand{\COOL@notation@BesselIParen}{p}
+\newcommand{\BesselI}[2]%
+{\COOL@notation@BesselISymb_{#1}\!\COOL@decide@paren{BesselI}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\BesselK}
+% Modified Bessel Function of the second kind, |\BesselK{\nu}{x}|, $\BesselK{\nu}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BesselKSymb}{K}
+	\newcommand{\COOL@notation@BesselKParen}{p}
+\newcommand{\BesselK}[2]%
+{\COOL@notation@BesselKSymb_{#1}\!\COOL@decide@paren{BesselK}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Airy Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\AiryAi}
+% Airy Ai Function, |\AiryAi{x}|, $\AiryAi{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@AiryAiParen}{p}
+	\DeclareMathOperator{\AiryAiSymb}{Ai}
+\newcommand{\AiryAi}[1]{\AiryAiSymb\!\COOL@decide@paren{AiryAi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\AiryBi}
+% Airy Bi Function, |\AiryBi{x}|, $\AiryBi{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@AiryBiParen}{p}
+	\DeclareMathOperator{\AiryBiSymb}{Bi}
+\newcommand{\AiryBi}[1]{\AiryBiSymb\!\COOL@decide@paren{AiryBi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Struve Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\StruveH}
+% Struve H function, |\StruveH{\nu}{z}|,  $\StruveH{\nu}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@StruveHParen}{p}
+\newcommand{\StruveH}[2]{ {\bf H}_{#1}\!\COOL@decide@paren{StruveH}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\StruveL}
+% Struve L function,  |\StruveL{\nu}{z}|, $\StruveL{\nu}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@StruveLParen}{p}
+\newcommand{\StruveL}[2]{ {\bf L}_{#1}\!\COOL@decide@paren{StruveL}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Integer Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Floor}
+% floor, |\Floor{x}|, $\Floor{x}$
+%    \begin{macrocode}
+\newcommand{\Floor}[1]{\lfloor #1 \rfloor}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Ceiling}
+% ceiling, |\Ceiling{x}|, $\Ceiling{x}$
+%    \begin{macrocode}
+\newcommand{\Ceiling}[1]{\lceil #1 \rceil}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Round}
+% round, |\Round{x}|, $\Round{x}$
+%    \begin{macrocode}
+\newcommand{\Round}[1]{\lfloor #1 \rceil}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iPart}
+% \begin{macro}{\IntegerPart}
+% The integer part of a real number, |\iPart{x}|, |\IntegerPart{x}|, $\iPart{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@IntegerPartParen}{p}
+	\DeclareMathOperator{\iPartSymb}{int}
+\newcommand{\iPart}[1]{\iPartSymb\COOL@decide@paren{IntegerPart}{#1}}
+\newcommand{\IntegerPart}[1]{\iPart{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fPart}
+% \begin{macro}{\FractionalPart}
+% the fractional part of a real number, |\fPart{x}|, |\FractionalPart{x}|, $\fPart{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@FractionalPartParen}{p}
+	\DeclareMathOperator{\fPartSymb}{frac}
+\newcommand{\fPart}[1]{\fPartSymb\COOL@decide@paren{FractionalPart}{#1}}
+\newcommand{\FractionalPart}[1]{\fPart{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\Mod}
+% Modulo, |\Mod{n}{m}|, $\Mod{n}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ModDisplay}{mod}
+\newcommand{\Mod}[2]{%
+\ifthenelse{\equal{\COOL@notation@ModDisplay}{mod}}%
+	{%
+	#1 \mod #2%
+	}%
+% ElseIf
+{ \ifthenelse{\equal{\COOL@notation@ModDisplay}{bmod}}%
+	{%
+	#1 \bmod #2%
+	}%
+% ElseIf
+{ \ifthenelse{\equal{\COOL@notation@ModDisplay}{pmod}}%
+	{%
+	#1 \pmod #2%
+	}%
+% ElseIf
+{\ifthenelse{\equal{\COOL@notation@ModDisplay}{pod}}%
+	{%
+	#1 \pod #2%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Option Sent}%
+		{ModDisplay can only be `mod', `bmod', `pmod', or `pod'}%
+	}}}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Quotient}
+% quotient, |\Quotient{m}{n}|, $\Quotient{m}{n}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@QuotientParen}{p}
+	\DeclareMathOperator{\QuotientSymb}{quotient}
+\newcommand{\Quotient}[2]%
+{\QuotientSymb\COOL@decide@paren{Quotient}{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GCD}
+% greatest common divisor, |\GCD{n_1,n_2,\dots,n_m}|, $\GCD{n_1,n_2,\dots,n_m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@GCDParen}{p}
+\newcommand{\GCD}[1]{\gcd\COOL@decide@paren{GCD}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ExtendedGCD}
+% \begin{macro}{\EGCD}
+% Extended Greatest Common Divisor, 
+%
+%|\EGCD{n}{m}|, |\ExtendedGCD{n}{m}|, $\EGCD{n}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ExtendedGCDParen}{p}
+	\DeclareMathOperator{\ExtendedGCDSymb}{egcd}
+\newcommand{\ExtendedGCD}[2]%
+{\ExtendedGCDSymb\COOL@decide@paren{ExtendedGCD}{#1,#2}}
+\newcommand{\EGCD}[2]{\ExtendedGCD{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LCM}
+% Least Common Multiple, |\LCM{n_1,n_2,\ldots,n_m}|, $\LCM{n_1,n_2,\ldots,n_m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LCMParen}{p}
+	\DeclareMathOperator{\LCMSymb}{lcm}
+\newcommand{\LCM}[1]{\LCMSymb\COOL@decide@paren{LCM}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Fibonacci}
+% Fibonacci number, |\Fibonacci{n}|, $\Fibonacci{n}$, and 
+%
+% Fibonacci Polynomial, |\Fibonacci{n,x}|, $\Fibonacci{n,x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@FibonacciParen}{p}
+\newcommand{\Fibonacci}[1]{%
+\liststore{#1}{COOL@Fibonacci@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	F_{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	F_{\COOL@Fibonacci@arg@i}\!%
+		\COOL@decide@paren{Fibonacci}{\COOL@Fibonacci@arg@ii}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Fibonacci' can only accept a 
+		comma separate list of length 1 or 2}%
+	}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Euler}
+% Euler number, |\Euler{n}|, $\Euler{n}$, and Euler Polynomial, |\Euler{n,x}|, $\Euler{n,x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EulerParen}{p}
+\newcommand{\Euler}[1]{%
+\liststore{#1}{COOL@Euler@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	E_{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	E_{\COOL@Euler@arg@i}\!%
+		\COOL@decide@paren{Euler}{\COOL@Euler@arg@ii}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Euler' can only accept a 
+		comma separate list of length 1 or 2}%
+	}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Bernoulli}
+% Bernoulli number, |\Bernoulli{n}|, $\Bernoulli{n}$ and 
+%
+% Bernoulli Polynomial |\Bernoulli{n,x}|, $\Bernoulli{n,x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BernoulliParen}{p}
+\newcommand{\Bernoulli}[1]{%
+\liststore{#1}{COOL@Bernoulli@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	B_{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	B_{\COOL@Bernoulli@arg@i}\!%
+		\COOL@decide@paren{Bernoulli}{\COOL@Bernoulli@arg@ii}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Bernoulli' can only accept a 
+		comma separate list of length 1 or 2}%
+	}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\StirlingSOne}
+% Stirling number of the first kind |\StirlingSOne{n}{m}|, $\StirlingSOne{n}{m}$
+%    \begin{macrocode}
+\newcommand{\StirlingSOne}[2]{S_{#1}^{\inp{#2}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\StirlingSTwo}
+% Stirling number of the second kind, |\StirlingSTwo{n}{m}|, $\StirlingSTwo{n}{m}$
+%    \begin{macrocode}
+\newcommand{\StirlingSTwo}[2]{{\cal S}_{#1}^{\inp{#2}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\PartitionsP}
+% Number of unrestricted partitions of an integer, |\PartitionsP{x}|, $\PartitionsP{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PartitionsPParen}{p}
+\newcommand{\PartitionsP}[1]{p\!\COOL@decide@paren{PartitionsP}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\PartitionsQ}
+% number of partitions of an integer into distinct parts, |\PartitionsQ{x}|, $\PartitionsQ{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PartitionsQParen}{p}
+\newcommand{\PartitionsQ}[1]{q\!\COOL@decide@paren{PartitionsQ}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DiscreteDelta}
+% Discrete delta function,
+%
+% |\DiscreteDelta{n_1,n_2,\ldots,n_m}|, $\DiscreteDelta{n_1,n_2,\ldots,n_m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DiscreteDeltaParen}{p}
+\newcommand{\DiscreteDelta}[1]%
+{\delta\COOL@decide@paren{DiscreteDelta}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\KroneckerDelta}
+% Kronecker Delta, |\KroneckerDelta{n_1,n_2,\ldots,n_m}|, $\KroneckerDelta{n_1,n_2,\ldots,n_m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@KroneckerDeltaUseComma}{false}%
+	\newcommand{\COOL@notation@KroneckerDeltaIndicies}{local}
+\newcommand{\KroneckerDelta}[2][u]{%
+\liststore{#2}{COOL@arg@}%
+\listval{#2}{0}%
+\def\COOL@arg@temp{}%
+\forLoop{1}{\value{COOL@listpointer}}{COOL@ct}%
+	{%
+	\ifthenelse{\equal{\COOL@notation@KroneckerDeltaUseComma}{true}}%
+		{%
+		\ifthenelse{\NOT \value{COOL@ct} = 1}
+			{%
+			\edef\COOL@arg@temp%
+			{\COOL@arg@temp, \csname COOL@arg@\roman{COOL@ct}\endcsname}%
+			}%
+		% Else
+			{%
+			\edef\COOL@arg@temp%
+			{\COOL@arg@temp \csname COOL@arg@\roman{COOL@ct}\endcsname}%
+			}%
+		}%
+	% Else
+		{%
+		\edef\COOL@arg@temp%
+			{\COOL@arg@temp \csname COOL@arg@\roman{COOL@ct}\endcsname}%
+		}%
+	}%
+\delta\COOL@decide@indicies{KroneckerDelta}{#1}{\COOL@arg@temp}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LeviCivita}
+% \begin{macro}{\Signature}
+% Levi-Civita totally anti-symmetric Tensor density, 
+%
+% |\LeviCivita{n_1,n_2,\ldots,n_m}|, $\LeviCivita{n_1,n_2,\ldots,n_m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LeviCivitaUseComma}{false}
+	\newcommand{\COOL@notation@LeviCivitaIndicies}{local}
+\newcommand{\LeviCivita}[2][u]{%
+\liststore{#2}{COOL@arg@}%
+\listval{#2}{0}%
+\def\COOL@arg@temp{}%
+\forLoop{1}{\value{COOL@listpointer}}{COOL@ct}%
+	{%
+	\ifthenelse{\equal{\COOL@notation@LeviCivitaUseComma}{true}}%
+		{%
+		\ifthenelse{\NOT \value{COOL@ct} = 1}{,}{}%
+		\edef\COOL@arg@temp%
+			{\COOL@arg@temp \csname COOL@arg@\roman{COOL@ct}\endcsname}%
+		}%
+	% Else
+		{%
+		\edef\COOL@arg@temp%
+			{\COOL@arg@temp \csname COOL@arg@\roman{COOL@ct}\endcsname}%
+		}%
+	}%
+\epsilon\COOL@decide@indicies{LeviCivita}{#1}{\COOL@arg@temp}%
+}%
+\newcommand{\Signature}[2][u]{\LeviCivita[#1]{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Classical Orthogonal Polynomials}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\HermiteH}
+% Hermite Polynomial, |\HermiteH{n}{x}|, $\HermiteH{n}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@HermiteHParen}{p}
+	\newcommand{\COOL@notation@HermiteHSymb}{H}
+\newcommand{\HermiteH}[2]%
+{\COOL@notation@HermiteHSymb_{#1}\!\COOL@decide@paren{HermiteH}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LaugerreL}
+% Laugerre Polynomial, |\LaugerreL{\nu,x}|, $\LaugerreL{\nu,x}$ and 
+%
+% \noindent Generalized Laugerre Polynomial |\LaugerreL{\nu,\lambda,x}|, $\LaugerreL{\nu,\lambda,x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LaugerreLParen}{p}
+	\newcommand{\COOL@notation@LaugerreLSymb}{L}
+\newcommand{\LaugerreL}[1]{%
+\liststore{#1}{COOL@list@temp@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer}=2}%
+	{%
+	\COOL@notation@LaugerreLSymb_{\COOL@list@temp@i}%
+		\!\COOL@decide@paren{LaugerreL}{\COOL@list@temp@ii}%
+	}%
+% Else If
+{ \ifthenelse{\value{COOL@listpointer}=3}%
+	{%
+	\COOL@notation@LaugerreLSymb_{\COOL@list@temp@i}^{\COOL@list@temp@ii}%
+		\!\COOL@decide@paren{LaugerreL}{\COOL@list@temp@iii}%
+	}%
+% Else
+{%
+	\PackageError{cool}{Invalid Argument}%
+		{`LaugerrL' only accepts a comma separated list of length 2 or 3}%
+}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LegendreP}
+% Legendre Polynomials
+%
+% \begin{tabular}{lll}
+% Legendre Polynomial		& |\LegendreP{n,x}|		& $\LegendreP{n,x}$		\\
+% Associated Legendre Polynomial \\
+% \indent of the first kind of type 2
+%				& |\LegendreP{\ell,m,x}|	& $\LegendreP{\ell,m,x}$	\\
+%				& |\LegendreP{\ell,m,2,x}|	& $\LegendreP{\ell,m,2,x}$	\\
+% Associated Legendre Function \\
+% \indent of the first kind of type 3
+%				& |\LegendreP{\ell,m,3,x}|	& $\LegendreP{\ell,m,3,x}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LegendrePParen}{p}
+	\newcommand{\COOL@notation@LegendrePSymb}{P}
+\newcommand{\LegendreP}[1]{%
+\liststore{#1}{COOL@LegendreP@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\COOL@notation@LegendrePSymb_{\COOL@LegendreP@arg@i}\!%
+		\COOL@decide@paren{LegendreP}{\COOL@LegendreP@arg@ii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	\COOL@notation@LegendrePSymb_{\COOL@LegendreP@arg@i}%
+		^{\COOL@LegendreP@arg@ii}\!%
+		\COOL@decide@paren{LegendreP}{\COOL@LegendreP@arg@iii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 4}%
+	{%
+	\isint{\COOL@LegendreP@arg@iii}%
+	\ifthenelse{\boolean{COOL@isint}}%
+		{%
+		\ifcase\COOL@LegendreP@arg@iii\relax%
+		\PackageError{cool}{Invalid Argument}%
+			{`LegendreP' third argument must be $>$ 1}%
+		\or%
+		\PackageError{cool}{Invalid Argument}%
+			{`LegendreP' third argument must be $>$ 1}%
+		\or%
+		\COOL@notation@LegendrePSymb_{\COOL@LegendreP@arg@i}%
+			^{\COOL@LegendreP@arg@ii}\!%
+			\COOL@decide@paren{LegendreP}{\COOL@LegendreP@arg@iv}%
+		\or%
+		{\cal P}_{\COOL@LegendreP@arg@i}%
+			^{\COOL@LegendreP@arg@ii}\!%
+			\COOL@decide@paren{LegendreP}{\COOL@LegendreP@arg@iv}%
+		\else%
+		\PackageError{cool}{Invalid Argument}{unsupported}%
+		\fi%
+		}
+	% Else
+		{%
+		\PackageError{cool}{Invalid Argument}{third arg must be int}%
+		}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`LegendreP' can only accept a%
+		 comma separated list of length 2-4}%
+	}}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LegendreQ}
+% Legendre Polynomials of the second kind
+%
+% \begin{tabular}{lll}
+% Legendre Polynomial		& |\LegendreQ{n,x}|		& $\LegendreQ{n,x}$		\\
+% Associated Legendre Polynomial \\
+% \indent of the second kind of type 2
+%				& |\LegendreQ{\ell,m,x}|	& $\LegendreQ{\ell,m,x}$	\\
+%				& |\LegendreQ{\ell,m,2,x}|	& $\LegendreQ{\ell,m,2,x}$	\\
+% Associated Legendre Function \\
+% \indent of the second kind of type 3
+%				& |\LegendreQ{\ell,m,3,x}|	& $\LegendreQ{\ell,m,3,x}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LegendreQParen}{p}
+	\newcommand{\COOL@notation@LegendreQSymb}{Q}
+\newcommand{\LegendreQ}[1]{%
+\liststore{#1}{COOL@LegendreQ@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\COOL@notation@LegendreQSymb_{\COOL@LegendreQ@arg@i}\!%
+		\COOL@decide@paren{LegendreQ}{\COOL@LegendreQ@arg@ii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	\COOL@notation@LegendreQSymb_{\COOL@LegendreQ@arg@i}%
+		^{\COOL@LegendreQ@arg@ii}\!%
+		\COOL@decide@paren{LegendreQ}{\COOL@LegendreQ@arg@iii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 4}%
+	{%
+	\isint{\COOL@LegendreQ@arg@iii}%
+	\ifthenelse{\boolean{COOL@isint}}%
+		{%
+		\ifcase\COOL@LegendreQ@arg@iii\relax%
+		\PackageError{cool}{Invalid Argument}%
+			{`LegendreQ' third argument must be $>$ 1}%
+		\or%
+		\PackageError{cool}{Invalid Argument}%
+			{`LegendreQ' third argument must be $>$ 1}%
+		\or%
+		\COOL@notation@LegendreQSymb_{\COOL@LegendreQ@arg@i}%
+			^{\COOL@LegendreQ@arg@ii}\!%
+			\COOL@decide@paren{LegendreQ}{\COOL@LegendreQ@arg@iv}%
+		\or%
+		{\cal Q}_{\COOL@LegendreQ@arg@i}%
+			^{\COOL@LegendreQ@arg@ii}\!%
+			\COOL@decide@paren{LegendreQ}{\COOL@LegendreQ@arg@iv}%
+		\else%
+		\PackageError{cool}{Invalid Argument}{unsupported}%
+		\fi%
+		}
+	% Else
+		{%
+		\PackageError{cool}{Invalid Argument}{third arg must be int}%
+		}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`LegendreQ' can only accept a%
+		 comma separated list of length 2-4}%
+	}}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ChebyshevT}
+% Chebyshev Polynomial of the first kind, |ChebyshevT{n}{x}|, $ChebyshevT{n}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ChebyshevTParen}{p}
+	\newcommand{\COOL@notation@ChebyshevTSymb}{T}
+\newcommand{\ChebyshevT}[2]%
+{\COOL@notation@ChebyshevTSymb_{#1}\!\COOL@decide@paren{ChebyshevT}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ChebyshevU}, |\ChebyshevU{n}{z}|, $\ChebyshevU{n}{z}$
+% Chebyshev Polynomial of the second kind 
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ChebyshevUParen}{p}
+	\newcommand{\COOL@notation@ChebyshevUSymb}{U}
+\newcommand{\ChebyshevU}[2]%
+{\COOL@notation@ChebyshevUSymb_{#1}\!\COOL@decide@paren{ChebyshevU}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\JacobiP}
+% Jacobi Polynomial, |\JacobiP{n}{a}{b}{x}|, $\JacobiP{n}{a}{b}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiPParen}{p}
+	\newcommand{\COOL@notation@JacobiPSymb}{P}
+\newcommand{\JacobiP}[4]{%
+\COOL@notation@JacobiPSymb_{#1}^{\inp{#2, #3}}%
+\!\COOL@decide@paren{JacobiP}{#4}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Associated Polynomials}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\AssocLegendreP}
+% Associated Legendre Polynomial of the first kind of type 2
+%
+% |\AssocLegendreP{\ell}{m}{x}|, $\AssocLegendreP{\ell}{m}{x}$
+%    \begin{macrocode}
+\newcommand{\AssocLegendreP}[3]{\LegendreP{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\AssocLegendreQ}
+% Associated Legendre Polynomial of the second kind of type 2
+%
+% |\AssocLegendreQ{\ell}{m}{x}|, $\AssocLegendreQ{\ell}{m}{x}$
+%    \begin{macrocode}
+\newcommand{\AssocLegendreQ}[3]{\LegendreQ{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GegenbauerC}
+% Gegenbauer Polynomial, |\GegenbauerC{n}{\lambda}{x}|, $\GegenbauerC{n}{\lambda}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@GegenbauerCParen}{p}
+	\newcommand{\COOL@notation@GegenbauerCSymb}{C}
+\newcommand{\GegenbauerC}[3]{%
+\COOL@notation@GegenbauerCSymb_{#1}^{#2}%
+\!\COOL@decide@paren{GegenbauerC}{#3}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SphericalHarmonicY}
+% \begin{macro}{\SphericalHarmY}
+% \begin{macro}{\SpHarmY}
+% Spherical Harmonic, |\SpHarmY{\ell}{m}{\theta}{\phi}|, 
+%
+% |\SphericalHarmY{\ell}{m}{\theta}{\phi}|, 
+%
+% |\SphericalHarmonicY{\ell}{m}{\theta}{\phi}|, $\SpHarmY{\ell}{m}{\theta}{\phi}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SphericalHarmonicYParen}{p}
+	\newcommand{\COOL@notation@SphericalHarmonicYSymb}{Y}
+\newcommand{\SphericalHarmonicY}[4]{%
+\COOL@notation@SphericalHarmonicYSymb_{#1}^{#2}%
+\!\COOL@decide@paren{SphericalHarmonicY}{#3,#4}%
+}
+\newcommand{\SphericalHarmY}[4]{\SphericalHarmonicY{#1}{#2}{#3}{#4}}
+\newcommand{\SpHarmY}[4]{\SphericalHarmonicY{#1}{#2}{#3}{#4}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Other Polynomials}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\CyclotomicC}
+% Cyclotomic Polynomial, |\CyclotomicC{n}{z}|, $\CyclotomicC{n}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CyclotomicCParen}{p}
+\newcommand{\CyclotomicC}[2]%
+{C_{#1}\!\COOL@decide@paren{CyclotomicC}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\FibonacciF}
+% Fibonacci Polynomial, |\FibonacciF{n}{z}|, $\FibonacciF{n}{z}$
+%    \begin{macrocode}
+\newcommand{\FibonacciF}[2]{\Fibonacci{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\EulerE}
+% Euler Polynomial, |\EulerE{n}{z}|, $\EulerE{n}{z}$
+%    \begin{macrocode}
+\newcommand{\EulerE}[2]{\Euler{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\BernoulliB}
+% Bernoulli Polynomial, |\BernoulliB{n}{z}|, $\BernoulliB{n}{z}$
+%    \begin{macrocode}
+\newcommand{\BernoulliB}[2]{\Bernoulli{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Factorial Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Factorial}
+% Factorial, |\Factorial{n}|, $\Factorial{n}$
+%    \begin{macrocode}
+\newcommand{\Factorial}[1]{#1!}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DblFactorial}
+% Double Factorial, |\DblFactorial{n}|, $\DblFactorial{n}$
+%    \begin{macrocode}
+\newcommand{\DblFactorial}[1]{#1!!}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Binomial}
+% binomial, |\Binomial{n}{r}|, $\Binomial{n}{r}$
+%    \begin{macrocode}
+\newcommand{\Binomial}[2]{ \binom{#1}{#2} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Multinomial}
+% Multinomial, |\Multinomial{n_1,\ldots,n_m}|, $\Multinomial{n_1,\ldots,n_m}$
+%    \begin{macrocode}
+\newcommand{\Multinomial}[1]%
+{%
+\listval{#1}{0}% get the length of the list
+\setcounter{COOL@listlen}{\value{COOL@listpointer}}% record length
+\liststore{#1}{COOL@list@temp@}%
+\isint{\COOL@list@temp@i}% check that the entries are integers
+\setcounter{COOL@ct}{2}%
+\whiledo{	\boolean{COOL@isint} \AND 
+		\NOT \value{COOL@ct}>\value{COOL@listlen}	 }%
+	{%
+	\def\COOL@Multinomial@tempa%
+		{\csname COOL@list@temp@\roman{COOL@ct}\endcsname}%
+	\isint{\COOL@Multinomial@tempa}%
+	\stepcounter{COOL@ct}%
+	}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{%
+	% all of them are integers
+	\setcounter{COOL@ct@}{ \COOL@list@temp@i }% records the sum
+	\forLoop{2}{\value{COOL@listlen}}{COOL@ct}%
+		{%
+		\addtocounter{COOL@ct@}%
+			{\csname COOL@list@temp@\roman{COOL@ct}\endcsname}%
+		}%
+	\left(\arabic{COOL@ct@}%
+	}%
+% Else
+	{%
+	\left(%
+	\listval{#1}{1}%
+	\forLoop{2}{\value{COOL@listlen}}{COOL@ct}%
+		{%
+		+ \listval{#1}{\arabic{COOL@ct}}%
+		}%
+	}%
+;#1\right)%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Gamma Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\GammaFunc}
+% Gamma Function
+%
+% \noindent \begin{tabular}{lll}
+% Gamma Function			& |\GammaFunc{z}|	& $\GammaFunc{z}$		\\
+% Incomplete Gamma Function		& |\GammaFunc{a,z}|	& $\GammaFunc{a,z}$		\\
+% Generalized Incomplete Gamma Function	& |\GammaFunc{a,x,y}|	& $\GammaFunc{a,x,y}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@GammaFuncParen}{p}
+\newcommand{\GammaFunc}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	\Gamma\!\COOL@decide@paren{GammaFunc}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\Gamma\!\COOL@decide@paren{GammaFunc}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	\Gamma\!\COOL@decide@paren{GammaFunc}{#1}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`GammaFunc' can only accept a comma separate list of length 1 to 3}%
+	}%
+}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\IncGamma}
+% incomplete Gamma function, |\IncGamma{a}{x}|, $\IncGamma{a}{x}$
+%    \begin{macrocode}
+\newcommand{\IncGamma}[2]{\GammaFunc{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GenIncGamma}
+% Generalized Incomplete Gamma, |\GenIncGamma{a}{x}{y}|, $\GenIncGamma{a}{x}{y}$
+%    \begin{macrocode}
+\newcommand{\GenIncGamma}[3]{\GammaFunc{#1, #2, #3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GammaRegularized}
+% \begin{macro}{\RegIncGamma}
+% \begin{macro}{\GammaReg}
+% Regularized Incomplete Gamma 
+%
+% \begin{tabular}{ll}
+% |\GammaRegularized{a,x}|	& $\GammaRegularized{a,x}$		\\
+% |\RegIncGamma{a}{x}|		& $\RegIncGamma{a}{x}$			\\
+% |\GammaReg{a,x}|		& $\GammaReg{a,x}$			\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@GammaRegularizedParen}{p}%
+\newcommand{\GammaRegularized}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	Q\!\COOL@decide@paren{GammaRegularized}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	Q\!\COOL@decide@paren{GammaRegularized}{#1}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`GammaRegularized' can only accept comma%
+		 separated lists of length 2 or 3}%
+	}%
+}%
+}
+\newcommand{\RegIncGamma}[2]{\GammaRegularized{#1, #2}}
+\newcommand{\GammaReg}[1]{\GammaRegularized{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\RegIncGammaInv}
+% \begin{macro}{\InverseGammaRegularized}
+% \begin{macro}{\GammaRegInv}
+% Inverse of Regularized Incomplete Gamma,
+%
+% \begin{tabular}{ll}
+% |\RegIncGammaInv{a}{x}|		&  $\RegIncGammaInv{a}{x}$		\\
+% |\InverseGammaRegularized{a,x}|	& $\InverseGammaRegularized{a,x}$	\\
+% |\GammaRegInv{a,x}|			& $\GammaRegInv{a,x}$			\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@InverseGammaRegularizedParen}{p}
+\newcommand{\InverseGammaRegularized}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	Q^{-1}\!\COOL@decide@paren{InverseGammaRegularized}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	Q^{-1}\!\COOL@decide@paren{InverseGammaRegularized}{#1}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`InverseGammaRegularized' can only accept%
+		 a comma separated list of length 2 or 3}%
+	}%
+}%
+}
+\newcommand{\RegIncGammaInv}[2]{\InverseGammaRegularized{#1, #2}}
+\newcommand{\GammaRegInv}[1]{\InverseGammaRegularized{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\GenRegIncGamma}
+% Generalized Regularized Incomplete Gamma 
+%
+% \begin{tabular}{ll}
+% |\GenRegIncGamma{a}{x}{y}|	& $\GenRegIncGamma{a}{x}{y}$		\\
+% |\GammaRegularized{a,x,y}|	& $\GammaRegularized{a,x,y}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\GenRegIncGamma}[3]{\GammaRegularized{#1, #2, #3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GenRegIncGammaInv}
+% Inverse of Gen. Reg. Incomplete Gamma, |\GenRegIncGammaInv{a}{x}{y}|, $\GenRegIncGammaInv{a}{x}{y}$
+%    \begin{macrocode}
+\newcommand{\GenRegIncGammaInv}[3]{\InverseGammaRegularized{#1, #2, #3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Pochhammer}
+% Pochhammer Symbol |\Pochhammer{a}{n}|, $\Pochhammer{a}{n}$
+%    \begin{macrocode}
+\newcommand{\Pochhammer}[2]{\inp{#1}_{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LogGamma}
+% Log Gamma Function, |\LogGamma{x}|, $\LogGamma{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LogGammaParen}{p}
+	\DeclareMathOperator{\LogGammaSymb}{log\Gamma}
+\newcommand{\LogGamma}[1]{\LogGammaSymb\COOL@decide@paren{LogGamma}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Derivatives of Gamma Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\DiGamma}
+% Digamma function, |\DiGamma{x}|, $\DiGamma{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DiGammaParen}{p}
+\newcommand{\DiGamma}[1]{\digamma\!\COOL@decide@paren{DiGamma}{#1}}
+%    \end{macrocode}
+% \end{macro}
+% PolyGamma function, |\PolyGamma{\nu}{x}|, $\PolyGamma{\nu}{x}$
+% \begin{macro}{\PolyGamma}
+% 
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PolyGammaParen}{p}
+\newcommand{\PolyGamma}[2]%
+{\psi^{\inp{#1}}\!\COOL@decide@paren{PolyGamma}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\HarmNum}
+% Harmonic Number
+%
+% \begin{tabular}{lll}
+% Harmonic Number		& |\HarmNum{x}|		& $\HarmNum{x}$ 		\\
+% General Harmonic Number	& |\HarmNum{x,r}|	& $\HarmNum{x,r}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\HarmNum}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer}=1}%
+	{%
+	H_{#1}
+	}%
+% Else If
+{ \ifthenelse{\value{COOL@listpointer}=2}%
+	{%
+	\liststore{#1}{COOL@list@temp@}%
+	H^{\inp{\COOL@list@temp@ii}}_{\COOL@list@temp@i}%
+	}%
+% Else
+{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Harm Num' can only accept a comma separated list of length 1 or 2}%
+}}%	
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Beta Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Beta}
+% \begin{tabular}{lll}
+% Beta Function 			& |\Beta{a,b}|		& $\Beta{a,b}$		\\
+% Incomplete Beta Function		& |\Beta{z,a,b}|	& $\Beta{z,a,b}$	\\
+% Generalized Incomplete Beta Function	& |\Beta{z_1,z_2,a,b}|	& $\Beta{z_1,z_2,a,b}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BetaParen}{p}
+\newcommand{\Beta}[1]{%
+\liststore{#1}{COOL@Beta@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	B\!\COOL@decide@paren{Beta}{\COOL@Beta@arg@i, \COOL@Beta@arg@ii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	B_{\COOL@Beta@arg@i}\!%
+		\COOL@decide@paren{Beta}{\COOL@Beta@arg@ii, \COOL@Beta@arg@iii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 4}%
+	{%
+	B_{\inp{\COOL@Beta@arg@i,\COOL@Beta@arg@ii}}\!%
+		\COOL@decide@paren{Beta}{\COOL@Beta@arg@iii, \COOL@Beta@arg@iv}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Beta' can only accept a comma separated list of length 2 to 4}%
+	}%
+}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\IncBeta}
+% Incomplete Beta Function 
+%
+% \begin{tabular}{ll}
+% |\IncBeta{z}{a}{b}|	& $\IncBeta{z}{a}{b}$	\\
+% |\Beta{z,a,b}|	& $\Beta{z,a,b}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\IncBeta}[3]{\Beta{#1,#2, #3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GenIncBeta}
+% Generalized Incomplete Beta Function
+%
+% \begin{tabular}{ll}
+% |\GenIncBeta{x}{y}{a}{b}|	& $\GenIncBeta{x}{y}{a}{b}$	\\
+% |\Beta{x,y,a,b}|		& $\Beta{x,y,a,b}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\GenIncBeta}[4]{\Beta{#1,#2,#3,#4}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\BetaRegularized}
+% \begin{macro}{\BetaReg}
+% \begin{macro}{\RegIncBeta}
+% Regularized Incomplete Beta Function 
+% 
+% \begin{tabular}{ll}
+% |\BetaRegularized{z,a,b}|	& $\BetaRegularized{z,a,b}$	\\
+% |\BetaReg{z,a,b}|		& $\BetaReg{z,a,b}$		\\
+% |\RegIncBeta{z}{a}{b}|	& $\RegIncBeta{z}{a}{b}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@BetaRegularizedParen}{p}
+\newcommand{\BetaRegularized}[1]{%
+\liststore{#1}{COOL@BetaRegularized@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	I_{\COOL@BetaRegularized@arg@i}\!%
+		\COOL@decide@paren{BetaRegularized}%
+			{\COOL@BetaRegularized@arg@ii, \COOL@BetaRegularized@arg@iii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 4}%
+	{%
+	I_{\inp{\COOL@BetaRegularized@arg@i, \COOL@BetaRegularized@arg@ii}}\!%
+		\COOL@decide@paren{BetaRegularized}%
+			{\COOL@BetaRegularized@arg@iii, \COOL@BetaRegularized@arg@iv}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`BetaRegularized' can only accept%
+		 a comma separated list of length 3 or 4}%
+	}%
+}%
+}
+\newcommand{\RegIncBeta}[3]{\BetaRegularized{#1,#2,#3}}
+\newcommand{\BetaReg}[1]{\BetaRegularized{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\InverseBetaRegularized}
+% \begin{macro}{\BetaRegInv}
+% \begin{macro}{\RegIncBetaInv}
+% Inverse of Regularized Incomplete Beta Function
+%
+% \begin{tabular}{ll}
+% |\InverseBetaRegularized{z,a,b}|	& $\InverseBetaRegularized{z,a,b}$	\\
+% |\BetaRegInv{z,a,b}|			& $\BetaRegInv{z,a,b}$			\\
+% |\RegIncBetaInv{z}{a}{b}|		& $\RegIncBetaInv{z}{a}{b}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@InverseBetaRegularizedParen}{p}
+\newcommand{\InverseBetaRegularized}[1]{%
+\liststore{#1}{COOL@InverseBetaRegularized@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	I^{-1}_{\COOL@InverseBetaRegularized@arg@i}\!%
+		\COOL@decide@paren{InverseBetaRegularized}%
+			{\COOL@InverseBetaRegularized@arg@ii,%
+			 \COOL@InverseBetaRegularized@arg@iii}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 4}%
+	{%
+	I^{-1}_{\inp{	\COOL@InverseBetaRegularized@arg@i,%
+			\COOL@InverseBetaRegularized@arg@ii%
+		    }%
+		}\!%
+		\COOL@decide@paren{InverseBetaRegularized}%
+			{\COOL@InverseBetaRegularized@arg@iii,%
+			 \COOL@InverseBetaRegularized@arg@iv}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`InverseBetaRegularized' can only accept%
+		 a comma separated list of length 3 or 4}%
+	}%
+}%
+}
+\newcommand{\RegIncBetaInv}[3]{\InverseBetaRegularized{#1,#2,#3}}
+\newcommand{\BetaRegInv}[1]{\InverseBetaRegularized{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\GenRegIncBeta}
+% Generalized Regularized Incomplete Beta Func
+%
+% \begin{tabular}{ll}
+% |\GenRegIncBeta{x}{y}{a}{b}|	& $\GenRegIncBeta{x}{y}{a}{b}$		\\
+% |\Beta{x,y,a,b}|		& $\Beta{x,y,a,b}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\GenRegIncBeta}[4]{\Beta{#1,#2,#3,#4}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\GenRegIncBetaInv}
+% Inverse of Generalized Regularized Incomplete Beta Function
+%
+% \begin{tabular}{ll}
+% |\GenRegIncBetaInv{x}{y}{z}{b}|	& $\GenRegIncBetaInv{x}{y}{z}{b}$		\\
+% |\InverseBetaRegularized{x,y,z,b}|	& $\InverseBetaRegularized{x,y,z,b}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\GenRegIncBetaInv}[4]{\InverseBetaRegularized{#1,#2,#3,#4}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Error Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Erf}
+% \begin{tabular}{lll}
+% Error Function		& |\Erf{x}|		& $\Erf{x}$		\\
+% Generalized Error Function	& |\Erf{x,y}|		& $\Erf{x,y}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ErfParen}{p}
+	\DeclareMathOperator{\ErfSymb}{erf}
+\newcommand{\Erf}[1]{%
+\liststore{#1}{COOL@Erf@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	\ErfSymb\!\COOL@decide@paren{Erf}{#1}
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\ErfSymb\!\COOL@decide@paren{Erf}{#1}
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Erf' can only accept a comma separated list of length 1 or 2}%
+	}%
+}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ErfInv}
+% Inverse of Error Function
+%
+% \begin{tabular}{ll}
+% |\ErfInv{x}|		& $\ErfInv{x}$		\\
+% |\ErfInv{x,y}|	& $\ErfInv{x,y}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ErfInvParen}{p}
+\newcommand{\ErfInv}[1]{%
+\liststore{#1}{COOL@Erf@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	\ErfSymb^{-1}\!\COOL@decide@paren{ErfInv}{#1}
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\ErfSymb^{-1}\!\COOL@decide@paren{ErfInv}{#1}
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Erf' can only accept a comma separated list of length 1 or 2}%
+	}%
+}%
+}
+%    \end{macrocode}
+% \end{macro}
+
+%
+% \begin{macro}{\GenErf}
+% \begin{macro}{\GenErfInv}
+% Generalized Error Function and its inverse
+%
+% \begin{tabular}{ll}
+% |\GenErf{z_1}{z_2}|		& $\GenErf{z_1}{z_2}$	\\
+% |\GenErfInv{z_1}{z_2}|	& $\GenErfInv{z_1}{z_2}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\GenErf}[2]{\Erf{#1,#2}}
+\newcommand{\GenErfInv}[2]{\ErfInv{#1, #2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\Erfc}
+% Complimentary Error Function and its inverse
+%
+% \begin{tabular}{ll}
+% |\Erfc{z}|		& $\Erfc{z}$ 		\\
+% |\ErfcInv{z}|		& $\ErfcInv{z}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ErfcParen}{p}
+	\DeclareMathOperator{\ErfcSymb}{erfc}
+\newcommand{\Erfc}[1]{\ErfcSymb\!\COOL@decide@paren{Erfc}{#1}}
+	\newcommand{\COOL@notation@ErfcInvParen}{p}
+\newcommand{\ErfcInv}[1]%
+{\ErfcSymb^{-1}\!\COOL@decide@paren{ErfcInv}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Erfi}
+% Imaginary Error Function, |\Erfi{z}|, $\Erfi{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ErfiParen}{p}
+	\DeclareMathOperator{\ErfiSymb}{erfi}
+\newcommand{\Erfi}[1]{\ErfiSymb\!\COOL@decide@paren{Erfi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Fresnel Integrals}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\FresnelS}
+% Fresnel Integral, |\FresnelS{z}|, $\FresnelS{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@FresnelSParen}{p}
+\newcommand{\FresnelS}[1]{S\!\COOL@decide@paren{FresnelS}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\FresnelC}
+% Fresnel Integral, |\FresnelC{z}|, $\FresnelC{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@FresnelCParen}{p}
+\newcommand{\FresnelC}[1]{C\!\COOL@decide@paren{FresnelC}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Exponential Integrals}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\ExpIntE}
+% Exponential Integral, |\ExpIntE{\nu}{x}|, $\ExpIntE{\nu}{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ExpIntEParen}{p}
+\newcommand{\ExpIntE}[2]{E_{#1}\!\COOL@decide@paren{ExpIntE}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ExpIntEi}
+% Exponential Integral, |\ExpIntEi{x}|, $\ExpIntEi{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ExpIntEiParen}{p}
+	\DeclareMathOperator{\ExpIntEiSymb}{Ei}
+\newcommand{\ExpIntEi}[1]%
+{\ExpIntEiSymb\!\COOL@decide@paren{ExpIntEi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LogInt}
+% Logarithmic Integral, |\LogInt{x}|, $\LogInt{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LogIntParen}{p}
+	\DeclareMathOperator{\LogIntSymb}{li}
+\newcommand{\LogInt}[1]{\LogIntSymb\!\COOL@decide@paren{LogInt}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SinInt}
+% Sine Integral, |\SinInt{x}|, $\SinInt{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SinIntParen}{p}
+	\DeclareMathOperator{\SinIntSymb}{Si}
+\newcommand{\SinInt}[1]{\SinIntSymb\!\COOL@decide@paren{SinInt}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\CosInt}
+% Cosine Integral, |\CosInt{x}|, $\CosInt{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CosIntParen}{p}
+	\DeclareMathOperator{\CosIntSymb}{Ci}
+\newcommand{\CosInt}[1]{\CosIntSymb\!\COOL@decide@paren{CosInt}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SinhInt}
+% Hyberbolic Sine Integral, |\SinhInt{x}|, $\SinhInt{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SinhIntParen}{p}
+	\DeclareMathOperator{\SinhIntSymb}{Shi}
+\newcommand{\SinhInt}[1]{\SinhIntSymb\!\COOL@decide@paren{SinhInt}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\CoshInt}
+% Hyberbolic Cosine Integral, |\CoshInt{x}|, $\CoshInt{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CoshIntParen}{p}
+	\DeclareMathOperator{\CoshIntSymb}{Chi}
+\newcommand{\CoshInt}[1]{\CoshIntSymb\!\COOL@decide@paren{CoshInt}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Hypergeometric Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\COOL@Hypergeometric@pq@ab@value}
+% This macro is a decision maker that decides what to return for the Hypergeometric function since
+% its results vary based on the nature of the input.  This macro is called as
+%
+% |\COOL@Hypergeometric@pq@ab@value|
+% \DeleteShortVerb{\|}%
+% \verb|{|`p'\texttt{|}`q'\verb|}|%
+% \marg{p\_input\textnormal{\texttt{|}}q\_input}%
+% \verb|{|`a'\texttt{|}`b'\verb|}|%
+% \marg{a\_input\textnormal{\texttt{|}}b\_input}%
+% \MakeShortVerb{\|}
+%    \begin{macrocode}
+\newcommand{\COOL@Hypergeometric@pq@ab@value}[4]{%
+\ifthenelse{\boolean{COOL@#1@isint} \AND \boolean{COOL@#3@islist}}%
+	{% #1 is an INT and #3 is a LIST
+	\ifthenelse{ #2 = 0 }%
+		{%
+		\PackageWarning{cool}{`#3'-arg ignored}%
+		}%
+	% Else
+		{%
+		\ifthenelse{ #2 = 1 }%
+			{%
+			\PackageError{cool}{`Hypergeometric' `#1'-arg mismatch with `#3'-arg}{}%
+			}%
+		% Else
+			{%
+			#4%
+			}%
+		}%
+	}%
+% Else
+	{}%
+\ifthenelse{	\boolean{COOL@#1@isint} \AND 
+		\NOT \boolean{COOL@#3@islist}	 }%
+	{%
+	\ifthenelse{ #2 = 0 }%
+		{%
+		% return nothing
+		}%
+	% Else
+		{%
+		\ifthenelse{ #2 = 1 }%
+			{%
+			% return
+			#4%
+			}%
+		% Else
+			{%
+			\forLoop{1}{#2}{COOL@ct}
+				{% 
+				\ifthenelse{ \value{COOL@ct} = 1 }{}{,}%
+				#4_{\arabic{COOL@ct}}%
+				}% end for loop
+			}%
+		}%
+	}%
+% else
+	{}%
+\ifthenelse{ 	\NOT \boolean{COOL@#1@isint} \AND 
+		\boolean{COOL@#3@islist} 		}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`Hypergeometric': `#1'-arg is not int but `#3'-arg is list}
+	}%
+% else
+	{}%
+\ifthenelse{	\NOT \boolean{COOL@#1@isint} \AND 
+		\NOT \boolean{COOL@#3@islist} 		}%
+	{%
+	%return
+	#4_1,\ldots,#4_{#2}%
+	}%
+% else
+	{}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Hypergeometric}
+% Generalized Hypergeometric function. $\Hypergeometric{p}{q}{a}{b}{x}$
+%
+% \begin{tabular}{lr}
+% |\Hypergeometric{0}{0}{}{}{x}|	& $\Hypergeometric{0}{0}{}{}{x}$	\\
+% |\Hypergeometric{0}{1}{}{b}{x}|	& $\Hypergeometric{0}{1}{}{b}{x}$	\\
+% |\Hypergeometric{1}{1}{a}{b}{x}|	& $\Hypergeometric{1}{1}{a}{b}{x}$	\\
+% |\Hypergeometric{1}{1}{1}{1}{x}|	& $\Hypergeometric{1}{1}{1}{1}{x}$	\\
+% |\Hypergeometric{3}{5}{a}{b}{x}|	\\
+% 					\multicolumn{2}{r}{$\Hypergeometric{3}{5}{a}{b}{x}$}
+%										\\
+% |\Hypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}|
+%					\\
+%					\multicolumn{2}{r}{$\Hypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}$}
+%										\\
+% |\Hypergeometric{p}{5}{a}{b}{x}|	\\
+%					\multicolumn{2}{r}{$\Hypergeometric{p}{5}{a}{b}{x}$}
+%										\\
+% |\Hypergeometric{p}{3}{a}{1,2,3}{x}|	\\
+%					\multicolumn{2}{r}{$\Hypergeometric{p}{3}{a}{1,2,3}{x}$	}
+%										\\
+% |\Hypergeometric{p}{q}{a}{b}{x}|	\\
+%					\multicolumn{2}{r}{$\Hypergeometric{p}{q}{a}{b}{x}$}
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@HypergeometricParen}{p}
+	\newcommand{\COOL@notation@HypergeometricSymb}{F}
+\newcommand{\Hypergeometric}[6][F]{%
+\provideboolean{COOL@p@isint}%
+\provideboolean{COOL@q@isint}%
+\provideboolean{COOL@a@islist}%
+\provideboolean{COOL@b@islist}%
+\isint{#2}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{\setboolean{COOL@p@isint}{true}}%
+% Else
+	{\setboolean{COOL@p@isint}{false}}%
+\isint{#3}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{\setboolean{COOL@q@isint}{true}}%
+% Else
+	{\setboolean{COOL@q@isint}{false}}%
+\listval{#4}{0}%
+\ifthenelse{\value{COOL@listpointer}>1}%
+	{\setboolean{COOL@a@islist}{true}}%
+% Else
+	{\setboolean{COOL@a@islist}{false}}%
+%    \end{macrocode}
+% ensure that the submitted list is the same length as p
+%    \begin{macrocode}
+\ifthenelse{	\boolean{COOL@p@isint} \AND 
+		\boolean{COOL@a@islist} \AND 
+		\NOT \( #2 = \value{COOL@listpointer} \)	}%
+	{%
+	\PackageError{cool}{`Hypergeometric' `p'-arg mismatch with `a'-arg}{}%
+	}%
+% else
+	{}%
+\listval{#5}{0}%
+\ifthenelse{\value{COOL@listpointer}>1}%
+	{\setboolean{COOL@b@islist}{true}}%
+% Else
+	{\setboolean{COOL@b@islist}{false}}%
+%    \end{macrocode}
+% ensure that the submitted `b' list is the same length as q
+%    \begin{macrocode}
+\ifthenelse{	\boolean{COOL@q@isint} \AND 
+		\boolean{COOL@b@islist} \AND 
+		\NOT \( #3 = \value{COOL@listpointer} \)	}%
+	{%
+	\PackageError{cool}{`Hypergeometric' `q'-arg mismatch with `b'-arg}%
+		{`b' list is not the same length as `q'}%
+	}%
+% else
+	{}%
+% troubleshoot
+\ifthenelse{ \boolean{COOL@a@islist} \AND \NOT \boolean{COOL@p@isint} }%
+	{%
+	\PackageError{cool}{`Hypergeometric' `a'-arg mismatch with `p'-arg}%
+		{happens if `a'-arg is a list and `p'-arg isn't an integer}%
+	}%
+% else
+	{}%
+\ifthenelse{ \boolean{COOL@b@islist} \AND \NOT \boolean{COOL@q@isint} }%
+	{%
+	\PackageError{cool}{`Hypergeometric' `b'-arg mismatch with `q'-arg}%
+		{happens if `b'-arg is a list and `q'-arg isn't an integer}%
+	}%
+% else
+	{}%
+%    \end{macrocode}
+% First print the ${}_p F_q$
+%    \begin{macrocode}
+{}_{#2}{\COOL@notation@HypergeometricSymb}_{#3}\!%
+\COOL@decide@paren{Hypergeometric}%
+	{%
+	\COOL@Hypergeometric@pq@ab@value{p}{#2}{a}{#4};%
+	\COOL@Hypergeometric@pq@ab@value{q}{#3}{b}{#5};%
+	#6%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\RegHypergeometric}
+% Regularized hypergeometric function $\RegHypergeometric{p}{q}{a}{b}{x}$ 
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@RegHypergeometricParen}{p}
+	\newcommand{\COOL@notation@RegHypergeometricSymb}{\tilde{F}}
+\newcommand{\RegHypergeometric}[6][\tilde{F}]{%
+\provideboolean{COOL@p@isint}%
+\provideboolean{COOL@q@isint}%
+\provideboolean{COOL@a@islist}%
+\provideboolean{COOL@b@islist}%
+\isint{#2}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{\setboolean{COOL@p@isint}{true}}%
+% Else
+	{\setboolean{COOL@p@isint}{false}}%
+\isint{#3}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{\setboolean{COOL@q@isint}{true}}%
+% Else
+	{\setboolean{COOL@q@isint}{false}}%
+\listval{#4}{0}%
+\ifthenelse{\value{COOL@listpointer}>1}%
+	{\setboolean{COOL@a@islist}{true}}%
+% Else
+	{\setboolean{COOL@a@islist}{false}}%
+%    \end{macrocode}
+% ensure that the submitted list is the same length as p
+%    \begin{macrocode}
+\ifthenelse{	\boolean{COOL@p@isint} \AND 
+		\boolean{COOL@a@islist} \AND 
+		\NOT \( #2 = \value{COOL@listpointer} \)	}%
+	{%
+	\PackageError{cool}%
+		{`RegHypergeometric' `p'-arg mismatch with `a'-arg}{}%
+	}%
+% else
+	{}%
+\listval{#5}{0}%
+\ifthenelse{\value{COOL@listpointer}>1}%
+	{\setboolean{COOL@b@islist}{true}}%
+% Else
+	{\setboolean{COOL@b@islist}{false}}%
+%    \end{macrocode}
+% ensure that the submitted `b' list is the same length as q
+%    \begin{macrocode}
+\ifthenelse{	\boolean{COOL@q@isint} \AND 
+		\boolean{COOL@b@islist} \AND 
+		\NOT \( #3 = \value{COOL@listpointer} \)	}%
+	{%
+	\PackageError{cool}%
+		{`RegHypergeometric' `q'-arg mismatch with `b'-arg}%
+		{`b' list is not the same length as `q'}%
+	}%
+% else
+	{}%
+% troubleshoot
+\ifthenelse{ \boolean{COOL@a@islist} \AND \NOT \boolean{COOL@p@isint} }%
+	{%
+	\PackageError{cool}%
+		{`RegHypergeometric' `a'-arg mismatch with `p'-arg}%
+		{happens if `a'-arg is a list and `p'-arg isn't an integer}%
+	}%
+% else
+	{}%
+\ifthenelse{ \boolean{COOL@b@islist} \AND \NOT \boolean{COOL@q@isint} }%
+	{%
+	\PackageError{cool}%
+		{`RegHypergeometric' `b'-arg mismatch with `q'-arg}%
+		{happens if `b'-arg is a list and `q'-arg isn't an integer}%
+	}%
+% else
+	{}%
+%    \end{macrocode}
+% First print the ${}_p F_q$
+%    \begin{macrocode}
+{}_{#2}{\COOL@notation@RegHypergeometricSymb}_{#3}\!%
+\COOL@decide@paren{RegHypergeometric}%
+	{%
+	\COOL@Hypergeometric@pq@ab@value{p}{#2}{a}{#4};%
+	\COOL@Hypergeometric@pq@ab@value{q}{#3}{b}{#5};%
+	#6%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\AppellFOne}
+% Appell Hypergeometric Function 
+%
+% \begin{tabular}{ll}
+% |\AppellFOne{a}{b_1,b_2}{c}{z_1,z_2}|		& $\AppellFOne{a}{b_1,b_2}{c}{z_1,z_2}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@AppellFOneParen}{p}
+\newcommand{\AppellFOne}[4]%
+	{F_{1}\!\COOL@decide@paren{AppellFOne}{#1; #2; #3; #4}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\HypergeometricU}
+% Tricomi confluent hypergeometric function 
+%
+% \begin{tabular}{ll}
+% |\HypergeometricU{a}{b}{z}|	& $\HypergeometricU{a}{b}{z}$ 		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@HypergeometricUSymb}{U}
+\newcommand{\HypergeometricU}[3]%
+{\COOL@notation@HypergeometricUSymb\!\inp{#1, #2, #3}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\COOL@MeijerG@anp@value}
+% This macro is a decision maker for the |\MeijerG| macro.  Despite the name it is used for both $p$ and $q$.
+% It is called as
+%
+% |\COOL@MeijerG@anp@value|
+% \DeleteShortVerb{\|}
+% \marg{a\textnormal{\texttt{|}}b}
+% \marg{n\textnormal{\texttt{|}}m}
+% \marg{p\textnormal{\texttt{|}}q}
+% \MakeShortVerb{\|}
+%    \begin{macrocode}
+\newcommand{\COOL@MeijerG@anp@value}[3]{%
+\isint{#3}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{%
+	\isint{#2}%
+	\ifthenelse{\boolean{COOL@isint}}%
+		{%
+		\forLoop{1}{#3}{COOL@ct}%
+			{%
+			\ifthenelse{\value{COOL@ct}=1}{}{,}%
+			#1_{\arabic{COOL@ct}}%
+			}%
+		}%
+	% else
+		{%
+		#1_1,\ldots,#1_{#2},#1_{#2+1},\dots,#1_{#3}%
+		}%
+	}%
+% else
+	{%
+	\isint{#2}%
+	\ifthenelse{\boolean{COOL@isint}}%
+		{%
+		\forLoop{1}{#2}{COOL@ct}%
+			{%
+			\ifthenelse{\value{COOL@ct}=1}{}{,}%
+			#1_{\arabic{COOL@ct}}%
+			}%
+		\setcounter{COOL@ct}{#2}%
+		\addtocounter{COOL@ct}{1}%
+		,#1_{\arabic{COOL@ct}}, \ldots, #1_{#3}%
+		}%
+	% else
+		{%
+		#1_1,\ldots,#1_{#2},#1_{#2+1},\dots,#1_{#3}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\MeijerG}
+% |\MeijerG{|$a_1, \ldots, a_n$|}{|$a_{n+1}, \ldots, a_p$|}{|$b_1, \ldots, b_m$|}{|$b_{m+1}, \ldots, b_q$|}|\marg{x}
+%
+% \noindent |\MeijerG[|\meta{a list symbol},\meta{b list symbol}|]|\marg{n}\marg{p}\marg{m}\marg{q}\marg{x}
+%
+% \noindent |\MeijerG[|\meta{a list symbol}|]|\marg{n}\marg{p}|{|$b_1, \ldots, b_m$|}{|$b_{m+1}, \ldots, b_q$|}|\marg{x}
+%
+% \noindent |\MeijerG[,|\meta{b list symbol}|]{|$a_1, \ldots, a_n$|}{|$a_{n+1}, \ldots, a_p$|}|\marg{m}\marg{q}\marg{x}
+%
+% \hspace{0.25cm}
+%
+% \begin{tabular}{c}
+% Meijer $G$-Function
+% \\
+%	\begin{tabular}{ll}
+%	|\MeijerG[a,b]{n}{p}{m}{q}{z}|		& $\MeijerG[a,b]{n}{p}{m}{q}{z}$		\\
+%	\end{tabular}
+% \\
+% Meijer $G$-Function
+% \\
+%	\begin{tabular}{ll}
+%	|\MeijerG{1,2}{3}{a,b}{c,d}{z}|		& $\MeijerG{1,2}{3}{a,b}{c,d}{z}$		\\
+%	\end{tabular}
+% \\
+% Generalized Meijer $G$-Function
+% \\
+%	\begin{tabular}{ll}
+%	|\MeijerG[a,b]{n}{p}{m}{q}{z,r}|	& $\MeijerG[a,b]{n}{p}{m}{q}{z,r}$		\\
+%	\end{tabular}
+% \\
+% Generalized Meijer $G$-Function
+% \\
+%	\begin{tabular}{ll}
+%	|\MeijerG{1,2}{3}{a,b}{c,d}{z,r}|	& $\MeijerG{1,2}{3}{a,b}{c,d}{z,r}$
+%	\end{tabular}
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MeijerGSymb}{G}
+\newcommand{\MeijerG}[6][@,@]{%
+\listval{#1}{0}
+\ifthenelse{\value{COOL@listpointer}>2 \OR \value{COOL@listpointer}<1}%
+	{%
+	\PackageError{cool}{`MeijerG' Invalid Optional Argument}%
+		{Must be a comma separated list of length 1 or 2}%
+	}%
+% else
+	{%
+	}%
+\COOL@notation@MeijerGSymb%
+\ifthenelse{\equal{#1}{@,@}}%
+	{%
+	\listval{#2}{0}% n
+	\setcounter{COOL@ct}{\value{COOL@listpointer}}%
+	\listval{#4}{0}% m
+	\setcounter{COOL@ct@}{\value{COOL@listpointer}}%
+	^{\arabic{COOL@ct@},\arabic{COOL@ct}}%
+	\listval{#3}{0}% p - n
+	\addtocounter{COOL@ct}{\value{COOL@listpointer}}%
+	\listval{#5}{0}% q - m
+	\addtocounter{COOL@ct@}{\value{COOL@listpointer}}%
+	_{\arabic{COOL@ct},\arabic{COOL@ct@}}%
+	\!\left(%
+		#6%
+		\left|%
+		{ {#2,#3} \@@atop {#4,#5} }%
+	\right)\right.%
+	}%
+% else
+	{%
+	\listval{#1}{0}%
+	\ifthenelse{\value{COOL@listpointer}=2}%
+		{%
+		\provideboolean{COOL@MeijerG@opt@one@blank}%
+		\def\COOL@MeijerG@sniffer##1,##2\COOL@MeijerG@sniffer@end{%
+			\ifthenelse{\equal{##1}{}}%
+				{%
+				\setboolean{COOL@MeijerG@opt@one@blank}{true}%
+				}%
+			% else
+				{%
+				\setboolean{COOL@MeijerG@opt@one@blank}{false}%
+				}%
+			}%
+		\expandafter\COOL@MeijerG@sniffer#1\COOL@MeijerG@sniffer@end\relax%
+		\ifthenelse{\boolean{COOL@MeijerG@opt@one@blank}}%
+			{%
+%    \end{macrocode}
+% this is |\MeijerG[,b]{a_1,...,a_n}{a_{n++},...,a_p}{m}{q}{x}|
+%    \begin{macrocode}
+			\listval{#2}{0}% n
+			\setcounter{COOL@ct}{\value{COOL@listpointer}}%
+			^{#4,\arabic{COOL@ct}}%
+			\listval{#3}{0}% p
+			\addtocounter{COOL@ct}{\value{COOL@listpointer}}%
+			_{\arabic{COOL@ct},#5}%
+			\!\left(%
+			#6%
+			\left|%
+				{%
+				{#2,#3} \@@atop {\COOL@MeijerG@anp@value{\listval{#1}{2}}{#4}{#5}}
+				}%
+			\right)\right.%
+			}%
+		% else
+			{%
+			^{#4,#2}_{#3,#5}%
+			\!\left(%
+			#6%
+			\left|%
+			{%
+				{\COOL@MeijerG@anp@value{\listval{#1}{1}}{#2}{#3}}%
+				\@@atop%
+				{\COOL@MeijerG@anp@value{\listval{#1}{2}}{#4}{#5}}
+			}%
+			\right)\right.%
+			}%
+		}%
+	% else
+		{%
+%    \end{macrocode}
+% this is| \MeijerG[a]{n}{p}{b_1,...,b_m}{b_{m++},...,a_p}{x}|
+%    \begin{macrocode}
+		\listval{#4}{0}% m
+		\setcounter{COOL@ct}{\value{COOL@listpointer}}%
+		^{\arabic{COOL@ct}, #2}%
+		\listval{#5}{0}% q
+		\addtocounter{COOL@ct}{\value{COOL@listpointer}}%
+		_{#3, \arabic{COOL@ct}}%
+		\!\left(%
+		#6%
+		\left|%
+			{%
+			{\COOL@MeijerG@anp@value{#1}{#2}{#3}} \@@atop {#4,#5}
+			}%
+		\right)\right.%
+		}%
+	}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Angular Momentum Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\ClebschGordon}
+% Clebsch-Gordon Coefficients
+%
+% \begin{tabular}{ll}
+% |\ClebschGordon{j_1,m_1}{j_2,m_2}{j,m}|	& $\ClebschGordon{j_1,m_1}{j_2,m_2}{j,m}$	\\
+% \end{tabular}
+%
+% \noindent \url{http://functions.wolfram.com/HypergeometricFunctions/ClebschGordan/}
+%    \begin{macrocode}
+\newcommand{\ClebschGordon}[3]{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ClebschGordon' Invalid Argument}%
+		{Must have a comma separated list of length two}%
+	}%
+% else
+	{}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ClebschGordon' Invalid Argument}%
+		{Must have a comma separated list of length two}%
+	}%
+% else
+	{}%
+\listval{#3}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ClebschGordon' Invalid Argument}%
+		{Must have a comma separated list of length two}%
+	}%
+% else
+	{}%
+\left<%
+	\listval{#1}{1},\listval{#2}{1};%
+	\listval{#1}{2},\listval{#2}{2}%
+	\left|%
+	\listval{#1}{1},\listval{#2}{1};%
+	\listval{#3}{1},\listval{#3}{2}%
+\right>\right.%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\ThreeJSymbol}
+% Wigner 3-j Symbol
+%
+% \begin{tabular}{ll}
+% |\ThreeJSymbol{j_1,m_1}{j_2,m_2}{j_3,m_3}|	& $\ThreeJSymbol{j_1,m_1}{j_2,m_2}{j_3,m_3}$	\\
+% \end{tabular}
+%
+% \noindent \url{http://functions.wolfram.com/HypergeometricFunctions/ThreeJSymbol/}
+%    \begin{macrocode}
+\newcommand{\ThreeJSymbol}[3]{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ThreeJSymbol' Invalid Argument}%
+		{Must have comma separated list of length 2}%
+	}%
+% else
+	{}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ThreeJSymbol' Invalid Argument}%
+		{Must have comma separated list of length 2}%
+	}%
+% else
+	{}%
+\listval{#3}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=2}%
+	{%
+	\PackageError{cool}{`ThreeJSymbol' Invalid Argument}%
+		{Must have comma separated list of length 2}%
+	}%
+% else
+	{}%
+\mathchoice{%
+% displaystyle
+\inp{\!%
+	\begin{array}{ccc}%
+	\listval{#1}{1}	& \listval{#2}{1}	& \listval{#3}{1}	\\%
+	\listval{#1}{2}	& \listval{#2}{2}	& \listval{#3}{2}
+	\end{array}%
+     \!}%
+	   }%
+	   {%
+% inline
+\inp{\!%
+	{\listval{#1}{1} \@@atop \listval{#1}{2}}%
+	{\listval{#2}{1} \@@atop \listval{#2}{2}}%
+	{\listval{#3}{1} \@@atop \listval{#3}{2}}%
+     \!}%
+	   }%
+	   {%
+% subscript
+\inp{\!%
+	{\listval{#1}{1} \@@atop \listval{#1}{2}}%
+	{\listval{#2}{1} \@@atop \listval{#2}{2}}%
+	{\listval{#3}{1} \@@atop \listval{#3}{2}}%
+     \!}%
+	   }%
+	   {%
+% subsubscript
+\inp{\!%
+	{\listval{#1}{1} \@@atop \listval{#1}{2}}%
+	{\listval{#2}{1} \@@atop \listval{#2}{2}}%
+	{\listval{#3}{1} \@@atop \listval{#3}{2}}%
+     \!}%
+	   }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\SixJSymbol}
+% Racah 6-j Symbol
+%
+% \begin{tabular}{ll}
+% |\SixJSymbol{j_1,j_2,j_3}{j_4,j_5,j_6}|	& $\SixJSymbol{j_1,j_2,j_3}{j_4,j_5,j_6}$	\\
+% \end{tabular}
+%
+% \url{http://functions.wolfram.com/HypergeometricFunctions/SixJSymbol/}
+%    \begin{macrocode}
+\newcommand{\SixJSymbol}[2]{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=3}%
+	{%
+	\PackageError{cool}{`SixJSymbol' Invalid Argument}%
+		{Must have a comma separated list of length 3}%
+	}%
+%else
+	{}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer}=3}%
+	{%
+	\PackageError{cool}{`SixJSymbol' Invalid Argument}%
+		{Must have a comma separated list of length 3}%
+	}%
+%else
+	{}%
+\mathchoice{%
+% displaystyle
+\inbr{\!%
+\begin{array}{ccc}%
+\listval{#1}{1}	& \listval{#1}{2}	& \listval{#1}{3}	\\%
+\listval{#2}{1}	& \listval{#2}{2}	& \listval{#2}{3}%
+\end{array}%
+     \!}%
+	  }%
+	  {%
+% inline
+\inbr{\!%
+	{\listval{#1}{1} \@@atop \listval{#2}{1}}%
+	{\listval{#1}{2} \@@atop \listval{#2}{2}}%
+	{\listval{#1}{3} \@@atop \listval{#2}{3}}%
+     \!}%
+	  }%
+	  {%
+% superscript
+\inbr{\!%
+	{\listval{#1}{1} \@@atop \listval{#2}{1}}%
+	{\listval{#1}{2} \@@atop \listval{#2}{2}}%
+	{\listval{#1}{3} \@@atop \listval{#2}{3}}%
+     \!}%
+	  }%
+	  {%
+% supersuperscript
+\inbr{\!%
+	{\listval{#1}{1} \@@atop \listval{#2}{1}}%
+	{\listval{#1}{2} \@@atop \listval{#2}{2}}%
+	{\listval{#1}{3} \@@atop \listval{#2}{3}}%
+     \!}%
+	  }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Complete Elliptic Integrals}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\EllipticK}
+% Complete Elliptic Integral of the First Kind 
+%
+% \begin{tabular}{ll}
+% |\EllipticK{x}|	& $\EllipticK{x}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticKParen}{p}
+	\newcommand{\COOL@notation@EllipticKSymb}{K}
+\newcommand{\EllipticK}[1]%
+	{\COOL@notation@EllipticKSymb\!\COOL@decide@paren{EllipticK}{#1}}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\EllipticE}
+% Complete Elliptic Integral of the Second Kind 
+%
+% \begin{tabular}{ll}
+% |\EllipticE{x}|	& $\EllipticE{x}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticEParen}{p}
+	\newcommand{\COOL@notation@EllipticESymb}{E}
+\newcommand{\EllipticE}[1]{%
+\liststore{#1}{COOL@EllipticE@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 1}%
+	{%
+	\COOL@notation@EllipticESymb\!\COOL@decide@paren{EllipticE}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\COOL@notation@EllipticESymb\!%
+	\COOL@decide@paren{EllipticE}%
+		{\COOL@EllipticE@arg@i \left| \, \COOL@EllipticE@arg@ii \!\!\right.}%
+	}%
+% Else
+	{%
+	\PackageError{Invalid Argument}%
+		{`EllipticE' can only accept a comma separated list of length 1 or 2}%
+	}%
+}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\EllipticPi}
+% Complete Elliptic Integral of the Third Kind 
+% 
+% \begin{tabular}{ll}
+% |\EllipticPi{n,m}| 	& $\EllipticPi{n,m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticPiParen}{p}
+	\newcommand{\COOL@notation@EllipticPiSymb}{\Pi}
+\newcommand{\EllipticPi}[1]{%
+\liststore{#1}{COOL@EllipticPi@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\COOL@notation@EllipticPiSymb%
+	\!\COOL@decide@paren{EllipticPi}%
+		{\COOL@EllipticPi@arg@i \left| \, \COOL@EllipticPi@arg@ii \!\!\right.}%
+	}%
+% ElseIf
+{ \ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	\COOL@notation@EllipticPiSymb%
+	\!\COOL@decide@paren{EllipticPi}%
+		{	\COOL@EllipticPi@arg@i; \,%
+			\COOL@EllipticPi@arg@ii \left| \,%
+			\COOL@EllipticPi@arg@iii \!\!\right.%
+		}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`EllipticPi' can only accept a comma separated list of length 2 or 3}%
+	}%
+}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Incomplete Elliptic Integrals}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\EllipticF}
+% \begin{macro}{\IncEllipticF}
+% Incomplete Elliptic Integral of the First Kind 
+%
+% \begin{tabular}{ll}
+% |\EllipticF{z,m}|		& $\EllipticF{z,m}$ 		\\
+% |\IncEllipticF{z}{m}|		& $\IncEllipticF{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticFParen}{p}
+	\newcommand{\COOL@notation@EllipticFSymb}{F}
+\newcommand{\EllipticF}[1]{%
+\liststore{#1}{COOL@EllipticF@arg@}%
+\listval{#1}{0}%
+\ifthenelse{ \value{COOL@listpointer} = 2 }%
+	{%
+	\COOL@notation@EllipticFSymb%
+	\!\COOL@decide@paren{EllipticF}%
+		{\COOL@EllipticF@arg@i \left| \, \COOL@EllipticF@arg@ii \!\!\right.}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`EllipticF' can only accept a comma separated list of length 2}%
+	}%
+}
+\newcommand{\IncEllipticF}[2]{\EllipticF{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\IncEllipticE}
+% Incomplete Elliptic Integral of the Second Kind
+%
+% \begin{tabular}{ll}
+% |\IncEllipticE{z}{m}|		& $\IncEllipticE{z}{m}$		\\
+% |\EllipticE{z,m}|		& $\EllipticE{z,m}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\IncEllipticE}[2]{\EllipticE{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\IncEllipticPi}
+% \begin{macro}{\EllipticPi}
+% Incomplete Elliptic Integral of the Third Kind
+%
+% \begin{tabular}{ll}
+% |\IncEllipticPi{n}{z}{m}|	& $\IncEllipticPi{n}{z}{m}$		\\
+% |\EllipticPi{n,z,m}|		& $\EllipticPi{n,z,m}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\IncEllipticPi}[3]{\EllipticPi{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\JacobiZeta}
+% Jacobi Zeta Function 
+%
+% \begin{tabular}{ll}
+% |\JacobiZeta{z}{m}|	& $\JacobiZeta{z}{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiZetaParen}{p}
+	\newcommand{\COOL@notation@JacobiZetaSymb}{Z}
+\newcommand{\JacobiZeta}[2]{%
+\COOL@notation@JacobiZetaSymb
+\!\COOL@decide@paren{JacobiZeta}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Jacobi Theta Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\EllipticTheta}
+% \begin{macro}{\JacobiTheta}
+% Jacobi Theta Functions 
+% 
+% \begin{tabular}{ll}
+% |\JacobiTheta{1}{z}{q}|	& $\JacobiTheta{1}{z}{q}$	\\
+% |\JacobiTheta{2}{z}{q}|	& $\JacobiTheta{2}{z}{q}$	\\
+% |\JacobiTheta{3}{z}{q}|	& $\JacobiTheta{3}{z}{q}$	\\
+% |\JacobiTheta{4}{z}{q}|	& $\JacobiTheta{4}{z}{q}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticThetaParen}{p}
+\newcommand{\EllipticTheta}[3]%
+	{\vartheta_{#1}\!\COOL@decide@paren{EllipticTheta}{#2, #3}}
+\newcommand{\JacobiTheta}[3]{\EllipticTheta{#1}{#2}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Neville Theta Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\NevilleThetaC}
+% Neville Theta Function, |\NevilleThetaC{z}{m}|, $\NevilleThetaC{z}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@NevilleThetaCParen}{p}
+\newcommand{\NevilleThetaC}[2]{%
+	\vartheta_{c}\!\COOL@decide@paren{NevilleThetaC}%
+			{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\NevilleThetaD}
+% Neville Theta Function, |\NevilleThetaD{z}{m}|, $\NevilleThetaD{z}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@NevilleThetaDParen}{p}
+\newcommand{\NevilleThetaD}[2]{%
+	\vartheta_{d}\!\COOL@decide@paren{NevilleThetaD}%
+			{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\NevilleThetaN}
+% Neville Theta Function, |\NevilleThetaN{z}{m}|, $\NevilleThetaN{z}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@NevilleThetaNParen}{p}
+\newcommand{\NevilleThetaN}[2]{%
+	\vartheta_{n}\!\COOL@decide@paren{NevilleThetaN}%
+			{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\NevilleThetaS}
+% Neville Theta Function, |\NevilleThetaS{z}{m}|, $\NevilleThetaS{z}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@NevilleThetaSParen}{p}
+\newcommand{\NevilleThetaS}[2]{%
+	\vartheta_{s}\!\COOL@decide@paren{NevilleThetaS}%
+			{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Weierstrass Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\WeierstrassP}
+% \begin{macro}{\WeiP}
+% Weierstrass Elliptic Function
+%
+% \begin{tabular}{ll}
+% |\WeierstrassP{z}{g_2,g_3}|	& $\WeierstrassP{z}{g_2,g_3}$	\\
+% |\WeiP{z}{g_2,g_3}|		& $\WeiP{z}{g_2,g_3}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@WeierstrassPParen}{p}
+\newcommand{\WeierstrassP}[2]{%
+\liststore{#2}{COOL@WeiP@arg@g@}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassP' second argument must be%
+		 a comma separated list of length 2}%
+	}
+% Else
+	{%
+	\wp\!\COOL@decide@paren{WeierstrassP}{#1; #2}
+	}%
+}
+\newcommand{\WeiP}[2]{\WeierstrassP{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassPInv}
+% \begin{macro}{\WeiPInv}
+% Inverse of Weierstrass Elliptic Function
+%
+% \begin{tabular}{lll}
+% Inverse 		& |\WeiPInv{z}{g_2,g_3}|	& $\WeiPInv{z}{g_2,g_3}$
+%														\\
+% Generalized Inverse 	& |\WeiPInv{z_1,z_2}{g_2,g_3}|	& $\WeiPInv{z_1,z_2}{g_2,g_3}$
+%														\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@WeierstrassPInvParen}{p}
+\newcommand{\WeierstrassPInv}[2]{%
+\liststore{#1}{COOL@WeiPinv@arg@z@}%
+\liststore{#1}{COOL@WeiPinv@arg@g@}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassPInv' second argument must be%
+		 a comma separated list of length 2}%
+	}
+% Else
+	{
+	\listval{#1}{0}%
+	\ifthenelse{\value{COOL@listpointer} = 1}%
+		{%
+		\wp^{-1}\!\COOL@decide@paren{WeierstrassPInv}{#1; #2}%
+		}%
+	% ElseIf
+	{ \ifthenelse{\value{COOL@listpointer} = 2}%
+		{%
+		\wp^{-1}\!\COOL@decide@paren{WeierstrassPInv}{#1; #2}%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Argument}%
+			{`WeierstrassPInv' first argument must be%
+			 a comma separate list of length 1 or 2}%
+		}}%
+	}%
+}
+\newcommand{\WeiPInv}[2]{\WeierstrassPInv{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassPGenInv}
+% Generalized Inverse of Weierstrass Elliptic Function
+%
+% |\WierstrassPGenInv{z_1}{z_2}{g_1}{g_2}|
+%    \begin{macrocode}
+\newcommand{\WeierstrassPGenInv}[4]{\WeierstrassPInv{#1,#2}{#3,#4}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassSigma}
+% \begin{macro}{\WeiSigma}
+% Wierstrass Sigma Function
+%
+% \begin{tabular}{lll}
+% Sigma			& |\WeierstrassSigma{z}{g_2,g_3}|	& $\WeierstrassSigma{z}{g_2,g_3}$	\\
+% 			& |\WeiSigma{z}{g_2,g_3}|		& $\WeiSigma{z}{g_2,g_3}$		\\
+% Associated Sigma	& |\WeierstrassSigma{n,z}{g_2,g_3}|	& $\WeierstrassSigma{n,z}{g_2,g_3}$	\\
+% 			& |\WeiSigma{n,z}{g_2,g_3}|		& $\WeiSigma{n,z}{g_2,g_3}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\WeierstrassSigma}[2]{%
+\liststore{#1}{COOL@WeiSigma@arg@z@}%
+\liststore{#2}{COOL@WeiSigma@arg@g@}%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}
+	{%
+	\PackageError{cool}{Invalid Argument}%	
+		{`WeierstrassSigma' second argument must be%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\listval{#1}{0}%
+	\ifthenelse{\value{COOL@listpointer} = 1}%
+		{%
+		\sigma\!\inp{#1; #2}%
+		}%
+	% ElseIf
+	{ \ifthenelse{\value{COOL@listpointer} = 2}%
+		{%
+		\sigma_{\COOL@WeiSigma@arg@z@i}\!\inp{\COOL@WeiSigma@arg@z@ii; #2}%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Argument}%
+			{`WeierstrassSigma' first argument must be%
+			 a comma separated list of length 1 or 2}%
+		}}%
+	}%
+}
+\newcommand{\WeiSigma}[2]{\WeierstrassSigma{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\AssocWeierstrassSigma}
+% Associated Weierstrass Sigma Function
+%
+% \begin{tabular}{ll}
+% |\AssocWeierstrassSigma{n}{z}{g_2}{g_3}|	& $\AssocWeierstrassSigma{n}{z}{g_2}{g_3}$	\\
+% |\WeiSigma{n,z}{g_2,g_3}|			& $\WeiSigma{n,z}{g_2,g_3}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\AssocWeierstrassSigma}[4]{\WeierstrassSigma{#1,#2}{#3,#4}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassZeta}
+% \begin{macro}{\WeiZeta}
+% Weierstrass Zeta Function 
+%
+% \begin{tabular}{ll}
+% |\WeierstrassZeta{z}{g_2,g_3}|	& $\WeierstrassZeta{z}{g_2,g_3}$	\\
+% |\WeiZeta{z}{g_2,g_3}|		& $\WeiZeta{z}{g_2,g_3}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@WeierstrassZetaParen}{p}%
+\newcommand{\WeierstrassZeta}[2]{%
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassZeta' second argument must be%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\zeta\!\COOL@decide@paren{WeierstrassZeta}{#1; #2}%
+	}%
+}
+\newcommand{\WeiZeta}[2]{\WeierstrassZeta{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassHalfPeriods}
+% \begin{macro}{\WeiHalfPeriods}
+% Weierstrass half-periods 
+%
+% \begin{tabular}{ll}
+% |\WeierstrassHalfPeriods{g_2,g_3}|	& $\WeierstrassHalfPeriods{g_2,g_3}$	\\
+% |\WeiHalfPeriods{g_2,g_3}|		& $\WeiHalfPeriods{g_2,g_3}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\WeierstrassHalfPeriods}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassHalfPeriods' can only accept%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\{ \omega_1\!\inp{#1}, \omega_3\!\inp{#1} \}%
+	}%
+}
+\newcommand{\WeiHalfPeriods}[1]{\WeierstrassHalfPeriods{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassInvariants}
+% Weierstrass Invariants 
+%
+% \noindent
+% \begin{tabular}{ll}
+% |\WeierstrassInvariants{\omega_1,\omega_3}|	& $\WeierstrassInvariants{\omega_1,\omega_3}$	\\
+% |\WeiInvars{\omega_1,\omega_3}|		& $\WeiInvars{\omega_1,\omega_3}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\WeierstrassInvariants}[1]{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassInvariants' can only accept%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\{ g_2\!\inp{#1}, g_3\!\inp{#1} \}%
+	}%
+}
+\newcommand{\WeiInvars}[1]{\WeierstrassInvariants{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\COOL@hideOnSF}
+% Used to hide inputs or other when style is |sf|
+%
+% \begin{tabular}{ll}
+% |sf|	& short form	\\
+% |ff|	& full form
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@hideOnSF}[2]
+		{%
+		\ifthenelse{ \equal{\csname COOL@notation@#1\endcsname}{sf} }%
+			{}%
+		% Else
+			{#2}%
+		}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassPHalfPeriodValues}
+% \begin{macro}{\WeiPHalfPeriodVal}
+% Weierstrass elliptic function values at half-periods 
+%
+% \begin{tabular}{c}
+% |\Style{WeierstrassPHalfPeriodValuesDisplay=sf}| (Default)	\\
+% |\WeierstrassPHalfPeriodValues{g_2,g_3}|			\\
+% |\WeiPHalfPeriodVal{g_2,g_3}|					\\
+% $\WeiPHalfPeriodVal{g_2,g_3}$					\\
+%								\\
+% |\Style{WeierstrassPHalfPeriodValuesDisplay=ff}|
+% \Style{WeierstrassPHalfPeriodValuesDisplay=ff}%		\\
+% |\WeierstrassPHalfPeriodValues{g_2,g_3}|			\\
+% |\WeiPHalfPeriodVal{g_2,g_3}|					\\
+% $\WeiPHalfPeriodVal{g_2,g_3}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@WeierstrassPHalfPeriodValuesDisplay}{sf}
+\newcommand{\WeierstrassPHalfPeriodValues}[1]
+{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassPHalfPeriodValues' can only accept%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\{ 	e_1\COOL@hideOnSF{WeierstrassPHalfPeriodValuesDisplay}{\!\inp{#1}},%
+		e_2\COOL@hideOnSF{WeierstrassPHalfPeriodValuesDisplay}{\!\inp{#1}},%
+		e_3\COOL@hideOnSF{WeierstrassPHalfPeriodValuesDisplay}{\!\inp{#1}}%
+	\}%
+	}%
+}
+\newcommand{\WeiPHalfPeriodVal}[1]{\WeierstrassPHalfPeriodValues{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\WeierstrassZetaHalfPeriodValues}
+% \begin{macro}{\WeiZetaHalfPeriodVal}
+% Weierstrass zeta function values at half-periods
+%
+% \begin{tabular}{c}
+% |\Style{WeierstrassZetaHalfPeriodValuesDisplay=sf}| (Default)	\\
+% |\WeierstrassZetaHalfPeriodValues{g_2,g_3}|			\\
+% |\WeiZetaHalfPeriodVal{g_2,g_3}|				\\
+% $\WeiZetaHalfPeriodVal{g_2,g_3}$				\\
+%								\\
+% |\Style{WeierstrassZetaHalfPeriodValuesDisplay=ff}|
+% \Style{WeierstrassZetaHalfPeriodValuesDisplay=ff}%		\\
+% |\WeierstrassZetaHalfPeriodValues{g_2,g_3}|			\\
+% |\WeiZetaHalfPeriodVal{g_2,g_3}|				\\
+% $\WeiZetaHalfPeriodVal{g_2,g_3}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@WeierstrassZetaHalfPeriodValuesDisplay}{sf}
+\newcommand{\WeierstrassZetaHalfPeriodValues}[1]
+{%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`WeierstrassZetaHalfPeriodValues' can only accept%
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\{%
+	\eta_1\COOL@hideOnSF%
+		{WeierstrassZetaHalfPeriodValuesDisplay}{\!\inp{#1}},%
+	\eta_2\COOL@hideOnSF%
+		{WeierstrassZetaHalfPeriodValuesDisplay}{\!\inp{#1}},%
+	\eta_3\COOL@hideOnSF%
+		{WeierstrassZetaHalfPeriodValuesDisplay}{\!\inp{#1}}%
+	\}%
+	}%
+}
+\newcommand{\WeiZetaHalfPeriodVal}[1]%
+	{\WeierstrassZetaHalfPeriodValues{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Jacobi Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\JacobiAmplitude}
+% Amplitude, |\JacobiAmplitude{z}{m}|, $\JacobiAmplitude{z}{m}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiAmplitudeParen}{p}
+	\DeclareMathOperator{\JacobiAmplitudeSymb}{am}
+\newcommand{\JacobiAmplitude}[2]{%
+\JacobiAmplitudeSymb\!\COOL@decide@paren%
+	{JacobiAmplitude}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\JacobiCD}
+% \begin{macro}{\JacobiCDInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiCD{z}{m}|	& $\JacobiCD{z}{m}$ 	\\
+% |\JacobiCDInv{z}{m}|	& $\JacobiCDInv{z}{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiCDParen}{p}
+	\newcommand{\COOL@notation@JacobiCDInvParen}{p}
+	\DeclareMathOperator{\JacobiCDSymb}{cd}
+\newcommand{\JacobiCD}[2]{%
+\JacobiCDSymb\!\COOL@decide@paren%
+	{JacobiCD}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiCDInv}[2]{%
+\JacobiCDSymb^{-1}\!\COOL@decide@paren%
+	{JacobiCDInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiCN}
+% \begin{macro}{\JacobiCNInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiCN{z}{m}|	& $\JacobiCN{z}{m}$	\\
+% |\JacobiCNInv{z}{m}|	& $\JacobiCNInv{z}{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiCNParen}{p}
+	\newcommand{\COOL@notation@JacobiCNInvParen}{p}
+	\DeclareMathOperator{\JacobiCNSymb}{cn}
+\newcommand{\JacobiCN}[2]{%
+\JacobiCNSymb\!\COOL@decide@paren%
+	{JacobiCN}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiCNInv}[2]{%
+\JacobiCNSymb^{-1}\!\COOL@decide@paren%
+	{JacobiCNInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiCS}
+% \begin{macro}{\JacobiCSInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiCS{z}{m}|		& $\JacobiCS{z}{m}$ 		\\
+% |\JacobiCSInv{z}{m}|		& $\JacobiCSInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiCSParen}{p}
+	\newcommand{\COOL@notation@JacobiCSInvParen}{p}
+	\DeclareMathOperator{\JacobiCSSymb}{cs}
+\newcommand{\JacobiCS}[2]{%
+\JacobiCSSymb\!\COOL@decide@paren%
+	{JacobiCS}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiCSInv}[2]{%
+\JacobiCSSymb^{-1}\!\COOL@decide@paren%
+	{JacobiCSInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiDC}
+% \begin{macro}{\JacobiDCInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiDC{z}{m}|		& $\JacobiDC{z}{m}$		\\
+% |\JacobiDCInv{z}{m}|		& $\JacobiDCInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiDCParen}{p}
+	\newcommand{\COOL@notation@JacobiDCInvParen}{p}
+	\DeclareMathOperator{\JacobiDCSymb}{dc}
+\newcommand{\JacobiDC}[2]{%
+\JacobiDCSymb\!\COOL@decide@paren%
+	{JacobiDC}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiDCInv}[2]{%
+\JacobiDCSymb^{-1}\!\COOL@decide@paren%
+	{JacobiDCInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiDN}
+% \begin{macro}{\JacobiDNInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiDN{z}{m}|		& $\JacobiDN{z}{m}$ 		\\
+% |\JacobiDNInv{z}{m}|		& $\JacobiDNInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiDNParen}{p}
+	\newcommand{\COOL@notation@JacobiDNInvParen}{p}
+	\DeclareMathOperator{\JacobiDNSymb}{dn}
+\newcommand{\JacobiDN}[2]{%
+\JacobiDNSymb\!\COOL@decide@paren%
+	{JacobiDN}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiDNInv}[2]{%
+\JacobiDNSymb^{-1}\!\COOL@decide@paren%
+	{JacobiDNInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiDS}
+% \begin{macro}{\JacobiDSInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiDS{z}{m}|		& $\JacobiDS{z}{m}$ 	\\
+% |\JacobiDSInv{z}{m}|		& $\JacobiDSInv{z}{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiDSParen}{p}
+	\newcommand{\COOL@notation@JacobiDSInvParen}{p}
+	\DeclareMathOperator{\JacobiDSSymb}{ds}
+\newcommand{\JacobiDS}[2]{%
+\JacobiDSSymb\!\COOL@decide@paren%
+	{JacobiDS}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiDSInv}[2]{%
+\JacobiDSSymb^{-1}\!\COOL@decide@paren%
+	{JacobiDSInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiNC}
+% \begin{macro}{\JacobiNCInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiNC{z}{m}|		& $\JacobiNC{z}{m}$ 		\\
+% |\JacobiNCInv{z}{m}|		& $\JacobiNCInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiNCParen}{p}
+	\newcommand{\COOL@notation@JacobiNCInvParen}{p}
+	\DeclareMathOperator{\JacobiNCSymb}{nc}
+\newcommand{\JacobiNC}[2]{%
+\JacobiNCSymb\!\COOL@decide@paren%
+	{JacobiNC}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiNCInv}[2]{%
+\JacobiNCSymb^{-1}\!\COOL@decide@paren%
+	{JacobiNCInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiND}
+% \begin{macro}{\JacobiNDinv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiND{z}{m}|		& $\JacobiND{z}{m}$ 		\\
+% |\JacobiNDInv{z}{m}|		& $\JacobiNDInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiNDParen}{p}
+	\newcommand{\COOL@notation@JacobiNDInvParen}{p}
+	\DeclareMathOperator{\JacobiNDSymb}{nd}
+\newcommand{\JacobiND}[2]{%
+\JacobiNDSymb\!\COOL@decide@paren%
+	{JacobiND}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiNDInv}[2]{%
+\JacobiNDSymb^{-1}\!\COOL@decide@paren%
+	{JacobiNDInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiNS}
+% \begin{macro}{\JacobiNSInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiNS{z}{m}|		& $\JacobiNS{z}{m}$ 	\\
+% |\JacobiNSInv{z}{m}|		& $\JacobiNSInv{z}{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiNSParen}{p}
+	\newcommand{\COOL@notation@JacobiNSInvParen}{p}
+	\DeclareMathOperator{\JacobiNSSymb}{ns}
+\newcommand{\JacobiNS}[2]{%
+\JacobiNSSymb\!\COOL@decide@paren%
+	{JacobiNS}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiNSInv}[2]{%
+\JacobiNSSymb^{-1}\!\COOL@decide@paren%
+	{JacobiNSInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiSC}
+% \begin{macro}{\JacobiSCInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiSC{z}{m}|		& $\JacobiSC{z}{m}$		\\
+% |\JacobiSCInv{z}{m}|		& $\JacobiSCInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiSCParen}{p}
+	\newcommand{\COOL@notation@JacobiSCInvParen}{p}
+	\DeclareMathOperator{\JacobiSCSymb}{sc}
+\newcommand{\JacobiSC}[2]{%
+\JacobiSCSymb\!\COOL@decide@paren%
+	{JacobiSC}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiSCInv}[2]{%
+\JacobiSCSymb^{-1}\!\COOL@decide@paren%
+	{JacobiSCInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiSD}
+% \begin{macro}{\JacobiSDInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiSD{z}{m}|		& $\JacobiSD{z}{m}$		\\
+% |\JacobiSDInv{z}{m}|		& $\JacobiSDInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiSDParen}{p}
+	\newcommand{\COOL@notation@JacobiSDInvParen}{p}
+	\DeclareMathOperator{\JacobiSDSymb}{sd}
+\newcommand{\JacobiSD}[2]{%
+\JacobiSDSymb\!\COOL@decide@paren%
+	{JacobiSD}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiSDInv}[2]{%
+\JacobiSDSymb^{-1}\!\COOL@decide@paren%
+	{JacobiSDInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\JacobiSN}
+% \begin{macro}{\JacobiSNInv}
+% Jacobi elliptic function and its inverse
+%
+% \begin{tabular}{ll}
+% |\JacobiSN{z}{m}|		& $\JacobiSN{z}{m}$		\\
+% |\JacobiSNInv{z}{m}|		& $\JacobiSNInv{z}{m}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@JacobiSNParen}{p}
+	\newcommand{\COOL@notation@JacobiSNInvParen}{p}
+	\DeclareMathOperator{\JacobiSNSymb}{sn}
+\newcommand{\JacobiSN}[2]{%
+\JacobiSNSymb\!\COOL@decide@paren%
+	{JacobiSN}{#1 \left| \, #2 \right.\!\!}%
+}
+\newcommand{\JacobiSNInv}[2]{%
+\JacobiSNSymb^{-1}\!\COOL@decide@paren%
+	{JacobiSNInv}{#1 \left| \, #2 \right.\!\!}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Modular Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\DedekindEta}
+% Dedekind eta modular function, |\DedekindEta{z}|, $\DedekindEta{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DedekindEtaParen}{p}
+\newcommand{\DedekindEta}[1]{\eta\!\COOL@decide@paren{DedekindEta}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\KleinInvariantJ}
+% Klein invariant modular function, |\KleinInvariantJ{z}|, $\KleinInvariantJ{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@KleinInvariantJParen}{p}
+\newcommand{\KleinInvariantJ}[1]%
+	{J\!\COOL@decide@paren{KleinInvariantJ}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ModularLambda}
+% Modular lambda function, |\ModularLambda{z}|, $\ModularLambda{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ModularLambdaParen}{p}
+\newcommand{\ModularLambda}[1]%
+	{\lambda\!\COOL@decide@paren{ModularLambda}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\EllipticNomeQ}
+% \begin{macro}{\EllipticNomeQInv}
+% Nome and its inverse
+%
+% \begin{tabular}{ll}
+% |\EllipticNomeQ{m}|		& $\EllipticNomeQ{m}$		\\
+% |\EllipticNomeQInv{m}|	& $\EllipticNomeQInv{m}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticNomeQParen}{p}
+	\newcommand{\COOL@notation@EllipticNomeQInvParen}{p}
+\newcommand{\EllipticNomeQ}[1]%
+	{q\!\COOL@decide@paren{EllipticNomeQ}{#1}}
+\newcommand{\EllipticNomeQInv}[1]%
+	{q^{-1}\!\COOL@decide@paren{EllipticNomeQ}{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Arithmetic Geometric Mean}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\ArithGeoMean}
+% \begin{macro}{\AGM}
+% Arithmetic Geometric Mean
+%
+% \begin{tabular}{ll}
+% |\ArithGeoMean{a}{b}|		& $\ArithGeoMean{a}{b}$		\\
+% |\AGM{a}{b}|			& $\AGM{a}{b}$			\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ArithGeoMeanParen}{p}
+	\DeclareMathOperator{\ArithGeoMeanSymb}{agm}
+\newcommand{\ArithGeoMean}[2]%
+	{\ArithGeoMeanSymb\!\COOL@decide@paren{ArithGeoMean}{#1, #2}}
+\newcommand{\AGM}[2]{\ArithGeoMean{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Elliptic Exp and Log}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\EllipticExp}
+% \begin{macro}{\EExp}
+% Elliptic exponential
+%
+% \begin{tabular}{ll}
+% |\EllipticExp{z}{a,b}|	& $\EllipticExp{z}{a,b}$	\\
+% |\EExp{z}{a,b}|		& $\EExp{z}{a,b}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticExpParen}{p}
+	\DeclareMathOperator{\EllipticExpSymb}{eexp}
+\newcommand{\EllipticExp}[2]{%
+\liststore{#2}{COOL@EllipticExp@arg@}
+\listval{#2}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`EllipticExp' second argument must be
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\EllipticExpSymb\!\COOL@decide@paren{EllipticExp}{#1; #2}%
+	}%
+}
+\newcommand{\EExp}[2]{\EllipticExp{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\EllipticLog}
+% \begin{macro}{\ELog}
+% Elliptic logarithm
+%
+% \begin{tabular}{ll}
+% |\EllipticLog{z_1,z_2}{a,b}|	& $\EllipticLog{z_1,z_2}{a,b}$		\\
+% |\ELog{z_1,z_2}{a,b}|		& $\ELog{z_1,z_2}{a,b}$			\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EllipticLogParen}{p}
+	\DeclareMathOperator{\EllipticLogSymb}{elog}
+\newcommand{\EllipticLog}[2]{%
+\liststore{#1}{COOL@EllipticLog@arg@z@}%
+\liststore{#2}{COOL@EllipticLog@arg@a@}%
+\listval{#1}{0}%
+\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+	{%
+	\PackageError{cool}{Invalid Argument}%
+		{`EllipticLog' first argument must be
+		 a comma separated list of length 2}%
+	}%
+% Else
+	{%
+	\listval{#2}{0}%
+	\ifthenelse{\NOT \value{COOL@listpointer} = 2}%
+		{%
+		\PackageError{cool}{Invalid Argument}%
+			{`EllipticLog' second argument must be%
+			 a comma separated list of length 2}%
+		}%
+	% Else
+		{%
+		\EllipticLogSymb\!\COOL@decide@paren{EllipticLog}{#1; #2}%
+		}%
+	}%
+}
+\newcommand{\ELog}[2]{\EllipticLog{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Zeta Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\RiemannZeta}
+% Riemann Zeta Function
+%
+% \begin{tabular}{ll}
+% |\RiemannZeta{s}|	& $\RiemannZeta{s}$	\\
+% |\Zeta{s}|		& $\Zeta{s}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\RiemannZeta}[1]{\Zeta{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\HurwitzZeta}
+% Hurwitz Zeta Function 
+%
+% \begin{tabular}{ll}
+% |\HurwitzZeta{s}{a}|	& $\HurwitzZeta{s}{a}$	\\
+% |\Zeta{s,a}|		& $\Zeta{s,a}$
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\HurwitzZeta}[2]{\Zeta{#1,#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Zeta}
+% Riemann and Hurwitz Zeta
+%
+% \begin{tabular}{lll}
+% Riemann Zeta	& |\Zeta{s}|	& $\Zeta{s}$	\\
+% Hurwitz Zeta	& |\Zeta{s,a}|	& $\Zeta{s,a}$
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ZetaParen}{p}
+\newcommand{\Zeta}[1]{%
+\liststore{#1}{COOL@Zeta@arg@}%
+\listval{#1}{0}% get the list length
+\ifthenelse{\value{COOL@listpointer} = 2}%
+	{%
+	\zeta\!\COOL@decide@paren{Zeta}{\COOL@Zeta@arg@i,\COOL@Zeta@arg@ii}%
+	}%
+% else
+	{%
+	\ifthenelse{\value{COOL@listpointer} = 1}%
+		{%
+		\zeta\!\COOL@decide@paren{Zeta}{#1}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{`Zeta' Invalid Argument}%
+			{the Zeta function can only accept%
+			 a comma deliminated list of length 1 or 2}
+		}%
+	}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\RiemannSiegelTheta}
+% Riemann-Siegel Theta Function, |\RiemannSiegelTheta{z}|, $\RiemannSiegelTheta{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@RiemannSiegelThetaParen}{p}
+\newcommand{\RiemannSiegelTheta}[1]%
+	{\vartheta\!\COOL@decide@paren{RiemannSiegelTheta}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\RiemannSiegelZ}
+% Riemann-Siegel Z Function, |\RiemannSiegelZ{z}|, $\RiemannSiegelZ{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@RiemannSiegelZParen}{p}
+\newcommand{\RiemannSiegelZ}[1]%
+	{Z\!\COOL@decide@paren{RiemannSiegelZ}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\StieltjesGamma}
+% Stieltjes Constant, |\StieltjesGamma{n}|, $\StieltjesGamma{n}$
+%    \begin{macrocode}
+\newcommand{\StieltjesGamma}[1]{\gamma_{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LerchPhi}
+% Lerch transcendent, |\LerchPhi{z}{s}{a}|, $\LerchPhi{z}{s}{a}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@LerchPhiParen}{p}
+\newcommand{\LerchPhi}[3]{\Phi\!\COOL@decide@paren{LerchPhi}{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Polylogarithms}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\NielsenPolyLog}
+% Nielsen Polylogarithm, |\NielsenPolyLog{\nu}{p}{z}|, $\NielsenPolyLog{\nu}{p}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@NielsenPolyLogParen}{p}
+\newcommand{%
+\NielsenPolyLog}[3]{S_{#1}^{#2}\!%
+	\COOL@decide@paren{NielsenPolyLog}{#3}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\PolyLog}
+% Polylogarithm
+%
+% \begin{tabular}{lll}
+% Nielsen PolyLog	& |\PolyLog{\nu,p,z}|	& $\PolyLog{\nu,p,z}$		\\
+% PolyLog		& |\PolyLog{\nu,z}|	& $\PolyLog{\nu,z}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PolyLogParen}{p}
+	\DeclareMathOperator{\PolyLogSymb}{Li}
+\newcommand{\PolyLog}[1]{%
+\liststore{#1}{COOL@PolyLog@arg@}%
+\listval{#1}{0}%
+\ifthenelse{\value{COOL@listpointer} = 3}%
+	{%
+	\NielsenPolyLog{\COOL@PolyLog@arg@i}%
+		{\COOL@PolyLog@arg@ii}{\COOL@PolyLog@arg@iii}%
+	}%
+% else
+	{%
+	\ifthenelse{ \value{COOL@listpointer} = 2 }%
+		{%
+		\PolyLogSymb_{\COOL@PolyLog@arg@i}\!%
+			\COOL@decide@paren{PolyLog}{\COOL@PolyLog@arg@ii}%
+		}%
+	% else
+		{%
+		\PackageError{cool}{`PolyLog' Invalid Argument}%
+			{This function returns either the Polylogarithm or the%
+			 Nielsen Polylogarithm.  It therefore only accepts a comma%
+			 deliminated list of length two or three (1 or 2 commas)}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DiLog}
+% Dilogarithm (alias for |\PolyLog{2,x}|); |\DiLog{x}|, $\DiLog{x}$
+%    \begin{macrocode}
+\newcommand{\DiLog}[1]{\PolyLog{2,#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Mathieu Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\MathieuC}
+% Even Mathieu Function, |\MathieuC{a}{q}{z}|, $\MathieuC{a}{q}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MathieuCParen}{p}
+	\DeclareMathOperator{\MathieuCSymb}{Ce}
+\newcommand{\MathieuC}[3]%
+	{\MathieuCSymb\!\COOL@decide@paren{MathieuC}{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\MathieuS}
+% Odd Mathieu Function, |\MathieuS{a}{q}{z}|, $\MathieuS{a}{q}{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MathieuSParen}{p}
+	\DeclareMathOperator{\MathieuSSymb}{Se}
+\newcommand{\MathieuS}[3]%
+	{\mathord{\MathieuSSymb}\!\COOL@decide@paren{MathieuS}{#1,#2,#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Mathieu Characteristics}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\MathieuCharacteristicA}
+% \begin{macro}{\MathieuCharisticA}
+% Characteristic Value of Even Mathieu Function 
+%
+% \begin{tabular}{ll}
+% |\MathieuCharacteristicA{r}{q}|	& $\MathieuCharacteristicA{r}{q}$	\\
+% |\MathieuCharisticA{r}{q}|		& $\MathieuCharisticA{r}{q}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MathieuCharacteristicAParen}{p}
+\newcommand{\MathieuCharacteristicA}[2]%
+	{a_{#1}\!\COOL@decide@paren{MathieuCharacteristicA}{#2}}
+\newcommand{\MathieuCharisticA}[2]{\MathieuCharacteristicA{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\MathieuCharacteristicB}
+% \begin{macro}{\MathieuCharisticB}
+% Characteristic Value of Even Mathieu Fucntion 
+%
+% \begin{tabular}{ll}
+% |\MathieuCharacteristicB{r}{q}|	& $\MathieuCharacteristicB{r}{q}$	\\
+% |\MathieuCharisticB{r}{q}|		& $\MathieuCharisticB{r}{q}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MathieuCharacteristicBParen}{p}
+\newcommand{\MathieuCharacteristicB}[2]%
+	{b_{#1}\!\COOL@decide@paren{MathieuCharacteristicB}{#2}}
+\newcommand{\MathieuCharisticB}[2]{\MathieuCharacteristicB{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\MathieuCharacteristicExponent}
+% \begin{macro}{\MathieuCharisticExp}
+% Characteristic Exponent of a Mathieu Fucntion
+%
+% \begin{tabular}{ll}
+% |\MathieuCharateristicExponent{a}{q}|		& $\MathieuCharacteristicExponent{a}{q}$	\\
+% |\MathieuCharisticExp{a}{q}|			& $\MathieuCharisticExp{a}{q}$			\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MathieuCharacteristicExponentParen}{p}
+\newcommand{\MathieuCharacteristicExponent}[2]%
+	{r\!\COOL@decide@paren{MathieuCharacteristicExponent}{#1,#2}}
+\newcommand{\MathieuCharisticExp}[2]%
+	{\MathieuCharacteristicExponent{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Complex variables}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Abs}
+% Absolute value, |\Abs{z}|, $\Abs{z}$
+%    \begin{macrocode}
+\newcommand{\Abs}[1]{ \left|#1\right| }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Arg}
+% Argument, |\Arg{z}|, $\Arg{z}$
+%    \begin{macrocode}
+\newcommand{\Arg}[1]{ \arg\!\inp{#1} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Conjugate}
+% \begin{macro}{\Conj}
+% Complex Conjugate
+%
+% \begin{tabular}{ll}
+% |\Conj{z}|		& $\Conj{z}$		\\
+% |\Conjugate{z}|	& $\Conjugate{z}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\def\COOL@notation@Conjugate{star}
+	\newcommand{\COOL@notation@ConjugateParen}{inv}
+\newcommand{\Conjugate}[1]{\Conj{#1}}
+\newcommand{\Conj}[1]{%
+\ifthenelse{\equal{\COOL@notation@Conjugate}{bar}}%
+	{%
+	\bar{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\equal{\COOL@notation@Conjugate}{overline}}%
+	{%
+	\overline{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\equal{\COOL@notation@Conjugate}{star}}%
+	{%
+	\COOL@decide@paren{Conjugate}{#1}^*%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Option Sent}%
+		{`Conjugate' can only be set at `star', `bar', or `overline'}%
+	}%
+}}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\Real}
+% Real Part, |\Real{z}|, $\Real{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@RealParen}{none}
+	\DeclareMathOperator{\RealSymb}{Re}
+\newcommand{\Real}[1]{%
+%    \end{macrocode}
+% we put a space if there is no parentheses, or leave it out if there are
+%    \begin{macrocode}
+\ifthenelse{\equal{\COOL@notation@ImagParen}{none}}%
+	{%
+	\RealSymb{#1}%
+	}%
+% Else
+	{%
+	\RealSymb\!\COOL@decide@paren{Imag}{#1}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Imag}
+% Imaginary Part, |\Imag{z}|, $\Imag{z}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@ImagParen}{none}
+	\DeclareMathOperator{\ImagSymb}{Im}
+\newcommand{\Imag}[1]{%
+%    \end{macrocode}
+% we put a space if there is no parentheses, or leave it out if there are
+%    \begin{macrocode}
+\ifthenelse{\equal{\COOL@notation@ImagParen}{none}}%
+	{%
+	\ImagSymb{#1}%
+	}%
+% Else
+	{%
+	\ImagSymb\!\COOL@decide@paren{Imag}{#1}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Sign}
+% Sign function, |\Sign{x}|, $\Sign{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@SignParen}{p}
+\newcommand{\Sign}[1]{\operatorname{sgn}\!\COOL@decide@paren{Sign}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Number Theory Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\FactorInteger}
+% \begin{macro}{\Factors}
+% Prime decomposition, |\Factors{n}|, $\Factors{n}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@FactorIntegerParen}{p}
+	\DeclareMathOperator{\FactorIntegerSymb}{factors}
+\newcommand{\FactorInteger}[1]%
+	{\FactorIntegerSymb\!\COOL@decide@paren{FactorInteger}{#1}}
+\newcommand{\Factors}[1]{\FactorInteger{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\Divisors}
+% Divisors, |\Divisors{n}|, $\Divisors{n}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DivisorsParen}{p}
+	\DeclareMathOperator{\DivisorsSymb}{divisors}
+\newcommand{\Divisors}[1]%
+	{\mathord{\DivisorsSymb}\!\COOL@decide@paren{Divisors}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Prime}
+% The $n$th Prime, |\Prime{n}|, $\Prime{n}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PrimeParen}{p}
+	\DeclareMathOperator{\PrimeSymb}{prime}
+\newcommand{\Prime}[1]%
+	{\mathord{\PrimeSymb}\!\COOL@decide@paren{Prime}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\PrimePi}
+% Prime counting function, |\PrimePi{x}|, $\PrimePi{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@PrimePiParen}{p}
+\newcommand{\PrimePi}[1]{\pi\!\COOL@decide@paren{PrimePi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DivisorSigma}
+% Sum of divisor powers, |\DivisorSigma{k}{n}|, $\DivisorSigma{k}{n}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DivisorSigmaParen}{p}
+\newcommand{\DivisorSigma}[2]%
+	{\sigma_{#1}\!\COOL@decide@paren{DivisorSigma}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\EulerPhi}
+% Euler Totient Function, |\EulerPhi{x}|, $\EulerPhi{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@EulerPhiParen}{p}
+\newcommand{\EulerPhi}[1]{\varphi\!\COOL@decide@paren{EulerPhi}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\MoebiusMu}
+% Moebius Function, |\MoebiusMu{x}|, $\MoebiusMu{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@MoebiusMuParen}{p}
+\newcommand{\MoebiusMu}[1]{\mu\!\COOL@decide@paren{MoebiusMu}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\JacobiSymbol}
+% Jacobi Symbol, |\JacobiSymbol{n}{m}|, $\JacobiSymbol{n}{m}$
+%    \begin{macrocode}
+\newcommand{\JacobiSymbol}[2]{\inp{\frac{#1}{#2}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\CarmichaelLambda}
+% Carmichael Lambda Function, |\CarmichaelLambda{x}|, $\CarmichaelLambda{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@CarmichaelLambdaParen}{p}
+\newcommand{\CarmichaelLambda}[1]%
+	{\lambda\!\COOL@decide@paren{CarmichaelLambda}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DigitCount}
+% Count the digits of an integer n for a given base b
+%
+% \begin{tabular}{c}
+% |\DigitCount{n}{b}|		\\
+% $\DigitCount{n}{b}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\DigitCount}[2]{%
+\isint{#2}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{%
+	\{%
+	\setcounter{COOL@ct@}{#2}%
+	\addtocounter{COOL@ct@}{-1}%
+	\forLoop{1}{\arabic{COOL@ct@}}{COOL@ct}%
+		{%
+		s^{\arabic{COOL@ct}}_{#2}\!\inp{#1},
+		}%
+	s^{\inp{0}}_{#2}\!\inp{#1}%
+	\}%
+	}%
+% else
+	{%
+	\{%
+		s^{\inp{1}}_{#2}\!\inp{#1},%
+		s^{\inp{2}}_{#2}\!\inp{#1},%
+		\ldots,%
+		s^{\inp{#2} - 1}_{#2}\!\inp{#1},%
+		s^{\inp{0}}_{#2}\!\inp{#1}%
+	\}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Generalized Functions}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\DiracDelta}
+% Dirac Delta Function, |\DiracDelta{x}|, $\DiracDelta{x}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DiracDeltaParen}{p}
+\newcommand{\DiracDelta}[1]{\delta\!\COOL@decide@paren{DiracDelta}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\HeavisideStep}
+% \begin{macro}{\UnitStep}
+% Heaviside Step Function
+%
+% \begin{tabular}{ll}
+% |\HeavisideStep{x}|		& $\HeavisideStep{x}$	\\
+% |\UnitStep{x}|		& $\UnitStep{x}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@HeavisideStepParen}{p}
+\newcommand{\HeavisideStep}[1]%
+	{\theta\!\COOL@decide@paren{HeavisideStep}{#1}}
+\newcommand{\UnitStep}[1]{\HeavisideStep{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% 
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Calculus}
+% %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\COOL@notation@DDisplayFunc}
+% \begin{macro}{\COOL@notation@DShorten}
+% Both |\D| and |\pderiv| are controlled by these keys.
+%
+% |DDisplayFunc| controls how the function is displayed, it can take the values:
+%
+% \begin{tabular}{ll}
+% inset 	& Display as $\frac{d f}{d x}$		\\
+% outset	& Display as $\frac{d}{d x} f$
+% \end{tabular}
+%
+% |DShorten| is for multiple derivatives.  it can take the values
+%
+% \begin{tabular}{ll}
+% true		& force derivatives to be consolidated, as in $\frac{d^2}{dx dy} f$		\\
+% false		& expand derivatives as in $\frac{d}{dx} \frac{d}{dx} f$
+% \end{tabular}
+%
+%    \begin{macrocode}
+	\newcounter{COOL@multideriv}
+	\newcommand{\COOL@notation@DDisplayFunc}{inset}
+	\newcommand{\COOL@notation@DShorten}{true}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\COOL@derivative}
+% Both |\D| and |pderiv| have the same basic operation, so a macro is defined that does the internals
+%
+% |\COOL@derivative{|\meta{derivative power(s)}|}{|\meta{function}|}{|\meta{wrt}|}{|\meta{symbol}|}|
+%
+% \meta{wrt} is a comma separated list of length $\ge$ 1.
+%
+% \meta{symbol} is passed by |\D| or |\pderiv| and is `d' or `$\partial$' respectively
+%
+% \begin{tabular}{ll}
+% |\COOL@derivative{2,3}{f}{x,y,z}{d}| 		& \makeatletter 
+%						  $\COOL@derivative{2,3}{f}{x,y,z}{d}$
+%						  \makeatother
+%						  \vspace{.15cm}
+% \\
+% |\COOL@derivative{2,3,4,5}{f}{x,y,z}{d}| 	& \makeatletter 
+%						  $\COOL@derivative{2,3,4,5}{f}{x,y,z}{d}$
+%						  \makeatother
+%						  \vspace{.15cm}
+% \\
+% |\COOL@derivative{2,n,1}{f}{x,y,z}{d}| 	& \makeatletter
+%						  $\COOL@derivative{2,n,1}{f}{x,y,z}{d}$
+%						  \makeatother
+%						  \vspace{.15cm}
+% \\
+% |\COOL@derivative{2,n}{f}{x,y,z}{d}| 		& \makeatletter
+%						  $\COOL@derivative{2,n}{f}{x,y,z}{d}$
+%						  \makeatother
+% \\
+% \\
+% |\Style{DDisplayFunc=outset}| \Style{DDisplayFunc=outset}
+% \\
+% |\COOL@derivative{2,n}{f}{x,y,z}{d}| 		& \makeatletter 
+%						  $\COOL@derivative{2,n}{f}{x,y,z}{d}$
+%						  \makeatother
+% \\
+% \\
+% |\Style{DShorten=false,DDisplayFunc=inset}| \Style{DShorten=false}\Style{DDisplayFunc=inset}
+% \\
+% |\COOL@derivative{2,n}{f}{x,y,z}{d}| 		& \makeatletter
+%						  $\COOL@derivative{2,n}{f}{x,y,z}{d}$
+%						  \makeatother
+%						  \vspace{.15cm}
+% \\
+% |\COOL@derivative{2,3,4,5}{f}{x,y,z}{d}|	& \makeatletter
+%						  $\COOL@derivative{2,3,4,5}{f}{x,y,z}{d}$
+%						  \makeatother
+% \\
+% \\
+% |\Style{DShorten=false,DDisplayFunc=outset}| \Style{DShorten=false}\Style{DDisplayFunc=outset}
+% \\
+% |\COOL@derivative{2,n}{f}{x,y,z}{d}|		& \makeatletter
+%						  $\COOL@derivative{2,n}{f}{x,y,z}{d}$
+%						  \makeatother
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\COOL@derivative}[4]{%
+%    \end{macrocode}
+% Get the length of \meta{wrt} argument.
+% |\listval{#3}{0}| gives the length of the list since lists begin indexing at 1.
+%    \begin{macrocode}
+\listval{#3}{0}%
+\setcounter{COOL@listlen}{\value{COOL@listpointer}}%
+%    \end{macrocode}
+% Store the \meta{wrt} list and get the length of \meta{derivative power(s)}.
+%    \begin{macrocode}
+\liststore{#3}{COOL@deriv@wrt@}%
+\listval{#1}{0}%
+\setcounter{COOL@ct}{\value{COOL@listpointer}}%
+\ifthenelse{\value{COOL@ct}>\value{COOL@listlen}}%
+	{\setcounter{COOL@ct}{\value{COOL@listlen}}}{}%
+\liststore{#1}{COOL@deriv@powers@}%
+%    \end{macrocode}
+% Check to see if all of the powers are integers---if they are, then we may sum them in the usual sense
+%    \begin{macrocode}
+\isint{\COOL@deriv@powers@i}%
+\setcounter{COOL@multideriv}{2}%
+\whiledo{	\boolean{COOL@isint} \AND 
+		\NOT \value{COOL@multideriv}>\value{COOL@ct}	 }%
+	{%
+	\def\COOL@tempd%
+		{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+	\isint{\COOL@tempd}%
+	\stepcounter{COOL@multideriv}%
+	}%
+%    \end{macrocode}
+% If the length of \meta{derivative power(s)} is less than the length of \meta{wrt}, then we assume that 
+% the last value applies to \emph{all} the remaining derivatives.
+%
+%^^A ==================================================================================================================
+%^^A ============================================ BEGIN SHORTEN AND INSET =============================================
+%^^A ==================================================================================================================
+%    \begin{macrocode}
+\ifthenelse{	\equal{\COOL@notation@DShorten}{true} \AND 
+		\equal{\COOL@notation@DDisplayFunc}{inset}	}%
+	{%
+	\ifthenelse{ \boolean{COOL@isint} }%
+		{%
+		\def\COOL@temp@D@bot{}%
+		\setcounter{COOL@ct@}{0}%
+		\forLoop{1}{\value{COOL@ct}}{COOL@multideriv}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+			\edef\COOL@wrt@temp%
+				{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+			\addtocounter{COOL@ct@}{\COOL@power@temp}%
+			\ifthenelse{ \value{COOL@multideriv}=1 }{}%
+				{\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}}%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+		\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+			\stepcounter{COOL@ct}%
+			\forLoop{\value{COOL@ct}}{\value{COOL@listlen}}{COOL@multideriv}%
+				{%
+				\edef\COOL@wrt@temp%
+					{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+				\addtocounter{COOL@ct@}{\COOL@power@temp}%
+				\ifthenelse{ \value{COOL@multideriv}=1 }{}%
+					{\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}}%
+				\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+					}%
+				}%
+			}%
+		% Else
+			{}%
+		\ifthenelse{\value{COOL@ct@}=1}%
+			{%
+			\frac{#4 #2}{\COOL@temp@D@bot}%
+			}%
+		% Else
+			{%
+			\frac{#4^{\arabic{COOL@ct@}} #2}{\COOL@temp@D@bot}%
+			}%
+		}%
+	% Else
+		{%
+%    \end{macrocode}
+% Powers are not all Integers
+%    \begin{macrocode}
+		\edef\COOL@temp@D@bot{}%
+		\def\COOL@temp@D@top@power{}%
+		\forLoop{1}{\value{COOL@ct}}{COOL@multideriv}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+			\edef\COOL@wrt@temp%
+				{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+			\ifthenelse{ \value{COOL@multideriv} = 1}%
+				{%
+				\edef\COOL@temp@D@top@power{\COOL@power@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@top@power%
+					{\COOL@temp@D@top@power + \COOL@power@temp}%
+				\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}%
+				}%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+		\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+			\stepcounter{COOL@ct}%
+			\forLoop{\value{COOL@ct}}{\value{COOL@listlen}}{COOL@multideriv}%
+				{%
+				\edef\COOL@wrt@temp%
+					{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+				\ifthenelse{ \value{COOL@multideriv} = 1}%
+					{%
+					\edef\COOL@temp@D@top@power{\COOL@power@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@top@power%
+						{\COOL@temp@D@top@power + \COOL@power@temp}%
+					\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}%
+					}%
+				\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+					}%
+				}%
+			}%
+		% Else
+			{}%
+		\frac{#4^{\COOL@temp@D@top@power} #2}{\COOL@temp@D@bot}%
+		}%
+	}%
+%    \end{macrocode}
+%^^A ==================================================================================================================
+%^^A ============================================= END SHORTEN AND INSET ==============================================
+%^^A ==================================================================================================================
+%
+%^^A ==================================================================================================================
+%^^A ============================================ BEGIN SHORTEN AND OUTSET ============================================
+%^^A ==================================================================================================================
+%    \begin{macrocode}
+% Else If
+{ \ifthenelse{	\equal{\COOL@notation@DShorten}{true} \AND 
+		\equal{\COOL@notation@DDisplayFunc}{outset}	 }%
+	{%
+	\ifthenelse{ \boolean{COOL@isint} }%
+		{%
+		\def\COOL@temp@D@bot{}%
+		\setcounter{COOL@ct@}{0}%
+		\forLoop{1}{\value{COOL@ct}}{COOL@multideriv}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+			\edef\COOL@wrt@temp%
+				{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+			\addtocounter{COOL@ct@}{\COOL@power@temp}%
+			\ifthenelse{ \value{COOL@multideriv}=1 }{}%
+				{\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}}%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+		\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+			\stepcounter{COOL@ct}%
+			\forLoop{\value{COOL@ct}}{\value{COOL@listlen}}{COOL@multideriv}%
+				{%
+				\edef\COOL@wrt@temp%
+					{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+				\addtocounter{COOL@ct@}{\COOL@power@temp}%
+				\ifthenelse{ \value{COOL@multideriv}=1 }{}%
+					{\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}}%
+				\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+					}%
+				}%
+			}%
+		% Else
+			{}%
+		\ifthenelse{\value{COOL@ct@}=1}%
+			{%
+			\frac{#4}{\COOL@temp@D@bot} #2%
+			}%
+		% Else
+			{%
+			\frac{#4^{\arabic{COOL@ct@}}}{\COOL@temp@D@bot} #2%
+			}%
+		}%
+	% Else
+		{%
+%    \end{macrocode}
+% Powers are not all Integers
+%    \begin{macrocode}
+		\edef\COOL@temp@D@bot{}%
+		\def\COOL@temp@D@top@power{}%
+		\forLoop{1}{\value{COOL@ct}}{COOL@multideriv}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+			\edef\COOL@wrt@temp%
+				{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+			\ifthenelse{ \value{COOL@multideriv} = 1}%
+				{%
+				\edef\COOL@temp@D@top@power{\COOL@power@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@top@power%
+					{\COOL@temp@D@top@power + \COOL@power@temp}%
+				\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}%
+				}%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@bot%
+					{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+		\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+			{%
+			\edef\COOL@power@temp%
+				{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+			\stepcounter{COOL@ct}%
+			\forLoop{\value{COOL@ct}}{\value{COOL@listlen}}{COOL@multideriv}%
+				{%
+				\edef\COOL@wrt@temp%
+					{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+				\ifthenelse{ \value{COOL@multideriv} = 1}%
+					{%
+					\edef\COOL@temp@D@top@power{\COOL@power@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@top@power%
+						{\COOL@temp@D@top@power + \COOL@power@temp}%
+					\edef\COOL@temp@D@bot{\COOL@temp@D@bot \,}%
+					}%
+				\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp}%
+					}%
+				% Else
+					{%
+					\edef\COOL@temp@D@bot%
+						{\COOL@temp@D@bot #4 \COOL@wrt@temp^\COOL@power@temp}%
+					}%
+				}%
+			}%
+		% Else
+			{}%
+		\frac{#4^{\COOL@temp@D@top@power} }{\COOL@temp@D@bot} #2%
+		}%
+	}%
+%    \end{macrocode}
+%^^A ==================================================================================================================
+%^^A ============================================= END SHORTEN AND OUTSET =============================================
+%^^A ==================================================================================================================
+%
+%^^A ==================================================================================================================
+%^^A =========================================== BEGIN NO SHORTEN AND INSET ===========================================
+%^^A ==================================================================================================================
+%    \begin{macrocode}
+% Else If
+{ \ifthenelse{	\equal{\COOL@notation@DShorten}{false} \AND
+		\equal{\COOL@notation@DDisplayFunc}{inset}	}%
+	{%
+	\def\COOL@temp@D@result{}%
+	\def\COOL@temp@D@bot{}%
+	\def\COOL@temp@D@top{}%
+	\setcounter{COOL@ct@}{\value{COOL@ct}}%
+	\addtocounter{COOL@ct@}{-1}
+	\forLoop{1}{\value{COOL@ct@}}{COOL@multideriv}%
+		{%
+		\edef\COOL@power@temp%
+			{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+		\edef\COOL@wrt@temp%
+			{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+		\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+			{%
+			\edef\COOL@temp@D@top{#4}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+			}%
+		% Else
+			{%
+			\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+			}%
+		\edef\COOL@temp@D@result%
+			{\COOL@temp@D@result \frac{\COOL@temp@D@top}{\COOL@temp@D@bot}}%
+		}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+	\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+		{%
+%    \end{macrocode}
+% Must pick up the one for |\value{COOL@ct}|
+%    \begin{macrocode}
+		\edef\COOL@power@temp%
+			{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+		\edef\COOL@wrt@temp%
+			{\csname COOL@deriv@wrt@\roman{COOL@ct}\endcsname}%
+		\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+			{%
+			\edef\COOL@temp@D@top{#4}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+			}%
+		% Else
+			{%
+			\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+			}%
+		\edef\COOL@temp@D@result%
+			{\COOL@temp@D@result \frac{\COOL@temp@D@top}{\COOL@temp@D@bot}}%
+%    \end{macrocode}
+% Now add the ones beyond 
+%    \begin{macrocode}
+		\stepcounter{COOL@ct}%
+		\setcounter{COOL@ct@}{\value{COOL@listlen}}%
+		\addtocounter{COOL@ct@}{-1}%
+		\forLoop{\value{COOL@ct}}{\value{COOL@ct@}}{COOL@multideriv}%
+			{%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@top{#4}%
+				\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+				\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			\edef\COOL@temp@D@result%
+				{\COOL@temp@D@result \frac{\COOL@temp@D@top}{\COOL@temp@D@bot}}%
+			}%
+%    \end{macrocode}
+% Must pick up the one for |\value{COOL@listlen}|
+%    \begin{macrocode}
+		\edef\COOL@wrt@temp%
+			{\csname COOL@deriv@wrt@\roman{COOL@listlen}\endcsname}%
+		\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+			{%
+			\edef\COOL@temp@D@top{#4}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+			}%
+		% Else
+			{%
+			\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+			}%
+		\edef\COOL@temp@D@result%
+			{\COOL@temp@D@result \frac{\COOL@temp@D@top #2}{\COOL@temp@D@bot}}%
+		}%
+	% Else
+		{%
+%    \end{macrocode}
+% Must pick up the one for |\value{COOL@ct}|
+%    \begin{macrocode}
+		\edef\COOL@power@temp%
+			{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+		\edef\COOL@wrt@temp%
+			{\csname COOL@deriv@wrt@\roman{COOL@ct}\endcsname}%
+		\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+			{%
+			\edef\COOL@temp@D@top{#4}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+			}%
+		% Else
+			{%
+			\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+			}%
+		\edef\COOL@temp@D@result%
+			{\COOL@temp@D@result \frac{\COOL@temp@D@top #2}{\COOL@temp@D@bot}}%
+		}%
+	\COOL@temp@D@result%
+	}%
+%    \end{macrocode}
+%^^A ==================================================================================================================
+%^^A ============================================ END NO SHORTEN AND INSET ============================================
+%^^A ==================================================================================================================
+%
+%^^A ==================================================================================================================
+%^^A =========================================== BEGIN NO SHORTEN AND OUTSET ==========================================
+%^^A ==================================================================================================================
+%    \begin{macrocode}
+% Else If
+{ \ifthenelse{	\equal{\COOL@notation@DShorten}{false} \AND 
+		\equal{\COOL@notation@DDisplayFunc}{outset}	}%
+	{%
+	\def\COOL@temp@D@result{}%
+	\def\COOL@temp@D@bot{}%
+	\def\COOL@temp@D@top{}%
+	\forLoop{1}{\value{COOL@ct}}{COOL@multideriv}%
+		{%
+		\edef\COOL@power@temp%
+			{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
+		\edef\COOL@wrt@temp%
+			{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+		\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+			{%
+			\edef\COOL@temp@D@top{#4}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+			}%
+		% Else
+			{%
+			\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+			\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+			}%
+		\edef\COOL@temp@D@result%
+			{\COOL@temp@D@result \frac{\COOL@temp@D@top}{\COOL@temp@D@bot}}%
+		}%
+%    \end{macrocode}
+% we're done with the length of the \meta{derivative power(s)} argument, and we want to start at it $+ \; 1$
+% to add the remainders
+%    \begin{macrocode}
+	\ifthenelse{\value{COOL@ct}<\value{COOL@listlen}}%
+		{%
+		\edef\COOL@power@temp%
+			{\csname COOL@deriv@powers@\roman{COOL@ct}\endcsname}%
+		\stepcounter{COOL@ct}%
+		\forLoop{\value{COOL@ct}}{\value{COOL@listlen}}{COOL@multideriv}%
+			{%
+			\edef\COOL@wrt@temp%
+				{\csname COOL@deriv@wrt@\roman{COOL@multideriv}\endcsname}%
+			\ifthenelse{ \equal{\COOL@power@temp}{1} }%
+				{%
+				\edef\COOL@temp@D@top{#4}%
+				\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp}%
+				}%
+			% Else
+				{%
+				\edef\COOL@temp@D@top{#4^\COOL@power@temp}%
+				\edef\COOL@temp@D@bot{#4 \COOL@wrt@temp^\COOL@power@temp}%
+				}%
+			\edef\COOL@temp@D@result%
+				{\COOL@temp@D@result \frac{\COOL@temp@D@top}{\COOL@temp@D@bot}}%
+			}%
+		}%
+	% Else
+		{%
+		}%
+	\COOL@temp@D@result #2
+	}%
+%    \end{macrocode}
+%^^A ==================================================================================================================
+%^^A ============================================ END NO SHORTEN AND OUTSET ===========================================
+%^^A ==================================================================================================================
+%    \begin{macrocode}
+% Else
+	{%
+	\PackageError{cool}{Invalid Option Sent}%
+		{DShorten can only be `true' or `false';%
+		 DDisplayFunc can only be `inset' or `outset'}%
+	}%
+}}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\D}
+% \begin{macro}{\pderiv}
+% Derivatives
+%
+% \begin{tabular}{ll}
+% |\D{f}{x}|			& \vspace{0.15cm}$\D{f}{x}$			\\
+% |\D[n]{f}{x}|			& \vspace{0.15cm}$\D[n]{f}{x}$			\\
+% |\D{f}{x,y,z}|		& \vspace{0.15cm}$\D{f}{x,y,z}$			\\
+% |\D[1,2,1]{f}{x,y,z}|		& \vspace{0.15cm}$\D[1,2,1]{f}{x,y,z}$		\\
+% |\pderiv{f}{x}|		& \vspace{0.15cm}$\pderiv{f}{x}$		\\
+% |\pderiv[n]{f}{x}|		& \vspace{0.15cm}$\pderiv[n]{f}{x}$		\\
+% |\pderiv{f}{x,y,z}|		& \vspace{0.15cm}$\pderiv{f}{x,y,z}$		\\
+% |\pderiv[1,2,1]{f}{x,y,z}|	& \vspace{0.15cm}$\pderiv[1,2,1]{f}{x,y,z}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\D}[3][1]{\COOL@derivative{#1}{#2}{#3}{d}}
+\newcommand{\pderiv}[3][1]{\COOL@derivative{#1}{#2}{#3}{\partial}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\Integrate}
+% \begin{macro}{\Int}
+% Integrate
+%
+% This has the option |IntegrateDisplayFunc| which can be |inset| or |outset|:
+%
+% \begin{tabular}{c}
+% |\Style{IntegrateDisplayFunc=inset}| (Default)%
+% \Style{IntegrateDisplayFunc=inset}						
+% \\
+% 	\begin{tabular}{ll}
+%	|\Integrate{f}{x}|		& \vspace{0.15cm}$\Integrate{f}{x}$		\\
+% 	|\Int{f}{x}|			& \vspace{0.15cm}$\Int{f}{x}$			\\
+% 	|\Integrate{f}{x,A}|		& \vspace{0.15cm}$\Integrate{f}{x,A}$		\\
+% 	|\Int{f}{x,A}|		& \vspace{0.15cm}$\Int{f}{x,A}$				\\
+% 	|\Integrate{f}{x,a,b}|	& \vspace{0.15cm}$\Integrate{f}{x,a,b}$			\\
+% 	|\Int{f}{x,a,b}|		& \vspace{0.15cm}$\Int{f}{x,a,b}$		\\
+%	\end{tabular}
+% \\
+% \\
+% |\Style{IntegrateDisplayFunc=outset}|%
+% \Style{IntegrateDisplayFunc=outset}
+% \\
+%	\begin{tabular}{ll}
+%	|\Integrate{f}{x}|		& \vspace{0.15cm}$\Integrate{f}{x}$		\\
+%	|\Int{f}{x}|			& \vspace{0.15cm}$\Int{f}{x}$			\\
+%	|\Integrate{f}{x,A}|		& \vspace{0.15cm}$\Integrate{f}{x,A}$		\\
+%	|\Int{f}{x,A}|		& \vspace{0.15cm}$\Int{f}{x,A}$				\\
+%	|\Integrate{f}{x,a,b}|	& \vspace{0.15cm}$\Integrate{f}{x,a,b}$			\\
+%	|\Int{f}{x,a,b}|		& \vspace{0.15cm}$\Int{f}{x,a,b}$		\\
+%	\end{tabular}
+% \Style{IntegrateDisplayFunc=inset}
+% \\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@IntegrateDisplayFunc}{inset}
+\newcommand{\Integrate}[2]{%
+\listval{#2}{0}%
+%    \end{macrocode}
+% record the length of the list
+%    \begin{macrocode}
+\setcounter{COOL@listlen}{\value{COOL@listpointer}}%
+\ifthenelse{ \value{COOL@listlen} = 1 }%
+	{%
+	\ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{outset}}%
+		{%
+		\int \! d#2 \, #1%
+		}%
+	% ElseIf
+	{ \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}%
+		{%
+		\int #1 \, d#2%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Option Sent}%
+			{`DisplayFunc' can only be `inset' or `outset'}%
+		}}%
+	}%
+% ElseIf
+{ \ifthenelse{ \value{COOL@listlen} = 2 }%
+	{%
+	\ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{outset}}%
+		{%
+		\int_{\listval{#2}{2}} \! d{\listval{#2}{1}} \, #1%
+		}%
+	% ElseIf
+	{ \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}%
+		{%
+		\int_{\listval{#2}{2}} #1 \, d{\listval{#2}{1}}%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Option Sent}%
+			{`DisplayFunc' can only be `inset' or `outset'}%
+		}}%
+	}%
+% ElseIf
+{ \ifthenelse{ \value{COOL@listlen} = 3 }%
+	{%
+	\ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{outset}}%
+		{%
+		\int_{\listval{#2}{2}}^{\listval{#2}{3}} \! d{\listval{#2}{1}} \, #1%
+		}%
+	% ElseIf
+	{ \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}%
+		{%
+		\int_{\listval{#2}{2}}^{\listval{#2}{3}} #1 \, d{\listval{#2}{1}}%
+		}%
+	% Else
+		{%
+		\PackageError{cool}{Invalid Option Sent}%
+			{`DisplayFunc' can only be `inset' or `outset'}%
+		}}%
+	}%
+% Else
+	{%
+	\PackageError{cool}{`Integrate' has invalid parameter list}%
+		   {this happens when the second argument has more than two commas}%
+	}}}%
+}%
+\newcommand{\Int}[2]{\Integrate{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\Sum}
+% Sum
+%
+% \begin{tabular}{ll}
+% |\Sum{a_n}{n}|		& \vspace{0.1cm}$\Sum{a_n}{n}$			\\
+% |\Sum{a_n}{n,1,N}|		& \vspace{0.1cm}$\Sum{a_n}{n,1,N}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\Sum}[2]{%
+\listval{#2}{0}%
+%    \end{macrocode}
+% record the length of the list
+%    \begin{macrocode}
+\setcounter{COOL@listlen}{\value{COOL@listpointer}}
+\ifthenelse{ \value{COOL@listlen} = 1 }%
+	{%
+	\sum_{#2} #1%
+	}%
+% else
+	{%
+	\ifthenelse{ \value{COOL@listlen} = 3 }%
+		{%
+		\sum_{ \listval{#2}{1} = \listval{#2}{2} }^{ \listval{#2}{3} } #1
+		}%
+	% else
+		{%
+		\PackageError{cool}{Invalid list length for `Sum'}%
+			{can only have none or two commas for second argument}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Prod}
+% Product
+%
+% \begin{tabular}{ll}
+% |\Prod{a_n}{n}|		& \vspace{0.1cm}$\Prod{a_n}{n}$		\\
+% |\Prod{a_n}{n,1,N}|		& \vspace{0.1cm}$\Prod{a_n}{n,1,N}$	\\
+% \end{tabular}
+%    \begin{macrocode}
+\newcommand{\Prod}[2]{%
+\listval{#2}{0}%
+%    \end{macrocode}
+% record the length of the list
+%    \begin{macrocode}
+\setcounter{COOL@listlen}{\value{COOL@listpointer}}
+\ifthenelse{ \value{COOL@listlen} = 1 }%
+	{%
+	\prod_{#2} #1%
+	}%
+% else
+	{%
+	\ifthenelse{ \value{COOL@listlen} = 3 }%
+		{%
+		\prod_{ \listval{#2}{1} = \listval{#2}{2} }^{ \listval{#2}{3} } #1
+		}%
+	% else
+		{%
+		\PackageError{cool}{Invalid list length for `Prod'}%
+			{can only have none or two commas for second argument}%
+		}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Vector Operators}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\DotProduct}
+% The dot product, |\DotProduct{\vec{A}}{\vec{B}}|, $\DotProduct{\vec{A}}{\vec{B}}$
+%    \begin{macrocode}
+\newcommand{\DotProduct}[2]{#1 \cdot #2}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Cross}
+% The cross product, |\Cross{\vec{A}}{\vec{B}}|, $\Cross{\vec{A}}{\vec{B}}$
+%    \begin{macrocode}
+\newcommand{\Cross}[2]{#1 \times #2}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Div}
+% the divergence, |\Div{\vec{A}}|, $\Div{\vec{A}}$
+%    \begin{macrocode}
+\newcommand{\Div}[1]{\nabla \cdot #1}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Grad}
+% The gradient, |\Grad{f}|, $\Grad{f}$
+%    \begin{macrocode}
+\newcommand{\Grad}[1]{\nabla #1}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Curl}
+% The curl, |\Curl{\vec{A}}|, $\Curl{\vec{A}}$
+%    \begin{macrocode}
+\newcommand{\Curl}[1]{\nabla \times #1}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Laplacian}
+% The laplacian, |\Laplacian{f}|, $\Laplacian{f}$
+%    \begin{macrocode}
+\newcommand{\Laplacian}[1]{\nabla^2 #1}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Matrix Operations}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\Transpose}
+% Transpose of a matrix, |\Transpose{A}|, $\Transpose{A}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@TransposeParen}{inv}
+\newcommand{\Transpose}[1]{ \COOL@decide@paren{Transpose}{#1}^T }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Dagger}
+% Conjugate Transpose of a matrix, |\Dagger{A}|, $\Dagger{A}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DaggerParen}{inv}
+\newcommand{\Dagger}[1]{ \COOL@decide@paren{Dagger}{#1}^\dagger }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Det}
+% determinant of a matrix
+%
+% \begin{tabular}{ll}
+% |\Style{DetDisplay=det}|%
+% \Style{DetDisplay=det} (Default)		\\
+% |\Det{A}|		& $\Det{A}$		\\
+% |\Style{DetDisplay=barenc}|%
+% \Style{DetDisplay=barenc}			\\
+% |\Det{A}|		& $\Det{A}$		\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@DetParen}{none}
+	\newcommand{\COOL@notation@DetDisplay}{det}
+\newcommand{\Det}[1]{%
+\ifthenelse{\equal{\COOL@notation@DetDisplay}{det}}%
+	{%
+	\det\COOL@decide@paren{Det}{#1}%
+	}%
+% ElseIf
+{ \ifthenelse{\equal{\COOL@notation@DetDisplay}{barenc}}%
+	{%
+	\left|#1\right|%
+	}%
+% Else
+	{%
+	\PackageError{cool}{Invalid Option Sent}%
+		{`DetDisplay' can only be `det' or `barenc'}%
+	}}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Tr}
+% Trace of a Matrix, |\Tr{A}|, $\Tr{A}$
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@TrParen}{none}
+\newcommand{\Tr}[2][]{%
+\ifthenelse{\equal{#1}{}}
+	{%
+	\operatorname{Tr}\COOL@decide@paren{Tr}{#2}%
+	}%
+% Else
+	{%
+	\operatorname{Tr}_{#1}\COOL@decide@paren{Tr}{#2}%
+	}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% \subsubsection{Matricies}
+% %  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %%  %
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \begin{macro}{\IdentityMatrix}
+% The Identity Matrix
+%
+% \begin{tabular}{cc}
+% |\IdentityMatrix|	& $\IdentityMatrix$	\\
+% |\IdentityMatrix[2]|	& $\IdentityMatrix[2]$	\\
+% \end{tabular}
+%    \begin{macrocode}
+	\newcommand{\COOL@notation@IdentityMatrixParen}{p}
+		\newcounter{COOL@row}%
+		\newcounter{COOL@col}%
+\newcommand{\IdentityMatrix}[1][0]{%
+\isint{#1}%
+\ifthenelse{\boolean{COOL@isint}}%
+	{%
+	\ifthenelse{ #1=0 }%
+		{%
+		\mathbb{I}%
+		}%
+	% Else
+		{%
+		\setcounter{COOL@ct}{\value{MaxMatrixCols}}%
+		\setcounter{MaxMatrixCols}{#1}%
+		\ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{p}}%
+			{%
+			\begin{pmatrix}%
+			}%
+		% ElseIf
+		{ \ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{b}}%
+			{%
+			\begin{bmatrix}%
+			}%
+		% ElseIf
+		{ \ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{br}}%
+			{%
+			\begin{Bmatrix}%
+			}%
+		% Else
+			{%
+			\begin{matrix}%
+			}}}%
+		\forLoop{1}{#1}{COOL@row}%
+			{%
+			\ifthenelse{\NOT \value{COOL@row} = 1}{\\}{}%
+			\forLoop{1}{#1}{COOL@col}%
+				{%
+				\ifthenelse{ \NOT \value{COOL@col} = 1 }{&}{}%
+				\ifthenelse{ \value{COOL@row}=\value{COOL@col} }{1}{0}%
+				}%
+			}%
+		\ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{p}}%
+			{%
+			\end{pmatrix}%
+			}%
+		% ElseIf
+		{ \ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{b}}%
+			{%
+			\end{bmatrix}%
+			}%
+		% ElseIf
+		{ \ifthenelse{\equal{\COOL@notation@IdentityMatrixParen}{br}}%
+			{%
+			\end{Bmatrix}%
+			}%
+		% Else
+			{%
+			\end{matrix}%
+			}}}%
+		\setcounter{MaxMatrixCols}{\value{COOL@ct}}%
+		}%
+	}%
+% Else
+	{%
+	\mathbb{I}%
+	}%
+}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+% \Finale
+\endinput
diff --git a/Master/texmf-dist/source/latex/cool/cool.ins b/Master/texmf-dist/source/latex/cool/cool.ins
new file mode 100644
index 00000000000..0f41b595606
--- /dev/null
+++ b/Master/texmf-dist/source/latex/cool/cool.ins
@@ -0,0 +1,40 @@
+%%

+%% Copyright (C) 2005 by nsetzer

+%%

+%% This file may be distributed and/or modified under the

+%% conditions of the Lesser General Product License

+%%

+

+\input docstrip.tex

+

+\keepsilent

+

+\usedir{texmf/tex/latex/cool}

+

+\preamble

+

+This is a generated file

+

+This file may be distributed and/or modified under the

+conditions of the Limited General Product License

+

+\endpreamble

+

+

+\generate{\file{cool.sty}{\from{cool.dtx}{package}}}

+

+\obeyspaces

+\Msg{****************************************************}

+\Msg{*                                                  *}

+\Msg{* To finish the installation you have to move the  *}

+\Msg{* following file into a directory searched by TeX: *}

+\Msg{*                                                  *}

+\Msg{* cool.sty                                         *}

+\Msg{*                                                  *}

+\Msg{* To produce the documentation run the file        *}

+\Msg{* cool.dtx through LaTeX.                          *}

+\Msg{*                                                  *}

+\Msg{*                                                  *}

+\Msg{****************************************************}

+

+\endbatchfile
\ No newline at end of file