% \iffalse % %<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01] %<package>\ProvidesPackage{cool} %<package> [2023/05/03 v1.35 COntent Oriented LaTeX] %<package>\RequirePackage{ifthen} %<package>\RequirePackage{coollist} %<package>\RequirePackage{coolstr} %<package>\RequirePackage{forloop} %<package>\RequirePackage{amsmath} %<package>\RequirePackage{amssymb} %<package>\RequirePackage{bbm} % % Update on 2023/05/03 purely to clarify the license; no code changes. % This package is released under the GNU LGPL. % %<*driver> \documentclass{ltxdoc} \usepackage{cool} \usepackage[bbgreekl]{mathbbol} \usepackage{url} \EnableCrossrefs \CodelineIndex \RecordChanges \begin{document} \DocInput{cool.dtx} \end{document} %</driver> % \fi % % \CheckSum{3591} % %% \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} % \changes{v1.3}{2006/10/07}{Redefined the {\tt in*} commands to have a {\tt mathopen} before the {\tt left}. Added {\tt IntegrateDifferentialDSymb} and {\tt DSymb} options for {\tt Integrate} and {\tt D}. Added {\tt IdentityMatrixSymb} for {\tt IdentityMatrix} and changed the default to display a double-struck $1$. Added {\tt ESymb}, {\tt ISymb}, {\tt PISymb}, and {\tt EulerGammaSymb} for fundamental constants} % \changes{v1.35}{2006/12/29}{Adjusted package to be compatible with new \textsf{coolstr}} % % \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. % % Please note that there are examples of use of each of the defined commands at the location where they are defined. % % 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]{\mathopen{}\left(#2\parbox[h][#1]{0cm}{}\right)} % in parentheses () \newcommand{\inb}[2][0cm]{\mathopen{}\left[#2\parbox[h][#1]{0cm}{}\right]} % in brackets [] \newcommand{\inbr}[2][0cm]{\mathopen{}\left\{#2\parbox[h][#1]{0cm}{}\right\}} % in braces {} \newcommand{\inap}[2][0cm]{\mathopen{}\left<{#2}\parbox[h][#1]{0cm}{}\right>} % in angular parentheses <> \newcommand{\nop}[1]{\mathopen{}\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, $\I = \sqrt{-1}$. % % |\Style{ISymb=\mathbbm{i}}| \Style{ISymb=\mathbbm{i}}, |\I| gives $\I$. \Style{ISymb=i} % \begin{macrocode} \newcommand{\COOL@notation@ISymb}{i} \newcommand{\I}{\COOL@notation@ISymb} % \end{macrocode} % \end{macro} % % \begin{macro}{\E} % Euler's constant and the base of the natural logarithm, $\E$. % %|\Style{ESymb=\mathbbm{e}}| \Style{ESymb=\mathbbm{e}}, |\E| gives $\E$. \Style{ESymb=e} % \begin{macrocode} \newcommand{\COOL@notation@ESymb}{e} \newcommand{\E}{\COOL@notation@ESymb} % \end{macrocode} % \end{macro} % % \begin{macro}{\PI} % Pi---the ratio of the circumference of a circle to its diameter, $\PI$. % % |\Style{PISymb=\bbpi}| \footnote{to get the `bbpi' symbol , you will need to use the package \textsf{mathbbol} and pass the \textsf{bbgreekl} option} \Style{PISymb=\bbpi}, |\PI| gives $\PI$. \Style{PISymb=\pi} % \begin{macrocode} \newcommand{\COOL@notation@PISymb}{\pi} \newcommand{\PI}{\COOL@notation@PISymb} % \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, $\EulerGamma$. % %|\Style{EulerGammaSymb=\gamma_E}| \Style{EulerGammaSymb=\gamma_E}, |\EulerGamma| gives $\EulerGamma$ \Style{EulerGammaSymb=\gamma} % \begin{macrocode} \newcommand{\COOL@notation@EulerGammaSymb}{\gamma} \newcommand{\EulerGamma}{\COOL@notation@EulerGammaSymb} % \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}% }% }% % 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}{COOL@isint}% \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}{COOL@isint}% \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}{COOL@isint}% 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}{COOL@isint}% \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}{COOL@isint}% \ifthenelse{\boolean{COOL@isint}}% {\setboolean{COOL@p@isint}{true}}% % Else {\setboolean{COOL@p@isint}{false}}% \isint{#3}{COOL@isint}% \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}{COOL@isint}% \ifthenelse{\boolean{COOL@isint}}% {\setboolean{COOL@p@isint}{true}}% % Else {\setboolean{COOL@p@isint}{false}}% \isint{#3}{COOL@isint}% \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}{COOL@isint}% \ifthenelse{\boolean{COOL@isint}}% {% \isint{#2}{COOL@isint}% \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}{COOL@isint}% \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@}}% \mathopen{}\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}% \mathopen{}\left(% #6% \left|% {% {#2,#3} \@@atop {\COOL@MeijerG@anp@value{\listval{#1}{2}}{#4}{#5}} }% \right)\right.% }% % else {% ^{#4,#2}_{#3,#5}% \mathopen{}\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}}% \mathopen{}\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}{COOL@isint}% \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 |\COOL@notation@DSymb| 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@notation@DSymb}{d} \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}{COOL@isint}% \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}{COOL@isint}% \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} % |\Style{DSymb={\mathrm d}}| \Style{DSymb={\mathrm d}} \\ % |\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}{{\COOL@notation@DSymb}}} \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,IntegrateDifferentialDSymb=\text{d}}|% % \Style{IntegrateDisplayFunc=outset,IntegrateDifferentialDSymb=\text{d}} % \\ % \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{\COOL@notation@IntegrateDifferentialDSymb}{d} \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 \! \COOL@notation@IntegrateDifferentialDSymb{}#2 \, #1% }% % ElseIf { \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}% {% \int #1 \, \COOL@notation@IntegrateDifferentialDSymb{}#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}} \! \COOL@notation@IntegrateDifferentialDSymb{}{\listval{#2}{1}} \, #1% }% % ElseIf { \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}% {% \int_{\listval{#2}{2}} #1 \, \COOL@notation@IntegrateDifferentialDSymb{}{\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}} \! \COOL@notation@IntegrateDifferentialDSymb{}{\listval{#2}{1}} \, #1% }% % ElseIf { \ifthenelse{\equal{\COOL@notation@IntegrateDisplayFunc}{inset}}% {% \int_{\listval{#2}{2}}^{\listval{#2}{3}} #1 \, \COOL@notation@IntegrateDifferentialDSymb{}{\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{\COOL@notation@IdentityMatrixSymb}{\mathbbm{1}} \newcommand{\IdentityMatrix}[1][0]{% \isint{#1}{COOL@isint}% \ifthenelse{\boolean{COOL@isint}}% {% \ifthenelse{ #1=0 }% {% \COOL@notation@IdentityMatrixSymb% }% % 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 {% \COOL@notation@IdentityMatrixSymb% }% }% % \end{macrocode} % \end{macro} % % % % % \Finale \endinput