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authorYann Herklotz <ymherklotz@gmail.com>2017-03-12 15:23:31 +0000
committerYann Herklotz <ymherklotz@gmail.com>2017-03-12 15:23:31 +0000
commitd774e219f020321e89318e7473166b030ff15b80 (patch)
tree020297680b4f24ba024996cf924957c35699894c
parent199d2797b945f13818c116521e1a6aab2d14fab1 (diff)
downloadNumericalAnalysis-d774e219f020321e89318e7473166b030ff15b80.tar.gz
NumericalAnalysis-d774e219f020321e89318e7473166b030ff15b80.zip
updating report
Diffstat
-rw-r--r--Report/report/coursework.tex179
-rw-r--r--Report/report/dsfont.sty9
-rw-r--r--Report/report/figures/RLC.PNGbin0 -> 8058 bytes
-rw-r--r--Report/report/figures/imperial.pdfbin0 -> 11201 bytes
-rw-r--r--Report/report/includes.tex253
-rw-r--r--Report/report/kpfonts.sty1680
-rw-r--r--Report/report/notation.tex77
-rw-r--r--Report/report/titlepage.tex54
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diff --git a/Report/report/coursework.tex b/Report/report/coursework.tex
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+\documentclass[12pt,twoside]{article}
+
+\newcommand{\reporttitle}{Numerical Analysis of ODEs using Matlab}
+\newcommand{\reportauthor}{Mwana}
+\newcommand{\reportauthora}{Aufar}
+\newcommand{\reportauthorb}{Zihan}
+\newcommand{\reportauthorc}{Calvin}
+\newcommand{\reportauthord}{Yann Herklotz}
+\newcommand{\reporttype}{Mathematics Coursework}
+\newcommand{\email}{}
+\newcommand{\emaila}{apl115@ic.ac.uk}
+\newcommand{\emailb}{}
+\newcommand{\emailc}{}
+\newcommand{\emaild}{ymh15@ic.ac.uk}
+
+% include files that load packages and define macros
+\input{includes} % various packages needed for maths etc.
+\input{notation} % short-hand notation and macros
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{document}
+% front page
+\input{titlepage}
+
+\tableofcontents
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% Main document
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% Introduction
+
+\newpage
+\section{Introduction}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% Part 1
+
+\newpage
+\section{RL Circuit}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% Part 2: Exercise 3: RLC Circuit
+
+\newpage
+\section{RLC Circuit}
+
+\subsection{RLC Circuit Equation}
+
+An RLC circuit consists of a resistor, capacitor and an inductor. For the purpose of this example, we have a series RLC circuit, as shown in the figure below.
+
+\begin{figure}[h]
+\centering
+\includegraphics[width = 8cm]{./figures/RLC.PNG}\\[0.01cm]
+\caption{Series RLC Circuit}
+\end{figure}
+
+By applying Kirchoff's Voltage Law for each of the three components of the circuit, we can obtain the differential equation representing the circuit.
+
+\[
+V_{R} + V_{L} + V_{C} = V_{in}(t)
+\]
+
+\[
+L \frac{d}{dt}i_{L}(t) + R i_{L}(t) + \frac{1}{C} \int_0^t i_{L}(\tau) \,d\tau = V_{in}(t)
+\]
+
+\[
+L \frac{d^2}{dt^2} q_{C}(t) + R \frac{d}{dt} q_{C}(t) + \frac{1}{C} q_{C}(t) = V_{in}(t)
+\]
+
+We assume that the capacitor is pre-charged at time t = 0, with q$_{\text{C}}$(0) = 500nC. We also assume that no current flows through the inductor at time t = 0, so i$_{\text{L}}$(0) = $\frac{d}{dt}q_{\text{C}}$(0) = 0A.
+
+We were also given the values of resistances, capacitance and inductance of the components in the circuit:
+
+\begin{center}
+R = 250$\Omega$, C = 3$\mu$F, L = 650mH
+\end{center}
+
+\subsection{Runge-Kutta and Coupled Equations}
+\subsubsection{Runge-Kutta}
+Runge-Kutta 4th order method is a numerical technique used to solve ordinary differential equations of the form $\frac{dy}{dx} = f(x,y)$, where y(0) = y$_{\text{0}}$. Therefore, we can only use it to solve first order ordinary differential equations.
+
+\subsubsection{Coupled Equations}
+In order to solve the RLC equation derived earlier, we need to rewrite the equation in a \textit{coupled} form. We take the equation:
+\[
+L \frac{d^2}{dt^2} q_{C}(t) + R \frac{d}{dt} q_{C}(t) + \frac{1}{C} q_{C}(t) = V_{in}(t)
+\]
+
+By letting y = $\frac{d}{dt}q_{C}(t)$ = $\dot{q}$ and = $\frac{d^2}{dt^2}q_{C}(t)$ = $\ddot{q}$, we can do:
+
+\[
+L\ddot{q} + R\dot{q} + \frac{1}{C}q = V_{in}
+\]
+
+\[
+L
+\]
+
+\subsection{Matlab Script}
+
+\subsubsection{Runge-Kutta 3/8}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% Part 3: Exercise 4: Finite Differences for PDE
+
+\newpage
+\section{Finite Differences for PDE}
+
+\subsection{1-D Heat Equation}
+
+The 1-D heat equation \\
+
+\[
+\frac{\partial y}{\partial t} = \frac{\partial ^2 y}{\partial x^2},\quad 0 < x < 1,\quad t > 0
+\]\\
+
+with zero boundary conditions \( y(0, t) = y(1, t) = 0 \) and initial conditions \\
+\( y(x, 0) = y_0(x) \) can be solved numerically using the finite difference method.
+
+
+\subsection{Method}
+
+The finite difference method consists of approximating a differential equation using difference equations. As the
+1-D heat equation has depends on \( x \) and \( t \) we can use the finite difference method to approximate the heat
+equation when \( t = 0 \) and then increment \( t \) to get the heat equation as it changes over time.
+
+
+\subsection{Matlab Script}
+
+There were certain aspects of the finite difference method that had to be considered when implementing it in Matlab.
+We had to find the right values that would give the precision that we wanted and display the results properly. We used a
+\( (N+1) \times (m+1) \) matrix to store all the results from the finite difference method. The matrix has 1 added to \( N \) and
+\( m \) because Matlab starts its index at 1 and we want to go from \( 0..N \) and from \( 0..m \).
+
+\subsubsection{Boundary Conditions}
+
+First of all, we had to find a way of adding the boundary conditions that we wanted to the the finite differences method
+and still be able to change these easily, because we had to test different ones. We solved this by writing a function that enabled us
+to choose the function that we wanted to use as a boundary condition. To this Matlab function we could then easily add more functions
+that could then be used as a boundary condition and we could easily test these boundary conditions. The boundary conditions
+can also be expressed as \( U_0^m,\ U_N^m \). This means we just have to set all the numbers at index 1 and index \( N+1 \) to
+be equal to the initial condition. This way we can also set the initial condition to be a different constant, or even an equation that
+changes with time.
+
+
+\subsubsection{Central Algorithm}
+
+The main part of the finite difference method is the central algorithm, as this is the algorithm that is derived from the approximations
+of the initial differential equation that we want to solve.
+
+The central algorithm for the 1-D heat equation is
+
+\[
+U_{j}^{m+1} =\ v U_{j-1}^{m} + (1 - 2 v) U_{j}^{m} + v U_{j+1}^{m}
+\]\\
+
+We want to implement this algorithm for every value of from \( 0..m \) and every value from \( 0..N \). This can be done by using two
+for loops that will iterate over the matrix, and for every \( m \), to get \( m+1 \) we will pass the required values to the equation.
+
+As we have a matrix with all the previous values that have been calculated, we can use it to get the values of \( U_{j-1}^m,\ U_j^m,\
+U_{j+1}^m \) directly from the matrix.
+
+
+\subsubsection{Choosing Constants}
+
+\subsubsection{Plotting Results}
+
+
+\subsection{Solving the Heat Equation}
+
+\subsubsection{Tent Function Initial Condition}
+
+\subsubsection{Sinusoidal Function}
+
+
+\section{Bonus}
+
+
+\end{document}
diff --git a/Report/report/dsfont.sty b/Report/report/dsfont.sty
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+++ b/Report/report/dsfont.sty
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+\ProvidesPackage{dsfont}
+ [1995/08/01 v0.1 Double stroke roman fonts]
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diff --git a/Report/report/figures/RLC.PNG b/Report/report/figures/RLC.PNG
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diff --git a/Report/report/figures/imperial.pdf b/Report/report/figures/imperial.pdf
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diff --git a/Report/report/includes.tex b/Report/report/includes.tex
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+% Version 1.0 (27/12/12)
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+%
+% Original author:
+% WikiBooks (http://en.wikibooks.org/wiki/LaTeX/Title_Creation)
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+ \Huge \bfseries
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+{
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+{
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+ \left[
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+ \begin{array}
+ {@{}*{\elimination@num@variables}{R{\elimination@col@width}}
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+ &% moved second & here
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+}
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+%% Fast macro for column vectors
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+%%% To prevent this warning, use the 'nowarning' option %%%
+ \PackageWarning{kpfonts}%
+ {With 'easyscsl' option, don't fit together\MessageBreak
+ \textsl or \slshape and \textsc or \scshape\MessageBreak
+ with non 'kpfonts' fonts.}
+%%% To prevent this warning, use the 'nowarning' option %%%
+ \fi % end vos
+ \fi % end warning
+%
+%%% easyscsl, courtesy from François Pétiard
+%
+ \ifkp@easyscsl
+ \renewcommand{\itshape}{\not@math@alphabet\itshape\mathit%
+ \ifthenelse{\equal{\f@shape}{\scdefault}}{\fontshape{scsl}}{%
+ \fontshape\itdefault}\selectfont}
+ \renewcommand{\scshape}{\not@math@alphabet\scshape\relax%
+ \ifthenelse{\equal{\f@shape}{\sldefault}}{\fontshape{scsl}}{%
+ \ifthenelse{\equal{\f@shape}{\itdefault}}{\fontshape{scsl}}{\fontshape\scdefault}}\selectfont}
+ \renewcommand{\slshape}{\not@math@alphabet\slshape\relax%
+ \ifthenelse{\equal{\f@shape}{\scdefault}}{\fontshape{scsl}}{%
+ \fontshape\sldefault}\selectfont}
+ \fi
+%
+%%% famille, petitesmajuscules, style, f-ligatures and Q tail
+%
+ \ifkp@rmx\def\kp@famille{x}
+ \else
+ \ifkp@lighttext\def\kp@famille{l}
+ \else\def\kp@famille{}
+ \fi\fi
+ \ifkp@vos\def\kp@style{vos}
+ \else\ifkp@os\def\kp@style{os}
+ \else\ifkp@osn\def\kp@style{osn}
+ \else\def\kp@style{}
+ \fi\fi\fi
+ \ifkp@largesmallcaps\def\kp@petitesmajuscules{k}\def\kp@othersc{}
+ \else\def\kp@petitesmajuscules{}\def\kp@othersc{k}
+ \fi
+ \ifkp@nofligatures\def\kp@flig{f}
+ \else\def\kp@flig{}
+ \fi
+ \ifkp@Qtail\def\kp@othertail{}
+ \else\def\kp@othertail{os}
+ \fi
+ \ifkp@vos\def\kp@otherctst{}
+ \else\ifkp@os\def\kp@otherctst{}
+ \else\def\kp@otherctst{os}
+ \fi\fi
+%
+%%% start rm
+%
+ \renewcommand{\rmdefault}{jkp\kp@famille\kp@petitesmajuscules\kp@flig\kp@style}
+%
+%%% start sf
+%
+ \ifkp@sf
+ \renewcommand{\sfdefault}{jkpss\kp@petitesmajuscules\kp@flig\kp@style}
+ \fi
+%
+%%% start tt
+%
+ \ifkp@tt
+ \renewcommand{\ttdefault}{jkptt\kp@style}
+ \fi
+%
+%%% New slanted small-caps shape
+%
+ \newcommand{\textscsl}[1]{%
+ \begingroup%
+ \fontshape{scsl}\selectfont#1%
+ \endgroup}
+ \newcommand{\scslshape}{\fontshape{scsl}\selectfont}
+%
+%%% Courtesy from Christian Tellechea, package xstring
+%
+\def\SiFonteContient#1#2{%
+ \begingroup
+ \edef\temp@@a{#1}\edef\temp@@a{\detokenize\expandafter{\temp@@a}}%
+ \edef\temp@@b{#2}\edef\temp@@b{\detokenize\expandafter{\temp@@b}}%
+ \expandafter\expandafter\expandafter
+ \endgroup
+ \expandafter\expandafter\expandafter
+ \@SiFonteContient
+ \expandafter\expandafter\expandafter
+ {\expandafter\temp@@a\expandafter}\expandafter{\temp@@b}}
+
+\def\@SiFonteContient#1#2#3#4{%
+ \def\@@SiFonteContient##1#2##2\@nil{\ifx\@empty##2\@empty#4\else#3\fi}%
+ \@@SiFonteContient#1\@delimit#2\@nil}
+%
+%%% Other sc, other scsl
+%
+
+ \newcommand{\otherscshape}{%
+ \SiFonteContient{\fontname\the\font}{tt}{}{%
+ \SiFonteContient{\fontname\the\font}{ss}{\fontfamily{jkpss\kp@othersc\kp@flig\kp@style}}{%
+ \fontfamily{jkp\kp@famille\kp@othersc\kp@flig\kp@style}}}%
+ \fontshape{sc}\selectfont%
+ \ifkp@largesmallcaps\kp@largesmallcapsfalse\else\kp@largesmallcapstrue\fi%
+ \ifkp@largesmallcaps\def\kp@petitesmajuscules{k}\def\kp@othersc{}%
+ \else\def\kp@petitesmajuscules{}\def\kp@othersc{k}\fi}%
+ \newcommand{\textothersc}[1]{%
+ \begingroup%
+ \otherscshape#1%
+ \endgroup}
+ \newcommand{\otherscslshape}{%
+ \SiFonteContient{\fontname\the\font}{tt}{}{%
+ \SiFonteContient{\fontname\the\font}{ss}{\fontfamily{jkpss\kp@othersc\kp@flig\kp@style}}{%
+ \fontfamily{jkp\kp@famille\kp@othersc\kp@flig\kp@style}}}%
+ \fontshape{scsl}\selectfont%
+ \ifkp@largesmallcaps\kp@largesmallcapsfalse\else\kp@largesmallcapstrue\fi%
+ \ifkp@largesmallcaps\def\kp@petitesmajuscules{k}\def\kp@othersc{}%
+ \else\def\kp@petitesmajuscules{}\def\kp@othersc{k}\fi}%
+ \newcommand{\textotherscsl}[1]{%
+ \begingroup%
+ \otherscslshape#1%
+ \endgroup}
+%
+%%% Other Q and other smallcap q tails
+%
+ \newcommand{\othertailQ}{%
+ \begingroup%
+ \SiFonteContient{\fontname\the\font}{tt}{}{%
+ \SiFonteContient{\fontname\the\font}{ss}{\fontfamily{jkpss\kp@othertail}}{%
+ \fontfamily{jkp\kp@famille\kp@othertail}}}%
+ \selectfont{}Q%
+ \endgroup}
+%
+ \newcommand{\othertailscq}{%
+ \begingroup%
+ \SiFonteContient{\fontname\the\font}{tt}{}{%
+ \SiFonteContient{\fontname\the\font}{ss}{\fontfamily{jkpss\kp@petitesmajuscules\kp@othertail}}{%
+ \fontfamily{jkp\kp@famille\kp@petitesmajuscules\kp@othertail}}}%
+ \fontshape{sc}\selectfont{}q%
+ \endgroup}
+%
+ \newcommand{\othertailscslq}{%
+ \begingroup%
+ \SiFonteContient{\fontname\the\font}{tt}{}{%
+ \SiFonteContient{\fontname\the\font}{ss}{\fontfamily{jkpss\kp@petitesmajuscules\kp@othertail}}{%
+ \fontfamily{jkp\kp@famille\kp@petitesmajuscules\kp@othertail}}}%
+ \fontshape{scsl}\selectfont{}q%
+ \endgroup}
+
+%
+\fi % end text
+%
+
+
+%%%%%%%%
+% Math %
+%%%%%%%%
+
+\ifkp@math
+
+
+%
+%%% \kp@famillem \kp@stylem and \kp@widerm
+%
+
+ \ifkp@lightmath\def\kp@famillem{l}
+ \else\def\kp@famillem{}
+ \fi
+
+ \ifkp@vosm\def\kp@stylem{vos}
+ \else\ifkp@osm\def\kp@stylem{os}
+ \else\ifkp@osnm\def\kp@stylem{osn}
+ \else\def\kp@stylem{}
+ \fi\fi\fi
+ \ifkp@nofligatures\def\kp@fligm{f}
+ \else\def\kp@fligm{}
+ \fi
+
+ \ifkp@widermath\def\kp@widerm{w}
+ \else\def\kp@widerm{}
+ \fi
+ \ifkp@sfmath\def\kp@widerm{}\fi
+
+%
+%%% \kp@stylemi et \kp@stylemath
+%
+
+ \ifkp@vosm\def\kp@stylemi{vos}
+ \else\def\kp@stylemi{}\fi
+
+ \ifkp@sfmath
+ \def\kp@stylemath{ss}
+ \else
+ \def\kp@stylemath{}
+ \fi
+
+%
+%%% New math Versions
+%
+
+\DeclareMathVersion{rm}
+\DeclareMathVersion{boldrm}
+\DeclareMathVersion{sf}
+\DeclareMathVersion{boldsf}
+
+% Roman
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{operators}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{n}
+ \SetSymbolFont{operators}{bold}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \else
+ \DeclareSymbolFont{operators}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{n}
+ \SetSymbolFont{operators}{bold}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \fi
+ \SetSymbolFont{operators}{rm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{n}
+ \SetSymbolFont{operators}{boldrm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetSymbolFont{operators}{sf}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{n}
+ \SetSymbolFont{operators}{boldsf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+
+ \def\operator@font{\mathgroup\symoperators}
+
+ \DeclareMathAlphabet{\mathrm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathrm}{bold}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathrm}{rm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathrm}{boldrm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathrm}{sf}{OT1}{jkp\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathrm}{boldsf}{OT1}{jkp\kp@fligm\kp@stylem}{b}{n}
+
+ \DeclareSymbolFontAlphabet{\mathupright}{operators}
+ \let\mathup\mathupright
+
+ \ifkp@sfmath
+ \DeclareMathAlphabet{\mathbf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathbf}{bold}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \else
+ \DeclareMathAlphabet{\mathbf}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathbf}{bold}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \fi
+ \SetMathAlphabet{\mathbf}{rm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathbf}{boldrm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathbf}{sf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathbf}{boldsf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+
+ \ifkp@sfmath
+ \DeclareMathAlphabet{\mathit}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{it}
+ \SetMathAlphabet{\mathit}{bold}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{it}
+ \else
+ \DeclareMathAlphabet{\mathit}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{it}
+ \SetMathAlphabet{\mathit}{bold}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{it}
+ \fi
+ \SetMathAlphabet{\mathit}{rm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{m}{it}
+ \SetMathAlphabet{\mathit}{boldrm}{OT1}{jkp\kp@famillem\kp@fligm\kp@stylem}{b}{it}
+ \SetMathAlphabet{\mathit}{sf}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{it}
+ \SetMathAlphabet{\mathit}{boldsf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{it}
+
+
+% Sans Serif
+
+ \DeclareMathAlphabet{\mathsf}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathsf}{bold}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathsf}{rm}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathsf}{boldrm}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathsf}{sf}{OT1}{jkpss\kp@fligm\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathsf}{boldsf}{OT1}{jkpss\kp@fligm\kp@stylem}{b}{n}
+
+% Typewriter
+
+ \DeclareMathAlphabet{\mathtt}{OT1}{jkptt\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathtt}{bold}{OT1}{jkptt\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathtt}{rm}{OT1}{jkptt\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathtt}{boldrm}{OT1}{jkptt\kp@stylem}{b}{n}
+ \SetMathAlphabet{\mathtt}{sf}{OT1}{jkptt\kp@stylem}{m}{n}
+ \SetMathAlphabet{\mathtt}{boldsf}{OT1}{jkptt\kp@stylem}{b}{n}
+
+% Math Italic
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{letters}{OML}{jkpss\kp@stylemi}{m}{it}
+ \SetSymbolFont{letters}{bold}{OML}{jkpss\kp@stylemi}{bx}{it}
+ \else
+ \DeclareSymbolFont{letters}{OML}{jkp\kp@famillem\kp@stylemi\kp@widerm}{m}{it}
+ \SetSymbolFont{letters}{bold}{OML}{jkp\kp@famillem\kp@stylemi\kp@widerm}{bx}{it}
+ \fi
+ \SetSymbolFont{letters}{rm}{OML}{jkp\kp@famillem\kp@stylemi\kp@widerm}{m}{it}
+ \SetSymbolFont{letters}{boldrm}{OML}{jkp\kp@famillem\kp@stylemi\kp@widerm}{bx}{it}
+ \SetSymbolFont{letters}{sf}{OML}{jkpss\kp@stylemi}{m}{it}
+ \SetSymbolFont{letters}{boldsf}{OML}{jkpss\kp@stylemi}{bx}{it}
+ \DeclareFontSubstitution{OML}{jkp\kp@famillem\kp@stylemi\kp@widerm}{m}{it}
+
+% Math Italic A
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{lettersA}{U}{jkpssmia}{m}{it}
+ \SetSymbolFont{lettersA}{bold}{U}{jkpssmia}{bx}{it}
+ \else
+ \DeclareSymbolFont{lettersA}{U}{jkp\kp@famillem mia\kp@widerm}{m}{it}
+ \SetSymbolFont{lettersA}{bold}{U}{jkp\kp@famillem mia\kp@widerm}{bx}{it}
+ \fi
+ \SetSymbolFont{lettersA}{rm}{U}{jkp\kp@famillem mia\kp@widerm}{m}{it}
+ \SetSymbolFont{lettersA}{boldrm}{U}{jkp\kp@famillem mia\kp@widerm}{bx}{it}
+ \SetSymbolFont{lettersA}{sf}{U}{jkpssmia}{m}{it}
+ \SetSymbolFont{lettersA}{boldsf}{U}{jkpssmia}{bx}{it}
+ \DeclareFontSubstitution{U}{jkp\kp@famillem mia\kp@widerm}{m}{it}
+
+ \DeclareSymbolFontAlphabet{\mathfrak}{lettersA}
+
+
+% Math Symbol
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{symbols}{OMS}{jkp}{m}{n}
+ \SetSymbolFont{symbols}{bold}{OMS}{jkp}{bx}{n}
+ \else
+ \DeclareSymbolFont{symbols}{OMS}{jkp\kp@famillem\kp@widerm}{m}{n}
+ \SetSymbolFont{symbols}{bold}{OMS}{jkp\kp@famillem\kp@widerm}{bx}{n}
+ \fi
+ \SetSymbolFont{symbols}{rm}{OMS}{jkp\kp@famillem\kp@widerm}{m}{n}
+ \SetSymbolFont{symbols}{boldrm}{OMS}{jkp\kp@famillem\kp@widerm}{bx}{n}
+ \SetSymbolFont{symbols}{sf}{OMS}{jkp}{m}{n}
+ \SetSymbolFont{symbols}{boldsf}{OMS}{jkp}{bx}{n}
+ \DeclareFontSubstitution{OMS}{jkp\kp@famillem\kp@widerm}{m}{n}
+
+\ifkp@amsmath{
+ \renewcommand{\AmSfont}{%
+ \usefont{OMS}{jkp\kp@famillem\kp@widerm}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}}\fi
+
+ \DeclareSymbolFontAlphabet{\symb@ls@lph@}{symbols}
+
+
+% Math Symbols A (AMSa)
+
+
+ \DeclareSymbolFont{AMSa}{U}{jkpsya}{m}{n}
+ \SetSymbolFont{AMSa}{bold}{U}{jkpsya}{bx}{n}
+ \SetSymbolFont{AMSa}{rm}{U}{jkpsya}{m}{n}
+ \SetSymbolFont{AMSa}{boldrm}{U}{jkpsya}{bx}{n}
+ \SetSymbolFont{AMSa}{sf}{U}{jkpsya}{m}{n}
+ \SetSymbolFont{AMSa}{boldsf}{U}{jkpsya}{bx}{n}
+ \DeclareFontSubstitution{U}{jkpsya}{m}{n}
+
+
+% Math Symbols B (AMSb)
+
+\ifkp@rmmathbb
+ \ifkp@sfmath
+ \DeclareSymbolFont{AMSb}{U}{jkpsyb}{m}{n}% rmmathbb, sfmath
+ \SetSymbolFont{AMSb}{bold}{U}{jkpsyb}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsyb}{bx}{n}
+ \else
+ \DeclareSymbolFont{AMSb}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}% rmmathbb
+ \SetSymbolFont{AMSb}{bold}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsyb}{bx}{n}
+ \fi
+\else
+ \ifkp@sfmathbb
+ \ifkp@sfmath
+ \DeclareSymbolFont{AMSb}{U}{jkpsssyb}{m}{n}% sfmathbb, sfmath
+ \SetSymbolFont{AMSb}{bold}{U}{jkpsssyb}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkpss\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkpss\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsssyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsssyb}{bx}{n}
+ \else
+ \DeclareSymbolFont{AMSb}{U}{jkpss\kp@famillem syb\kp@widerm}{m}{n}% sfmathbb
+ \SetSymbolFont{AMSb}{bold}{U}{jkpss\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkpss\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkpss\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsssyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsssyb}{bx}{n}
+ \fi
+ \else
+ \ifkp@sfmath
+ \DeclareSymbolFont{AMSb}{U}{jkpsssyb}{m}{n}% sfmath
+ \SetSymbolFont{AMSb}{bold}{U}{jkpsssyb}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsssyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsssyb}{bx}{n}
+ \else
+ \DeclareSymbolFont{AMSb}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}% default
+ \SetSymbolFont{AMSb}{bold}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{rm}{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}
+ \SetSymbolFont{AMSb}{boldrm}{U}{jkp\kp@famillem syb\kp@widerm}{bx}{n}
+ \SetSymbolFont{AMSb}{sf}{U}{jkpsssyb}{m}{n}
+ \SetSymbolFont{AMSb}{boldsf}{U}{jkpsssyb}{bx}{n}
+ \fi
+ \fi
+\fi
+
+ \DeclareFontSubstitution{U}{jkp\kp@famillem syb\kp@widerm}{m}{n}
+ \DeclareSymbolFontAlphabet{\mathbb}{AMSb}
+
+
+% Math Symbols C
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{symbolsC}{U}{jkpsyc}{m}{n}
+ \SetSymbolFont{symbolsC}{bold}{U}{jkpsyc}{bx}{n}
+ \else
+ \DeclareSymbolFont{symbolsC}{U}{jkp\kp@famillem syc}{m}{n}
+ \SetSymbolFont{symbolsC}{bold}{U}{jkp\kp@famillem syc}{bx}{n}
+ \fi
+ \SetSymbolFont{symbolsC}{rm}{U}{jkp\kp@famillem syc}{m}{n}
+ \SetSymbolFont{symbolsC}{boldrm}{U}{jkp\kp@famillem syc}{bx}{n}
+ \SetSymbolFont{symbolsC}{sf}{U}{jkpsyc}{m}{n}
+ \SetSymbolFont{symbolsC}{boldsf}{U}{jkpsyc}{bx}{n}
+ \DeclareFontSubstitution{U}{jkp\kp@famillem syc}{m}{n}
+
+
+% Math Symbols D
+
+\ifkp@calasscr
+ \let\mathcal\undefined
+ \ifkp@sfmath
+ \DeclareMathAlphabet{\mathcal}{U}{jkpsyd}{m}{n}
+ \SetMathAlphabet{\mathcal}{bold}{U}{jkpsyd}{bx}{n}
+ \else
+ \DeclareMathAlphabet{\mathcal}{U}{jkp\kp@famillem syd\kp@widerm}{m}{n}
+ \SetMathAlphabet{\mathcal}{bold}{U}{jkp\kp@famillem syd\kp@widerm}{bx}{n}
+ \fi
+ \SetMathAlphabet{\mathcal}{rm}{U}{jkp\kp@famillem syd\kp@widerm}{m}{n}
+ \SetMathAlphabet{\mathcal}{boldrm}{U}{jkp\kp@famillem syd\kp@widerm}{bx}{n}
+ \SetMathAlphabet{\mathcal}{sf}{U}{jkpsyd}{m}{n}
+ \SetMathAlphabet{\mathcal}{boldsf}{U}{jkpsyd}{bx}{n}
+ \ifkp@mathscr
+ \DeclareSymbolFontAlphabet{\mathscr}{symbols}
+ \fi
+\else
+ \ifkp@mathscr
+ \ifkp@sfmath
+ \DeclareMathAlphabet{\mathscr}{U}{jkpsyd}{m}{n}
+ \SetMathAlphabet{\mathscr}{bold}{U}{jkpsyd}{bx}{n}
+ \else
+ \DeclareMathAlphabet{\mathscr}{U}{jkp\kp@famillem syd\kp@widerm}{m}{n}
+ \SetMathAlphabet{\mathscr}{bold}{U}{jkp\kp@famillem syd\kp@widerm}{bx}{n}
+ \fi
+ \SetMathAlphabet{\mathscr}{rm}{U}{jkp\kp@famillem syd\kp@widerm}{m}{n}
+ \SetMathAlphabet{\mathscr}{boldrm}{U}{jkp\kp@famillem syd\kp@widerm}{bx}{n}
+ \SetMathAlphabet{\mathscr}{sf}{U}{jkpsyd}{m}{n}
+ \SetMathAlphabet{\mathscr}{boldsf}{U}{jkpsyd}{bx}{n}
+ \fi
+\fi
+
+% Math Extension
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{largesymbols}{OMX}{jkpss}{m}{n}
+ \SetSymbolFont{largesymbols}{bold}{OMX}{jkpss}{bx}{n}
+ \else
+ \DeclareSymbolFont{largesymbols}{OMX}{jkp\kp@famillem}{m}{n}
+ \SetSymbolFont{largesymbols}{bold}{OMX}{jkp\kp@famillem}{bx}{n}
+ \fi
+ \SetSymbolFont{largesymbols}{rm}{OMX}{jkp\kp@famillem}{m}{n}
+ \SetSymbolFont{largesymbols}{boldrm}{OMX}{jkp\kp@famillem}{bx}{n}
+ \SetSymbolFont{largesymbols}{sf}{OMX}{jkpss}{m}{n}
+ \SetSymbolFont{largesymbols}{boldsf}{OMX}{jkpss}{bx}{n}
+ \DeclareFontSubstitution{OMX}{jkp\kp@famillem}{m}{n}
+
+
+% Math Extension A
+
+ \ifkp@sfmath
+ \DeclareSymbolFont{largesymbolsA}{U}{jkpexa}{m}{n}
+ \SetSymbolFont{largesymbolsA}{bold}{U}{jkpexa}{bx}{n}
+ \else
+ \DeclareSymbolFont{largesymbolsA}{U}{jkp\kp@famillem exa}{m}{n}
+ \SetSymbolFont{largesymbolsA}{bold}{U}{jkp\kp@famillem exa}{bx}{n}
+ \fi
+ \SetSymbolFont{largesymbolsA}{rm}{U}{jkp\kp@famillem exa}{m}{n}
+ \SetSymbolFont{largesymbolsA}{boldrm}{U}{jkp\kp@famillem exa}{bx}{n}
+ \SetSymbolFont{largesymbolsA}{sf}{U}{jkpexa}{m}{n}
+ \SetSymbolFont{largesymbolsA}{boldsf}{U}{jkpexa}{bx}{n}
+ \DeclareFontSubstitution{U}{jkp\kp@famillem exa}{m}{n}
+
+
+% Math fonts Sizes and Additional Math Spaces
+
+
+\def\defaultscriptratio{.76}
+\def\defaultscriptscriptratio{.6}
+\DeclareMathSizes{5} {6} {6} {6}
+\DeclareMathSizes{6} {6} {6} {6}
+\DeclareMathSizes{7} {6.8} {6} {6}
+\DeclareMathSizes{8} {8} {6.8} {6}
+\DeclareMathSizes{9} {9} {7.6} {6}
+\DeclareMathSizes{10} {10} {7.6} {6}
+\DeclareMathSizes{10.95}{10.95}{8.3} {6}
+\DeclareMathSizes{11} {11} {8.3} {6}
+\DeclareMathSizes{12} {12} {9} {7}
+\DeclareMathSizes{14.4} {14.4} {10} {8}
+\DeclareMathSizes{17.28}{17.28}{12} {9}
+\DeclareMathSizes{20.74}{20.74}{14.4}{10}
+\DeclareMathSizes{24.88}{24.88}{17.28}{12}
+
+\ifkp@widermath
+ \thinmuskip=3mu
+ \medmuskip=4mu plus 1.5mu minus 3mu
+ \thickmuskip=5mu plus 4mu
+\else
+ \thinmuskip=2mu
+ \medmuskip=3mu plus 1.5mu minus 3mu
+ \thickmuskip=4mu plus 3mu
+\fi
+
+% Common Macros
+
+
+\def\re@DeclareMathSymbol#1#2#3#4{%
+ \let#1=\undefined
+ \DeclareMathSymbol{#1}{#2}{#3}{#4}}
+
+\def\re@DeclareMathDelimiter#1#2#3#4#5#6{%
+ \let#1=\undefined
+ \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#5}{#6}}
+
+\def\re@DeclareMathAccent#1#2#3#4{%
+ \let#1=\undefined
+ \DeclareMathAccent{#1}{#2}{#3}{#4}}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Operator Definition %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\re@DeclareMathSymbol{\kppounds}{\mathord}{operators}{139}
+
+% \pounds classic bug in math mode
+
+\let\oldpounds\pounds%
+\def\pounds{%
+ \relax\ifmmode\kppounds%
+ \else\oldpounds\fi}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Italic (jkpmi) Definition %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\ifkp@partialup\re@DeclareMathSymbol{\partial}{\mathord}{letters}{128}\fi
+\re@DeclareMathSymbol{\partialup}{\mathord}{letters}{128}
+\re@DeclareMathSymbol{\partialsl}{\mathord}{letters}{64}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Symbol (jkpsy) Definition % synomymes and \Re, \Im
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \let\circledplus\oplus
+ \let\circledminus\ominus
+ \let\circledtimes\otimes
+ \let\circledslash\oslash
+ \let\circleddot\odot
+
+\ifkp@oldReIm
+ \re@DeclareMathSymbol{\Re}{\mathord}{lettersA}{82}
+ \re@DeclareMathSymbol{\Im}{\mathord}{lettersA}{73}
+\fi
+
+
+\re@DeclareMathSymbol{\varemptyset}{\mathord}{symbols}{128}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Symbol A Definitions % AMSa
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\re@DeclareMathSymbol{\boxdot}{\mathbin}{AMSa}{0}
+\re@DeclareMathSymbol{\boxplus}{\mathbin}{AMSa}{1}
+\re@DeclareMathSymbol{\boxtimes}{\mathbin}{AMSa}{2}
+\re@DeclareMathSymbol{\square}{\mathord}{AMSa}{3}
+\re@DeclareMathSymbol{\blacksquare}{\mathord}{AMSa}{4}
+\re@DeclareMathSymbol{\centerdot}{\mathbin}{AMSa}{5}
+\re@DeclareMathSymbol{\lozenge}{\mathord}{AMSa}{6}
+\re@DeclareMathSymbol{\blacklozenge}{\mathord}{AMSa}{7}
+\re@DeclareMathSymbol{\circlearrowright}{\mathrel}{AMSa}{8}
+\re@DeclareMathSymbol{\circlearrowleft}{\mathrel}{AMSa}{9}
+\re@DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{10}
+\re@DeclareMathSymbol{\leftrightharpoons}{\mathrel}{AMSa}{11}
+\re@DeclareMathSymbol{\boxminus}{\mathbin}{AMSa}{12}
+\re@DeclareMathSymbol{\Vdash}{\mathrel}{AMSa}{13}
+\re@DeclareMathSymbol{\Vvdash}{\mathrel}{AMSa}{14}
+\re@DeclareMathSymbol{\vDash}{\mathrel}{AMSa}{15}
+\re@DeclareMathSymbol{\twoheadrightarrow}{\mathrel}{AMSa}{16}
+\re@DeclareMathSymbol{\twoheadleftarrow}{\mathrel}{AMSa}{17}
+\re@DeclareMathSymbol{\leftleftarrows}{\mathrel}{AMSa}{18}
+\re@DeclareMathSymbol{\rightrightarrows}{\mathrel}{AMSa}{19}
+\re@DeclareMathSymbol{\upuparrows}{\mathrel}{AMSa}{20}
+\re@DeclareMathSymbol{\downdownarrows}{\mathrel}{AMSa}{21}
+\re@DeclareMathSymbol{\upharpoonright}{\mathrel}{AMSa}{22}
+ \let\restriction\upharpoonright
+\re@DeclareMathSymbol{\downharpoonright}{\mathrel}{AMSa}{23}
+\re@DeclareMathSymbol{\upharpoonleft}{\mathrel}{AMSa}{24}
+\re@DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{25}
+\re@DeclareMathSymbol{\rightarrowtail}{\mathrel}{AMSa}{26}
+\re@DeclareMathSymbol{\leftarrowtail}{\mathrel}{AMSa}{27}
+\re@DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{28}
+\re@DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{29}
+\re@DeclareMathSymbol{\Lsh}{\mathrel}{AMSa}{30}
+\re@DeclareMathSymbol{\Rsh}{\mathrel}{AMSa}{31}
+\re@DeclareMathSymbol{\rightsquigarrow}{\mathrel}{AMSa}{32}
+\re@DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{33}
+\re@DeclareMathSymbol{\looparrowleft}{\mathrel}{AMSa}{34}
+\re@DeclareMathSymbol{\looparrowright}{\mathrel}{AMSa}{35}
+\re@DeclareMathSymbol{\circeq}{\mathrel}{AMSa}{36}
+\re@DeclareMathSymbol{\succsim}{\mathrel}{AMSa}{37}
+\re@DeclareMathSymbol{\gtrsim}{\mathrel}{AMSa}{38}
+\re@DeclareMathSymbol{\gtrapprox}{\mathrel}{AMSa}{39}
+\re@DeclareMathSymbol{\multimap}{\mathrel}{AMSa}{40}
+\re@DeclareMathSymbol{\therefore}{\mathrel}{AMSa}{41}
+\re@DeclareMathSymbol{\because}{\mathrel}{AMSa}{42}
+\re@DeclareMathSymbol{\doteqdot}{\mathrel}{AMSa}{43}
+ \let\Doteq\doteqdot
+\re@DeclareMathSymbol{\triangleq}{\mathrel}{AMSa}{44}
+\re@DeclareMathSymbol{\precsim}{\mathrel}{AMSa}{45}
+\re@DeclareMathSymbol{\lesssim}{\mathrel}{AMSa}{46}
+\re@DeclareMathSymbol{\lessapprox}{\mathrel}{AMSa}{47}
+\re@DeclareMathSymbol{\eqslantless}{\mathrel}{AMSa}{48}
+\re@DeclareMathSymbol{\eqslantgtr}{\mathrel}{AMSa}{49}
+\re@DeclareMathSymbol{\curlyeqprec}{\mathrel}{AMSa}{50}
+\re@DeclareMathSymbol{\curlyeqsucc}{\mathrel}{AMSa}{51}
+\re@DeclareMathSymbol{\preccurlyeq}{\mathrel}{AMSa}{52}
+\re@DeclareMathSymbol{\leqq}{\mathrel}{AMSa}{53}
+\re@DeclareMathSymbol{\leqslant}{\mathrel}{AMSa}{54}
+\re@DeclareMathSymbol{\lessgtr}{\mathrel}{AMSa}{55}
+\re@DeclareMathSymbol{\backprime}{\mathord}{AMSa}{56}
+\re@DeclareMathSymbol{\risingdotseq}{\mathrel}{AMSa}{58}
+\re@DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{59}
+\re@DeclareMathSymbol{\succcurlyeq}{\mathrel}{AMSa}{60}
+\re@DeclareMathSymbol{\geqq}{\mathrel}{AMSa}{61}
+\re@DeclareMathSymbol{\geqslant}{\mathrel}{AMSa}{62}
+\re@DeclareMathSymbol{\gtrless}{\mathrel}{AMSa}{63}
+\re@DeclareMathSymbol{\sqsubset}{\mathrel}{AMSa}{64}
+\re@DeclareMathSymbol{\sqsupset}{\mathrel}{AMSa}{65}
+\re@DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{66}
+\re@DeclareMathSymbol{\vartriangleleft}{\mathrel}{AMSa}{67}
+\re@DeclareMathSymbol{\trianglerighteq}{\mathrel}{AMSa}{68}
+\re@DeclareMathSymbol{\trianglelefteq}{\mathrel}{AMSa}{69}
+\re@DeclareMathSymbol{\bigstar}{\mathord}{AMSa}{70}
+\re@DeclareMathSymbol{\between}{\mathrel}{AMSa}{71}
+\re@DeclareMathSymbol{\blacktriangledown}{\mathord}{AMSa}{72}
+\re@DeclareMathSymbol{\blacktriangleright}{\mathrel}{AMSa}{73}
+\re@DeclareMathSymbol{\blacktriangleleft}{\mathrel}{AMSa}{74}
+\re@DeclareMathSymbol{\vartriangle}{\mathrel}{AMSa}{77}
+\re@DeclareMathSymbol{\blacktriangle}{\mathord}{AMSa}{78}
+\re@DeclareMathSymbol{\triangledown}{\mathord}{AMSa}{79}
+\re@DeclareMathSymbol{\eqcirc}{\mathrel}{AMSa}{80}
+\re@DeclareMathSymbol{\lesseqgtr}{\mathrel}{AMSa}{81}
+\re@DeclareMathSymbol{\gtreqless}{\mathrel}{AMSa}{82}
+\re@DeclareMathSymbol{\lesseqqgtr}{\mathrel}{AMSa}{83}
+\re@DeclareMathSymbol{\gtreqqless}{\mathrel}{AMSa}{84}
+\re@DeclareMathSymbol{\Rrightarrow}{\mathrel}{AMSa}{86}
+\re@DeclareMathSymbol{\Lleftarrow}{\mathrel}{AMSa}{87}
+\re@DeclareMathSymbol{\veebar}{\mathbin}{AMSa}{89}
+\re@DeclareMathSymbol{\barwedge}{\mathbin}{AMSa}{90}
+\re@DeclareMathSymbol{\doublebarwedge}{\mathbin}{AMSa}{91}
+\re@DeclareMathSymbol{\angle}{\mathord}{AMSa}{92}
+\re@DeclareMathSymbol{\measuredangle}{\mathord}{AMSa}{93}
+\re@DeclareMathSymbol{\sphericalangle}{\mathord}{AMSa}{94}
+\re@DeclareMathSymbol{\varpropto}{\mathrel}{AMSa}{95}
+\re@DeclareMathSymbol{\smallsmile}{\mathrel}{AMSa}{96}
+\re@DeclareMathSymbol{\smallfrown}{\mathrel}{AMSa}{97}
+\re@DeclareMathSymbol{\Subset}{\mathrel}{AMSa}{98}
+\re@DeclareMathSymbol{\Supset}{\mathrel}{AMSa}{99}
+\re@DeclareMathSymbol{\Cup}{\mathbin}{AMSa}{100}
+ \let\doublecup\Cup
+\re@DeclareMathSymbol{\Cap}{\mathbin}{AMSa}{101}
+ \let\doublecap\Cap
+\re@DeclareMathSymbol{\curlywedge}{\mathbin}{AMSa}{102}
+\re@DeclareMathSymbol{\curlyvee}{\mathbin}{AMSa}{103}
+\re@DeclareMathSymbol{\leftthreetimes}{\mathbin}{AMSa}{104}
+\re@DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{105}
+\re@DeclareMathSymbol{\subseteqq}{\mathrel}{AMSa}{106}
+\re@DeclareMathSymbol{\supseteqq}{\mathrel}{AMSa}{107}
+\re@DeclareMathSymbol{\bumpeq}{\mathrel}{AMSa}{108}
+\re@DeclareMathSymbol{\Bumpeq}{\mathrel}{AMSa}{109}
+\re@DeclareMathSymbol{\lll}{\mathrel}{AMSa}{110}
+ \let\llless\lll
+\re@DeclareMathSymbol{\ggg}{\mathrel}{AMSa}{111}
+ \let\gggtr\ggg
+\re@DeclareMathDelimiter\ulcorner{\mathopen}{AMSa}{112}{AMSa}{112}
+\re@DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{113}{AMSa}{113}
+\re@DeclareMathSymbol{\circledS}{\mathord}{AMSa}{115}
+\re@DeclareMathSymbol{\pitchfork}{\mathrel}{AMSa}{116}
+\re@DeclareMathSymbol{\dotplus}{\mathbin}{AMSa}{117}
+\re@DeclareMathSymbol{\backsim}{\mathrel}{AMSa}{118}
+\re@DeclareMathSymbol{\backsimeq}{\mathrel}{AMSa}{119}
+\re@DeclareMathDelimiter\llcorner{\mathopen}{AMSa}{120}{AMSa}{120}
+\re@DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{121}{AMSa}{121}
+\re@DeclareMathSymbol{\complement}{\mathord}{AMSa}{123}
+\re@DeclareMathSymbol{\intercal}{\mathbin}{AMSa}{124}
+\re@DeclareMathSymbol{\circledcirc}{\mathbin}{AMSa}{125}
+\re@DeclareMathSymbol{\circledast}{\mathbin}{AMSa}{126}
+\re@DeclareMathSymbol{\circleddash}{\mathbin}{AMSa}{127}
+
+\let\Box=\square % LaTeX symbol
+\re@DeclareMathSymbol{\rhd}{\mathbin}{AMSa}{66} % LaTeX symbol
+\re@DeclareMathSymbol{\lhd}{\mathbin}{AMSa}{67} % LaTeX symbol
+\re@DeclareMathSymbol{\unrhd}{\mathbin}{AMSa}{68} % LaTeX symbol
+\re@DeclareMathSymbol{\unlhd}{\mathbin}{AMSa}{69} % LaTeX symbol
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Symbol B Definitions % AMSb
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\re@DeclareMathSymbol{\lvertneqq}{\mathrel}{AMSb}{0}
+\re@DeclareMathSymbol{\gvertneqq}{\mathrel}{AMSb}{1}
+\re@DeclareMathSymbol{\nleq}{\mathrel}{AMSb}{2}
+\re@DeclareMathSymbol{\ngeq}{\mathrel}{AMSb}{3}
+\re@DeclareMathSymbol{\nless}{\mathrel}{AMSb}{4}
+\re@DeclareMathSymbol{\ngtr}{\mathrel}{AMSb}{5}
+\re@DeclareMathSymbol{\nprec}{\mathrel}{AMSb}{6}
+\re@DeclareMathSymbol{\nsucc}{\mathrel}{AMSb}{7}
+\re@DeclareMathSymbol{\lneqq}{\mathrel}{AMSb}{8}
+\re@DeclareMathSymbol{\gneqq}{\mathrel}{AMSb}{9}
+\re@DeclareMathSymbol{\nleqslant}{\mathrel}{AMSb}{10}
+\re@DeclareMathSymbol{\ngeqslant}{\mathrel}{AMSb}{11}
+\re@DeclareMathSymbol{\lneq}{\mathrel}{AMSb}{12}
+\re@DeclareMathSymbol{\gneq}{\mathrel}{AMSb}{13}
+\re@DeclareMathSymbol{\npreceq}{\mathrel}{AMSb}{14}
+\re@DeclareMathSymbol{\nsucceq}{\mathrel}{AMSb}{15}
+\re@DeclareMathSymbol{\precnsim}{\mathrel}{AMSb}{16}
+\re@DeclareMathSymbol{\succnsim}{\mathrel}{AMSb}{17}
+\re@DeclareMathSymbol{\lnsim}{\mathrel}{AMSb}{18}
+\re@DeclareMathSymbol{\gnsim}{\mathrel}{AMSb}{19}
+\re@DeclareMathSymbol{\nleqq}{\mathrel}{AMSb}{20}
+\re@DeclareMathSymbol{\ngeqq}{\mathrel}{AMSb}{21}
+\re@DeclareMathSymbol{\precneqq}{\mathrel}{AMSb}{22}
+\re@DeclareMathSymbol{\succneqq}{\mathrel}{AMSb}{23}
+\re@DeclareMathSymbol{\precnapprox}{\mathrel}{AMSb}{24}
+\re@DeclareMathSymbol{\succnapprox}{\mathrel}{AMSb}{25}
+\re@DeclareMathSymbol{\lnapprox}{\mathrel}{AMSb}{26}
+\re@DeclareMathSymbol{\gnapprox}{\mathrel}{AMSb}{27}
+\re@DeclareMathSymbol{\nsim}{\mathrel}{AMSb}{28}
+\re@DeclareMathSymbol{\ncong}{\mathrel}{AMSb}{29}
+\re@DeclareMathSymbol{\diagup}{\mathord}{AMSb}{30}
+\re@DeclareMathSymbol{\diagdown}{\mathord}{AMSb}{31}
+\re@DeclareMathSymbol{\varsubsetneq}{\mathrel}{AMSb}{32}
+\re@DeclareMathSymbol{\varsupsetneq}{\mathrel}{AMSb}{33}
+\re@DeclareMathSymbol{\nsubseteqq}{\mathrel}{AMSb}{34}
+\re@DeclareMathSymbol{\nsupseteqq}{\mathrel}{AMSb}{35}
+\re@DeclareMathSymbol{\subsetneqq}{\mathrel}{AMSb}{36}
+\re@DeclareMathSymbol{\supsetneqq}{\mathrel}{AMSb}{37}
+\re@DeclareMathSymbol{\varsubsetneqq}{\mathrel}{AMSb}{38}
+\re@DeclareMathSymbol{\varsupsetneqq}{\mathrel}{AMSb}{39}
+\re@DeclareMathSymbol{\subsetneq}{\mathrel}{AMSb}{40}
+\re@DeclareMathSymbol{\supsetneq}{\mathrel}{AMSb}{41}
+\re@DeclareMathSymbol{\nsubseteq}{\mathrel}{AMSb}{42}
+\re@DeclareMathSymbol{\nsupseteq}{\mathrel}{AMSb}{43}
+\re@DeclareMathSymbol{\nparallel}{\mathrel}{AMSb}{44}
+\re@DeclareMathSymbol{\nmid}{\mathrel}{AMSb}{45}
+\re@DeclareMathSymbol{\nshortmid}{\mathrel}{AMSb}{46}
+\re@DeclareMathSymbol{\nshortparallel}{\mathrel}{AMSb}{47}
+\re@DeclareMathSymbol{\nvdash}{\mathrel}{AMSb}{48}
+\re@DeclareMathSymbol{\nVdash}{\mathrel}{AMSb}{49}
+\re@DeclareMathSymbol{\nvDash}{\mathrel}{AMSb}{50}
+\re@DeclareMathSymbol{\nVDash}{\mathrel}{AMSb}{51}
+\re@DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{AMSb}{52}
+\re@DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{AMSb}{53}
+\re@DeclareMathSymbol{\ntriangleleft}{\mathrel}{AMSb}{54}
+\re@DeclareMathSymbol{\ntriangleright}{\mathrel}{AMSb}{55}
+\re@DeclareMathSymbol{\nleftarrow}{\mathrel}{AMSb}{56}
+\re@DeclareMathSymbol{\nrightarrow}{\mathrel}{AMSb}{57}
+\re@DeclareMathSymbol{\nLeftarrow}{\mathrel}{AMSb}{58}
+\re@DeclareMathSymbol{\nRightarrow}{\mathrel}{AMSb}{59}
+\re@DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{AMSb}{60}
+\re@DeclareMathSymbol{\nleftrightarrow}{\mathrel}{AMSb}{61}
+\re@DeclareMathSymbol{\divideontimes}{\mathbin}{AMSb}{62}
+\re@DeclareMathSymbol{\varnothing}{\mathord}{AMSb}{63}
+\re@DeclareMathSymbol{\nexists}{\mathord}{AMSb}{64}
+\re@DeclareMathSymbol{\Finv}{\mathord}{AMSb}{96}
+\re@DeclareMathSymbol{\Game}{\mathord}{AMSb}{97}
+\re@DeclareMathSymbol{\mho}{\mathord}{AMSb}{102}
+\re@DeclareMathSymbol{\eth}{\mathord}{AMSb}{103}
+\re@DeclareMathSymbol{\eqsim}{\mathrel}{AMSb}{104}
+\re@DeclareMathSymbol{\beth}{\mathord}{AMSb}{105}
+\re@DeclareMathSymbol{\gimel}{\mathord}{AMSb}{106}
+\re@DeclareMathSymbol{\daleth}{\mathord}{AMSb}{107}
+\re@DeclareMathSymbol{\lessdot}{\mathbin}{AMSb}{108}
+\re@DeclareMathSymbol{\gtrdot}{\mathbin}{AMSb}{109}
+\re@DeclareMathSymbol{\ltimes}{\mathbin}{AMSb}{110}
+\re@DeclareMathSymbol{\rtimes}{\mathbin}{AMSb}{111}
+\re@DeclareMathSymbol{\shortmid}{\mathrel}{AMSb}{112}
+\re@DeclareMathSymbol{\shortparallel}{\mathrel}{AMSb}{113}
+\re@DeclareMathSymbol{\smallsetminus}{\mathbin}{AMSb}{114}
+\re@DeclareMathSymbol{\thicksim}{\mathrel}{AMSb}{115}
+\re@DeclareMathSymbol{\thickapprox}{\mathrel}{AMSb}{116}
+\re@DeclareMathSymbol{\approxeq}{\mathrel}{AMSb}{117}
+\re@DeclareMathSymbol{\succapprox}{\mathrel}{AMSb}{119}
+\re@DeclareMathSymbol{\precapprox}{\mathrel}{AMSb}{118}
+\re@DeclareMathSymbol{\curvearrowleft}{\mathrel}{AMSb}{120}
+\re@DeclareMathSymbol{\curvearrowright}{\mathrel}{AMSb}{121}
+\re@DeclareMathSymbol{\digamma}{\mathord}{AMSb}{122}
+\re@DeclareMathSymbol{\varkappa}{\mathord}{AMSb}{123}
+\re@DeclareMathSymbol{\Bbbk}{\mathord}{AMSb}{124}
+\re@DeclareMathSymbol{\hslash}{\mathord}{AMSb}{125}
+\re@DeclareMathSymbol{\hbar}{\mathord}{AMSb}{126}
+\re@DeclareMathSymbol{\backepsilon}{\mathrel}{AMSb}{127}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Symbol C Definitions % symbolsC
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\re@DeclareMathSymbol{\mappedfromchar}{\mathrel}{symbolsC}{0}
+ \def\mappedfrom{\leftarrow\mappedfromchar}
+ \def\longmappedfrom{\longleftarrow\mappedfromchar}
+\re@DeclareMathSymbol{\Mapstochar}{\mathrel}{symbolsC}{1}
+ \def\Mapsto{\Mapstochar\Rightarrow}
+ \def\Longmapsto{\Mapstochar\Longrightarrow}
+\re@DeclareMathSymbol{\Mappedfromchar}{\mathrel}{symbolsC}{2}
+ \def\Mappedfrom{\Leftarrow\Mappedfromchar}
+ \def\Longmappedfrom{\Longleftarrow\Mappedfromchar}
+\re@DeclareMathSymbol{\mmapstochar}{\mathrel}{symbolsC}{3}
+ \def\mmapsto{\mmapstochar\rightarrow}
+ \def\longmmapsto{\mmapstochar\longrightarrow}
+\re@DeclareMathSymbol{\mmappedfromchar}{\mathrel}{symbolsC}{4}
+ \def\mmappedfrom{\leftarrow\mmappedfromchar}
+ \def\longmmappedfrom{\longleftarrow\mmappedfromchar}
+\re@DeclareMathSymbol{\Mmapstochar}{\mathrel}{symbolsC}{5}
+ \def\Mmapsto{\Mmapstochar\Rightarrow}
+ \def\Longmmapsto{\Mmapstochar\Longrightarrow}
+\re@DeclareMathSymbol{\Mmappedfromchar}{\mathrel}{symbolsC}{6}
+ \def\Mmappedfrom{\Leftarrow\Mmappedfromchar}
+ \def\Longmmappedfrom{\Longleftarrow\Mmappedfromchar}
+\re@DeclareMathSymbol{\medcirc}{\mathbin}{symbolsC}{7}
+\re@DeclareMathSymbol{\medbullet}{\mathbin}{symbolsC}{8}
+\re@DeclareMathSymbol{\varparallel}{\mathrel}{symbolsC}{9}
+\re@DeclareMathSymbol{\varparallelinv}{\mathrel}{symbolsC}{10}
+\re@DeclareMathSymbol{\nvarparallel}{\mathrel}{symbolsC}{11}
+\re@DeclareMathSymbol{\nvarparallelinv}{\mathrel}{symbolsC}{12}
+\re@DeclareMathSymbol{\colonapprox}{\mathrel}{symbolsC}{13}
+\re@DeclareMathSymbol{\colonsim}{\mathrel}{symbolsC}{14}
+\re@DeclareMathSymbol{\Colonapprox}{\mathrel}{symbolsC}{15}
+\re@DeclareMathSymbol{\Colonsim}{\mathrel}{symbolsC}{16}
+\re@DeclareMathSymbol{\doteq}{\mathrel}{symbolsC}{17}
+\re@DeclareMathSymbol{\multimapinv}{\mathrel}{symbolsC}{18}
+\re@DeclareMathSymbol{\multimapboth}{\mathrel}{symbolsC}{19}
+\re@DeclareMathSymbol{\multimapdot}{\mathrel}{symbolsC}{20}
+\re@DeclareMathSymbol{\multimapdotinv}{\mathrel}{symbolsC}{21}
+\re@DeclareMathSymbol{\multimapdotboth}{\mathrel}{symbolsC}{22}
+\re@DeclareMathSymbol{\multimapdotbothA}{\mathrel}{symbolsC}{23}
+\re@DeclareMathSymbol{\multimapdotbothB}{\mathrel}{symbolsC}{24}
+\re@DeclareMathSymbol{\VDash}{\mathrel}{symbolsC}{25}
+\re@DeclareMathSymbol{\VvDash}{\mathrel}{symbolsC}{26}
+\re@DeclareMathSymbol{\cong}{\mathrel}{symbolsC}{27}
+\re@DeclareMathSymbol{\preceqq}{\mathrel}{symbolsC}{28}
+\re@DeclareMathSymbol{\succeqq}{\mathrel}{symbolsC}{29}
+\re@DeclareMathSymbol{\nprecsim}{\mathrel}{symbolsC}{30}
+\re@DeclareMathSymbol{\nsuccsim}{\mathrel}{symbolsC}{31}
+\re@DeclareMathSymbol{\nlesssim}{\mathrel}{symbolsC}{32}
+\re@DeclareMathSymbol{\ngtrsim}{\mathrel}{symbolsC}{33}
+\re@DeclareMathSymbol{\nlessapprox}{\mathrel}{symbolsC}{34}
+\re@DeclareMathSymbol{\ngtrapprox}{\mathrel}{symbolsC}{35}
+\re@DeclareMathSymbol{\npreccurlyeq}{\mathrel}{symbolsC}{36}
+\re@DeclareMathSymbol{\nsucccurlyeq}{\mathrel}{symbolsC}{37}
+\re@DeclareMathSymbol{\ngtrless}{\mathrel}{symbolsC}{38}
+\re@DeclareMathSymbol{\nlessgtr}{\mathrel}{symbolsC}{39}
+\re@DeclareMathSymbol{\nbumpeq}{\mathrel}{symbolsC}{40}
+\re@DeclareMathSymbol{\nBumpeq}{\mathrel}{symbolsC}{41}
+\re@DeclareMathSymbol{\nbacksim}{\mathrel}{symbolsC}{42}
+\re@DeclareMathSymbol{\nbacksimeq}{\mathrel}{symbolsC}{43}
+\re@DeclareMathSymbol{\neq}{\mathrel}{symbolsC}{44}
+ \let\ne=\neq
+\re@DeclareMathSymbol{\nasymp}{\mathrel}{symbolsC}{45}
+\re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46}
+\re@DeclareMathSymbol{\nsim}{\mathrel}{symbolsC}{47}
+\re@DeclareMathSymbol{\napprox}{\mathrel}{symbolsC}{48}
+\re@DeclareMathSymbol{\nsubset}{\mathrel}{symbolsC}{49}
+\re@DeclareMathSymbol{\nsupset}{\mathrel}{symbolsC}{50}
+\re@DeclareMathSymbol{\nll}{\mathrel}{symbolsC}{51}
+\re@DeclareMathSymbol{\ngg}{\mathrel}{symbolsC}{52}
+\re@DeclareMathSymbol{\nthickapprox}{\mathrel}{symbolsC}{53}
+\re@DeclareMathSymbol{\napproxeq}{\mathrel}{symbolsC}{54}
+\re@DeclareMathSymbol{\nprecapprox}{\mathrel}{symbolsC}{55}
+\re@DeclareMathSymbol{\nsuccapprox}{\mathrel}{symbolsC}{56}
+\re@DeclareMathSymbol{\npreceqq}{\mathrel}{symbolsC}{57}
+\re@DeclareMathSymbol{\nsucceqq}{\mathrel}{symbolsC}{58}
+\re@DeclareMathSymbol{\nsimeq}{\mathrel}{symbolsC}{59}
+\re@DeclareMathSymbol{\notin}{\mathrel}{symbolsC}{60}
+\re@DeclareMathSymbol{\notni}{\mathrel}{symbolsC}{61}
+ \let\notowns=\notni
+\re@DeclareMathSymbol{\nSubset}{\mathrel}{symbolsC}{62}
+\re@DeclareMathSymbol{\nSupset}{\mathrel}{symbolsC}{63}
+\re@DeclareMathSymbol{\nsqsubseteq}{\mathrel}{symbolsC}{64}
+\re@DeclareMathSymbol{\nsqsupseteq}{\mathrel}{symbolsC}{65}
+\re@DeclareMathSymbol{\coloneqq}{\mathrel}{symbolsC}{66}
+\re@DeclareMathSymbol{\eqqcolon}{\mathrel}{symbolsC}{67}
+\re@DeclareMathSymbol{\coloneq}{\mathrel}{symbolsC}{68}
+\re@DeclareMathSymbol{\eqcolon}{\mathrel}{symbolsC}{69}
+\re@DeclareMathSymbol{\Coloneqq}{\mathrel}{symbolsC}{70}
+\re@DeclareMathSymbol{\Eqqcolon}{\mathrel}{symbolsC}{71}
+\re@DeclareMathSymbol{\Coloneq}{\mathrel}{symbolsC}{72}
+\re@DeclareMathSymbol{\Eqcolon}{\mathrel}{symbolsC}{73}
+\re@DeclareMathSymbol{\strictif}{\mathrel}{symbolsC}{74}
+\re@DeclareMathSymbol{\strictfi}{\mathrel}{symbolsC}{75}
+\re@DeclareMathSymbol{\strictiff}{\mathrel}{symbolsC}{76}
+\re@DeclareMathSymbol{\invamp}{\mathbin}{symbolsC}{77}
+\re@DeclareMathDelimiter{\lbag}{\mathopen}{symbolsC}{78}{largesymbolsA}{48}
+\re@DeclareMathDelimiter{\rbag}{\mathclose}{symbolsC}{79}{largesymbolsA}{49}
+\re@DeclareMathSymbol{\Lbag}{\mathopen}{symbolsC}{80}
+\re@DeclareMathSymbol{\Rbag}{\mathclose}{symbolsC}{81}
+\re@DeclareMathSymbol{\circledless}{\mathrel}{symbolsC}{82}
+\re@DeclareMathSymbol{\circledgtr}{\mathrel}{symbolsC}{83}
+\re@DeclareMathSymbol{\circledwedge}{\mathbin}{symbolsC}{84}
+\re@DeclareMathSymbol{\circledvee}{\mathbin}{symbolsC}{85}
+\re@DeclareMathSymbol{\circledbar}{\mathbin}{symbolsC}{86}
+\re@DeclareMathSymbol{\circledbslash}{\mathbin}{symbolsC}{87}
+\re@DeclareMathSymbol{\lJoin}{\mathrel}{symbolsC}{88}
+\re@DeclareMathSymbol{\rJoin}{\mathrel}{symbolsC}{89}
+\re@DeclareMathSymbol{\Join}{\mathrel}{symbolsC}{90}
+ \let\lrJoin=\Join
+\re@DeclareMathSymbol{\openJoin}{\mathrel}{symbolsC}{91}
+\re@DeclareMathSymbol{\lrtimes}{\mathrel}{symbolsC}{92}
+% \let\bowtie\lrtimes
+\re@DeclareMathSymbol{\opentimes}{\mathrel}{symbolsC}{93}
+\re@DeclareMathSymbol{\Diamond}{\mathord}{symbolsC}{94}
+\re@DeclareMathSymbol{\Diamondblack}{\mathord}{symbolsC}{95}
+\re@DeclareMathSymbol{\nplus}{\mathbin}{symbolsC}{96}
+\re@DeclareMathSymbol{\nsqsubset}{\mathrel}{symbolsC}{97}
+\re@DeclareMathSymbol{\nsqsupset}{\mathrel}{symbolsC}{98}
+\re@DeclareMathSymbol{\dashleftarrow}{\mathrel}{symbolsC}{99}
+\re@DeclareMathSymbol{\dashrightarrow}{\mathrel}{symbolsC}{100}
+ \let\dasharrow\dashrightarrow
+\re@DeclareMathSymbol{\dashleftrightarrow}{\mathrel}{symbolsC}{101}
+\re@DeclareMathSymbol{\leftsquigarrow}{\mathrel}{symbolsC}{102}
+\re@DeclareMathSymbol{\ntwoheadrightarrow}{\mathrel}{symbolsC}{103}
+\re@DeclareMathSymbol{\ntwoheadleftarrow}{\mathrel}{symbolsC}{104}
+\re@DeclareMathSymbol{\boxast}{\mathbin}{symbolsC}{105}
+\re@DeclareMathSymbol{\boxbslash}{\mathbin}{symbolsC}{106}
+\re@DeclareMathSymbol{\boxbar}{\mathbin}{symbolsC}{107}
+\re@DeclareMathSymbol{\boxslash}{\mathbin}{symbolsC}{108}
+\re@DeclareMathSymbol{\Wr}{\mathbin}{symbolsC}{109}
+\re@DeclareMathSymbol{\lambdaslash}{\mathord}{symbolsC}{110}
+\re@DeclareMathSymbol{\lambdabar}{\mathord}{symbolsC}{111}
+\re@DeclareMathSymbol{\varclubsuit}{\mathord}{symbolsC}{112}
+\re@DeclareMathSymbol{\vardiamondsuit}{\mathord}{symbolsC}{113}
+\re@DeclareMathSymbol{\varheartsuit}{\mathord}{symbolsC}{114}
+\re@DeclareMathSymbol{\varspadesuit}{\mathord}{symbolsC}{115}
+\re@DeclareMathSymbol{\Nearrow}{\mathrel}{symbolsC}{116}
+\re@DeclareMathSymbol{\Searrow}{\mathrel}{symbolsC}{117}
+\re@DeclareMathSymbol{\Nwarrow}{\mathrel}{symbolsC}{118}
+\re@DeclareMathSymbol{\Swarrow}{\mathrel}{symbolsC}{119}
+\re@DeclareMathSymbol{\Top}{\mathord}{symbolsC}{120}
+\re@DeclareMathSymbol{\Bot}{\mathord}{symbolsC}{121}
+\re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121}
+\re@DeclareMathSymbol\leadstoext{\mathrel}{symbolsC}{122}
+\re@DeclareMathSymbol\leadsto{\mathrel}{symbolsC}{123}
+\re@DeclareMathSymbol{\sqcupplus}{\mathbin}{symbolsC}{124}
+\re@DeclareMathSymbol{\sqcapplus}{\mathbin}{symbolsC}{125}
+\re@DeclareMathDelimiter{\llbracket}{\mathopen}{symbolsC}{126}{largesymbolsA}{18}
+\re@DeclareMathDelimiter{\rrbracket}{\mathclose}{symbolsC}{127}{largesymbolsA}{19}
+\re@DeclareMathSymbol{\boxright}{\mathrel}{symbolsC}{128}
+\re@DeclareMathSymbol{\boxleft}{\mathrel}{symbolsC}{129}
+\re@DeclareMathSymbol{\boxdotright}{\mathrel}{symbolsC}{130}
+\re@DeclareMathSymbol{\boxdotleft}{\mathrel}{symbolsC}{131}
+\re@DeclareMathSymbol{\Diamondright}{\mathrel}{symbolsC}{132}
+\re@DeclareMathSymbol{\Diamondleft}{\mathrel}{symbolsC}{133}
+\re@DeclareMathSymbol{\Diamonddotright}{\mathrel}{symbolsC}{134}
+\re@DeclareMathSymbol{\Diamonddotleft}{\mathrel}{symbolsC}{135}
+\re@DeclareMathSymbol{\boxRight}{\mathrel}{symbolsC}{136}
+\re@DeclareMathSymbol{\boxLeft}{\mathrel}{symbolsC}{137}
+\re@DeclareMathSymbol{\boxdotRight}{\mathrel}{symbolsC}{138}
+\re@DeclareMathSymbol{\boxdotLeft}{\mathrel}{symbolsC}{139}
+\re@DeclareMathSymbol{\DiamondRight}{\mathrel}{symbolsC}{140}
+\re@DeclareMathSymbol{\DiamondLeft}{\mathrel}{symbolsC}{141}
+\re@DeclareMathSymbol{\DiamonddotRight}{\mathrel}{symbolsC}{142}
+\re@DeclareMathSymbol{\DiamonddotLeft}{\mathrel}{symbolsC}{143}
+\re@DeclareMathSymbol{\Diamonddot}{\mathord}{symbolsC}{144}
+\re@DeclareMathSymbol{\circleright}{\mathrel}{symbolsC}{145}
+\re@DeclareMathSymbol{\circleleft}{\mathrel}{symbolsC}{146}
+\re@DeclareMathSymbol{\circleddotright}{\mathrel}{symbolsC}{147}
+ \let\circledotright\circleddotright
+\re@DeclareMathSymbol{\circleddotleft}{\mathrel}{symbolsC}{148}
+ \let\circledotleft\circleddotleft
+\re@DeclareMathSymbol{\multimapbothvert}{\mathrel}{symbolsC}{149}
+\re@DeclareMathSymbol{\multimapdotbothvert}{\mathrel}{symbolsC}{150}
+\re@DeclareMathSymbol{\multimapdotbothBvert}{\mathrel}{symbolsC}{151}
+\re@DeclareMathSymbol{\multimapdotbothAvert}{\mathrel}{symbolsC}{152}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Greek letter's options %
+%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Absolute reference
+
+\re@DeclareMathSymbol{\Gammasl}{\mathord}{letters}{0}
+\re@DeclareMathSymbol{\Deltasl}{\mathord}{letters}{1}
+\re@DeclareMathSymbol{\Thetasl}{\mathord}{letters}{2}
+\re@DeclareMathSymbol{\Lambdasl}{\mathord}{letters}{3}
+\re@DeclareMathSymbol{\Xisl}{\mathord}{letters}{4}
+\re@DeclareMathSymbol{\Pisl}{\mathord}{letters}{5}
+\re@DeclareMathSymbol{\Sigmasl}{\mathord}{letters}{6}
+\re@DeclareMathSymbol{\Upsilonsl}{\mathord}{letters}{7}
+\re@DeclareMathSymbol{\Phisl}{\mathord}{letters}{8}
+\re@DeclareMathSymbol{\Psisl}{\mathord}{letters}{9}
+\re@DeclareMathSymbol{\Omegasl}{\mathord}{letters}{10}
+
+\re@DeclareMathSymbol{\Gammaup}{\mathalpha}{lettersA}{00}
+\re@DeclareMathSymbol{\Deltaup}{\mathalpha}{lettersA}{01}
+\re@DeclareMathSymbol{\Thetaup}{\mathalpha}{lettersA}{02}
+\re@DeclareMathSymbol{\Lambdaup}{\mathalpha}{lettersA}{03}
+\re@DeclareMathSymbol{\Xiup}{\mathalpha}{lettersA}{04}
+\re@DeclareMathSymbol{\Piup}{\mathalpha}{lettersA}{05}
+\re@DeclareMathSymbol{\Sigmaup}{\mathalpha}{lettersA}{06}
+\re@DeclareMathSymbol{\Upsilonup}{\mathalpha}{lettersA}{07}
+\re@DeclareMathSymbol{\Phiup}{\mathalpha}{lettersA}{08}
+\re@DeclareMathSymbol{\Psiup}{\mathalpha}{lettersA}{09}
+\re@DeclareMathSymbol{\Omegaup}{\mathalpha}{lettersA}{10}
+
+\re@DeclareMathSymbol{\alphaup}{\mathord}{lettersA}{11}
+\re@DeclareMathSymbol{\betaup}{\mathord}{lettersA}{12}
+\re@DeclareMathSymbol{\gammaup}{\mathord}{lettersA}{13}
+\re@DeclareMathSymbol{\deltaup}{\mathord}{lettersA}{14}
+\re@DeclareMathSymbol{\epsilonup}{\mathord}{lettersA}{15}
+\re@DeclareMathSymbol{\zetaup}{\mathord}{lettersA}{16}
+\re@DeclareMathSymbol{\etaup}{\mathord}{lettersA}{17}
+\re@DeclareMathSymbol{\thetaup}{\mathord}{lettersA}{18}
+\re@DeclareMathSymbol{\iotaup}{\mathord}{lettersA}{19}
+\re@DeclareMathSymbol{\kappaup}{\mathord}{lettersA}{20}
+\re@DeclareMathSymbol{\lambdaup}{\mathord}{lettersA}{21}
+\re@DeclareMathSymbol{\muup}{\mathord}{lettersA}{22}
+\re@DeclareMathSymbol{\nuup}{\mathord}{lettersA}{23}
+\re@DeclareMathSymbol{\xiup}{\mathord}{lettersA}{24}
+\re@DeclareMathSymbol{\piup}{\mathord}{lettersA}{25}
+\re@DeclareMathSymbol{\rhoup}{\mathord}{lettersA}{26}
+\re@DeclareMathSymbol{\sigmaup}{\mathord}{lettersA}{27}
+\re@DeclareMathSymbol{\tauup}{\mathord}{lettersA}{28}
+\re@DeclareMathSymbol{\upsilonup}{\mathord}{lettersA}{29}
+\re@DeclareMathSymbol{\phiup}{\mathord}{lettersA}{30}
+\re@DeclareMathSymbol{\chiup}{\mathord}{lettersA}{31}
+\re@DeclareMathSymbol{\psiup}{\mathord}{lettersA}{32}
+\re@DeclareMathSymbol{\omegaup}{\mathord}{lettersA}{33}
+\re@DeclareMathSymbol{\varepsilonup}{\mathord}{lettersA}{34}
+\re@DeclareMathSymbol{\varthetaup}{\mathord}{lettersA}{35}
+\re@DeclareMathSymbol{\varpiup}{\mathord}{lettersA}{36}
+\re@DeclareMathSymbol{\varrhoup}{\mathord}{lettersA}{37}
+\re@DeclareMathSymbol{\varsigmaup}{\mathord}{lettersA}{38}
+\re@DeclareMathSymbol{\varphiup}{\mathord}{lettersA}{39}
+
+\let\varkappaup\varkappa
+\let\digammaup\digamma
+
+\re@DeclareMathSymbol{\alphasl}{\mathord}{letters}{11}
+\re@DeclareMathSymbol{\betasl}{\mathord}{letters}{12}
+\re@DeclareMathSymbol{\gammasl}{\mathord}{letters}{13}
+\re@DeclareMathSymbol{\deltasl}{\mathord}{letters}{14}
+\re@DeclareMathSymbol{\epsilonsl}{\mathord}{letters}{15}
+\re@DeclareMathSymbol{\zetasl}{\mathord}{letters}{16}
+\re@DeclareMathSymbol{\etasl}{\mathord}{letters}{17}
+\re@DeclareMathSymbol{\thetasl}{\mathord}{letters}{18}
+\re@DeclareMathSymbol{\iotasl}{\mathord}{letters}{19}
+\re@DeclareMathSymbol{\kappasl}{\mathord}{letters}{20}
+\re@DeclareMathSymbol{\lambdasl}{\mathord}{letters}{21}
+\re@DeclareMathSymbol{\musl}{\mathord}{letters}{22}
+\re@DeclareMathSymbol{\nusl}{\mathord}{letters}{23}
+\re@DeclareMathSymbol{\xisl}{\mathord}{letters}{24}
+\re@DeclareMathSymbol{\pisl}{\mathord}{letters}{25}
+\re@DeclareMathSymbol{\rhosl}{\mathord}{letters}{26}
+\re@DeclareMathSymbol{\sigmasl}{\mathord}{letters}{27}
+\re@DeclareMathSymbol{\tausl}{\mathord}{letters}{28}
+\re@DeclareMathSymbol{\slsilonsl}{\mathord}{letters}{29}
+\re@DeclareMathSymbol{\phisl}{\mathord}{letters}{30}
+\re@DeclareMathSymbol{\chisl}{\mathord}{letters}{31}
+\re@DeclareMathSymbol{\psisl}{\mathord}{letters}{32}
+\re@DeclareMathSymbol{\omegasl}{\mathord}{letters}{33}
+\re@DeclareMathSymbol{\varepsilonsl}{\mathord}{letters}{34}
+\re@DeclareMathSymbol{\varthetasl}{\mathord}{letters}{35}
+\re@DeclareMathSymbol{\varpisl}{\mathord}{letters}{36}
+\re@DeclareMathSymbol{\varrhosl}{\mathord}{letters}{37}
+\re@DeclareMathSymbol{\varsigmasl}{\mathord}{letters}{38}
+\re@DeclareMathSymbol{\varphisl}{\mathord}{letters}{39}
+
+\let\varkappasl\varkappa
+\let\digammasl\digamma
+
+% Relative reference
+
+\ifkp@upgrk % lowercase
+
+ \re@DeclareMathSymbol{\alpha}{\mathord}{lettersA}{11}
+ \re@DeclareMathSymbol{\beta}{\mathord}{lettersA}{12}
+ \re@DeclareMathSymbol{\gamma}{\mathord}{lettersA}{13}
+ \re@DeclareMathSymbol{\delta}{\mathord}{lettersA}{14}
+ \re@DeclareMathSymbol{\epsilon}{\mathord}{lettersA}{15}
+ \re@DeclareMathSymbol{\zeta}{\mathord}{lettersA}{16}
+ \re@DeclareMathSymbol{\eta}{\mathord}{lettersA}{17}
+ \re@DeclareMathSymbol{\theta}{\mathord}{lettersA}{18}
+ \re@DeclareMathSymbol{\iota}{\mathord}{lettersA}{19}
+ \re@DeclareMathSymbol{\kappa}{\mathord}{lettersA}{20}
+ \re@DeclareMathSymbol{\lambda}{\mathord}{lettersA}{21}
+ \re@DeclareMathSymbol{\mu}{\mathord}{lettersA}{22}
+ \re@DeclareMathSymbol{\nu}{\mathord}{lettersA}{23}
+ \re@DeclareMathSymbol{\xi}{\mathord}{lettersA}{24}
+ \re@DeclareMathSymbol{\pi}{\mathord}{lettersA}{25}
+ \re@DeclareMathSymbol{\rho}{\mathord}{lettersA}{26}
+ \re@DeclareMathSymbol{\sigma}{\mathord}{lettersA}{27}
+ \re@DeclareMathSymbol{\tau}{\mathord}{lettersA}{28}
+ \re@DeclareMathSymbol{\upsilon}{\mathord}{lettersA}{29}
+ \re@DeclareMathSymbol{\phi}{\mathord}{lettersA}{30}
+ \re@DeclareMathSymbol{\chi}{\mathord}{lettersA}{31}
+ \re@DeclareMathSymbol{\psi}{\mathord}{lettersA}{32}
+ \re@DeclareMathSymbol{\omega}{\mathord}{lettersA}{33}
+ \re@DeclareMathSymbol{\varepsilon}{\mathord}{lettersA}{34}
+ \re@DeclareMathSymbol{\vartheta}{\mathord}{lettersA}{35}
+ \re@DeclareMathSymbol{\varpi}{\mathord}{lettersA}{36}
+ \re@DeclareMathSymbol{\varrho}{\mathord}{lettersA}{37}
+ \re@DeclareMathSymbol{\varsigma}{\mathord}{lettersA}{38}
+ \re@DeclareMathSymbol{\varphi}{\mathord}{lettersA}{39}
+
+ \re@DeclareMathSymbol{\otheralpha}{\mathord}{letters}{11}
+ \re@DeclareMathSymbol{\otherbeta}{\mathord}{letters}{12}
+ \re@DeclareMathSymbol{\othergamma}{\mathord}{letters}{13}
+ \re@DeclareMathSymbol{\otherdelta}{\mathord}{letters}{14}
+ \re@DeclareMathSymbol{\otherepsilon}{\mathord}{letters}{15}
+ \re@DeclareMathSymbol{\otherzeta}{\mathord}{letters}{16}
+ \re@DeclareMathSymbol{\othereta}{\mathord}{letters}{17}
+ \re@DeclareMathSymbol{\othertheta}{\mathord}{letters}{18}
+ \re@DeclareMathSymbol{\otheriota}{\mathord}{letters}{19}
+ \re@DeclareMathSymbol{\otherkappa}{\mathord}{letters}{20}
+ \re@DeclareMathSymbol{\otherlambda}{\mathord}{letters}{21}
+ \re@DeclareMathSymbol{\othermu}{\mathord}{letters}{22}
+ \re@DeclareMathSymbol{\othernu}{\mathord}{letters}{23}
+ \re@DeclareMathSymbol{\otherxi}{\mathord}{letters}{24}
+ \re@DeclareMathSymbol{\otherpi}{\mathord}{letters}{25}
+ \re@DeclareMathSymbol{\otherrho}{\mathord}{letters}{26}
+ \re@DeclareMathSymbol{\othersigma}{\mathord}{letters}{27}
+ \re@DeclareMathSymbol{\othertau}{\mathord}{letters}{28}
+ \re@DeclareMathSymbol{\otherupsilon}{\mathord}{letters}{29}
+ \re@DeclareMathSymbol{\otherphi}{\mathord}{letters}{30}
+ \re@DeclareMathSymbol{\otherchi}{\mathord}{letters}{31}
+ \re@DeclareMathSymbol{\otherpsi}{\mathord}{letters}{32}
+ \re@DeclareMathSymbol{\otheromega}{\mathord}{letters}{33}
+ \re@DeclareMathSymbol{\othervarepsilon}{\mathord}{letters}{34}
+ \re@DeclareMathSymbol{\othervartheta}{\mathord}{letters}{35}
+ \re@DeclareMathSymbol{\othervarpi}{\mathord}{letters}{36}
+ \re@DeclareMathSymbol{\othervarrho}{\mathord}{letters}{37}
+ \re@DeclareMathSymbol{\othervarsigma}{\mathord}{letters}{38}
+ \re@DeclareMathSymbol{\othervarphi}{\mathord}{letters}{39}
+
+\else
+
+ \re@DeclareMathSymbol{\alpha}{\mathord}{letters}{11}
+ \re@DeclareMathSymbol{\beta}{\mathord}{letters}{12}
+ \re@DeclareMathSymbol{\gamma}{\mathord}{letters}{13}
+ \re@DeclareMathSymbol{\delta}{\mathord}{letters}{14}
+ \re@DeclareMathSymbol{\epsilon}{\mathord}{letters}{15}
+ \re@DeclareMathSymbol{\zeta}{\mathord}{letters}{16}
+ \re@DeclareMathSymbol{\eta}{\mathord}{letters}{17}
+ \re@DeclareMathSymbol{\theta}{\mathord}{letters}{18}
+ \re@DeclareMathSymbol{\iota}{\mathord}{letters}{19}
+ \re@DeclareMathSymbol{\kappa}{\mathord}{letters}{20}
+ \re@DeclareMathSymbol{\lambda}{\mathord}{letters}{21}
+ \re@DeclareMathSymbol{\mu}{\mathord}{letters}{22}
+ \re@DeclareMathSymbol{\nu}{\mathord}{letters}{23}
+ \re@DeclareMathSymbol{\xi}{\mathord}{letters}{24}
+ \re@DeclareMathSymbol{\pi}{\mathord}{letters}{25}
+ \re@DeclareMathSymbol{\rho}{\mathord}{letters}{26}
+ \re@DeclareMathSymbol{\sigma}{\mathord}{letters}{27}
+ \re@DeclareMathSymbol{\tau}{\mathord}{letters}{28}
+ \re@DeclareMathSymbol{\upsilon}{\mathord}{letters}{29}
+ \re@DeclareMathSymbol{\phi}{\mathord}{letters}{30}
+ \re@DeclareMathSymbol{\chi}{\mathord}{letters}{31}
+ \re@DeclareMathSymbol{\psi}{\mathord}{letters}{32}
+ \re@DeclareMathSymbol{\omega}{\mathord}{letters}{33}
+ \re@DeclareMathSymbol{\varepsilon}{\mathord}{letters}{34}
+ \re@DeclareMathSymbol{\vartheta}{\mathord}{letters}{35}
+ \re@DeclareMathSymbol{\varpi}{\mathord}{letters}{36}
+ \re@DeclareMathSymbol{\varrho}{\mathord}{letters}{37}
+ \re@DeclareMathSymbol{\varsigma}{\mathord}{letters}{38}
+ \re@DeclareMathSymbol{\varphi}{\mathord}{letters}{39}
+
+ \re@DeclareMathSymbol{\otheralpha}{\mathord}{lettersA}{11}
+ \re@DeclareMathSymbol{\otherbeta}{\mathord}{lettersA}{12}
+ \re@DeclareMathSymbol{\othergamma}{\mathord}{lettersA}{13}
+ \re@DeclareMathSymbol{\otherdelta}{\mathord}{lettersA}{14}
+ \re@DeclareMathSymbol{\otherepsilon}{\mathord}{lettersA}{15}
+ \re@DeclareMathSymbol{\otherzeta}{\mathord}{lettersA}{16}
+ \re@DeclareMathSymbol{\othereta}{\mathord}{lettersA}{17}
+ \re@DeclareMathSymbol{\othertheta}{\mathord}{lettersA}{18}
+ \re@DeclareMathSymbol{\otheriota}{\mathord}{lettersA}{19}
+ \re@DeclareMathSymbol{\otherkappa}{\mathord}{lettersA}{20}
+ \re@DeclareMathSymbol{\otherlambda}{\mathord}{lettersA}{21}
+ \re@DeclareMathSymbol{\othermu}{\mathord}{lettersA}{22}
+ \re@DeclareMathSymbol{\othernu}{\mathord}{lettersA}{23}
+ \re@DeclareMathSymbol{\otherxi}{\mathord}{lettersA}{24}
+ \re@DeclareMathSymbol{\otherpi}{\mathord}{lettersA}{25}
+ \re@DeclareMathSymbol{\otherrho}{\mathord}{lettersA}{26}
+ \re@DeclareMathSymbol{\othersigma}{\mathord}{lettersA}{27}
+ \re@DeclareMathSymbol{\othertau}{\mathord}{lettersA}{28}
+ \re@DeclareMathSymbol{\otherupsilon}{\mathord}{lettersA}{29}
+ \re@DeclareMathSymbol{\otherphi}{\mathord}{lettersA}{30}
+ \re@DeclareMathSymbol{\otherchi}{\mathord}{lettersA}{31}
+ \re@DeclareMathSymbol{\otherpsi}{\mathord}{lettersA}{32}
+ \re@DeclareMathSymbol{\otheromega}{\mathord}{lettersA}{33}
+ \re@DeclareMathSymbol{\othervarepsilon}{\mathord}{lettersA}{34}
+ \re@DeclareMathSymbol{\othervartheta}{\mathord}{lettersA}{35}
+ \re@DeclareMathSymbol{\othervarpi}{\mathord}{lettersA}{36}
+ \re@DeclareMathSymbol{\othervarrho}{\mathord}{lettersA}{37}
+ \re@DeclareMathSymbol{\othervarsigma}{\mathord}{lettersA}{38}
+ \re@DeclareMathSymbol{\othervarphi}{\mathord}{lettersA}{39}
+
+\fi
+
+\let\othervarkappa\varkappa
+\let\otherdigamma\digamma
+
+\ifkp@slGrk % uppercase
+
+ \re@DeclareMathSymbol{\Gamma}{\mathord}{letters}{0}
+ \re@DeclareMathSymbol{\Delta}{\mathord}{letters}{1}
+ \re@DeclareMathSymbol{\Theta}{\mathord}{letters}{2}
+ \re@DeclareMathSymbol{\Lambda}{\mathord}{letters}{3}
+ \re@DeclareMathSymbol{\Xi}{\mathord}{letters}{4}
+ \re@DeclareMathSymbol{\Pi}{\mathord}{letters}{5}
+ \re@DeclareMathSymbol{\Sigma}{\mathord}{letters}{6}
+ \re@DeclareMathSymbol{\Upsilon}{\mathord}{letters}{7}
+ \re@DeclareMathSymbol{\Phi}{\mathord}{letters}{8}
+ \re@DeclareMathSymbol{\Psi}{\mathord}{letters}{9}
+ \re@DeclareMathSymbol{\Omega}{\mathord}{letters}{10}
+
+ \re@DeclareMathSymbol{\otherGamma}{\mathord}{lettersA}{00}
+ \re@DeclareMathSymbol{\otherDelta}{\mathord}{lettersA}{01}
+ \re@DeclareMathSymbol{\otherTheta}{\mathord}{lettersA}{02}
+ \re@DeclareMathSymbol{\otherLambda}{\mathord}{lettersA}{03}
+ \re@DeclareMathSymbol{\otherXi}{\mathord}{lettersA}{04}
+ \re@DeclareMathSymbol{\otherPi}{\mathord}{lettersA}{05}
+ \re@DeclareMathSymbol{\otherSigma}{\mathord}{lettersA}{06}
+ \re@DeclareMathSymbol{\otherUpsilon}{\mathord}{lettersA}{07}
+ \re@DeclareMathSymbol{\otherPhi}{\mathord}{lettersA}{08}
+ \re@DeclareMathSymbol{\otherPsi}{\mathord}{lettersA}{09}
+ \re@DeclareMathSymbol{\otherOmega}{\mathord}{lettersA}{10}
+
+ \re@DeclareMathSymbol{\varGamma}{\mathord}{lettersA}{00}
+ \re@DeclareMathSymbol{\varDelta}{\mathord}{lettersA}{01}
+ \re@DeclareMathSymbol{\varTheta}{\mathord}{lettersA}{02}
+ \re@DeclareMathSymbol{\varLambda}{\mathord}{lettersA}{03}
+ \re@DeclareMathSymbol{\varXi}{\mathord}{lettersA}{04}
+ \re@DeclareMathSymbol{\varPi}{\mathord}{lettersA}{05}
+ \re@DeclareMathSymbol{\varSigma}{\mathord}{lettersA}{06}
+ \re@DeclareMathSymbol{\varUpsilon}{\mathord}{lettersA}{07}
+ \re@DeclareMathSymbol{\varPhi}{\mathord}{lettersA}{08}
+ \re@DeclareMathSymbol{\varPsi}{\mathord}{lettersA}{09}
+ \re@DeclareMathSymbol{\varOmega}{\mathord}{lettersA}{10}
+
+\else
+
+ \re@DeclareMathSymbol{\Gamma}{\mathalpha}{lettersA}{00}
+ \re@DeclareMathSymbol{\Delta}{\mathalpha}{lettersA}{01}
+ \re@DeclareMathSymbol{\Theta}{\mathalpha}{lettersA}{02}
+ \re@DeclareMathSymbol{\Lambda}{\mathalpha}{lettersA}{03}
+ \re@DeclareMathSymbol{\Xi}{\mathalpha}{lettersA}{04}
+ \re@DeclareMathSymbol{\Pi}{\mathalpha}{lettersA}{05}
+ \re@DeclareMathSymbol{\Sigma}{\mathalpha}{lettersA}{06}
+ \re@DeclareMathSymbol{\Upsilon}{\mathalpha}{lettersA}{07}
+ \re@DeclareMathSymbol{\Phi}{\mathalpha}{lettersA}{08}
+ \re@DeclareMathSymbol{\Psi}{\mathalpha}{lettersA}{09}
+ \re@DeclareMathSymbol{\Omega}{\mathalpha}{lettersA}{10}
+
+ \re@DeclareMathSymbol{\otherGamma}{\mathord}{letters}{0}
+ \re@DeclareMathSymbol{\otherDelta}{\mathord}{letters}{1}
+ \re@DeclareMathSymbol{\otherTheta}{\mathord}{letters}{2}
+ \re@DeclareMathSymbol{\otherLambda}{\mathord}{letters}{3}
+ \re@DeclareMathSymbol{\otherXi}{\mathord}{letters}{4}
+ \re@DeclareMathSymbol{\otherPi}{\mathord}{letters}{5}
+ \re@DeclareMathSymbol{\otherSigma}{\mathord}{letters}{6}
+ \re@DeclareMathSymbol{\otherUpsilon}{\mathord}{letters}{7}
+ \re@DeclareMathSymbol{\otherPhi}{\mathord}{letters}{8}
+ \re@DeclareMathSymbol{\otherPsi}{\mathord}{letters}{9}
+ \re@DeclareMathSymbol{\otherOmega}{\mathord}{letters}{10}
+
+ \re@DeclareMathSymbol{\varGamma}{\mathord}{letters}{0}
+ \re@DeclareMathSymbol{\varDelta}{\mathord}{letters}{1}
+ \re@DeclareMathSymbol{\varTheta}{\mathord}{letters}{2}
+ \re@DeclareMathSymbol{\varLambda}{\mathord}{letters}{3}
+ \re@DeclareMathSymbol{\varXi}{\mathord}{letters}{4}
+ \re@DeclareMathSymbol{\varPi}{\mathord}{letters}{5}
+ \re@DeclareMathSymbol{\varSigma}{\mathord}{letters}{6}
+ \re@DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{7}
+ \re@DeclareMathSymbol{\varPhi}{\mathord}{letters}{8}
+ \re@DeclareMathSymbol{\varPsi}{\mathord}{letters}{9}
+ \re@DeclareMathSymbol{\varOmega}{\mathord}{letters}{10}
+
+\fi
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Extension (jkpex) Definition % largesymbols
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\DeclareMathAccent{\widearc}{\mathord}{largesymbols}{134}
+\DeclareMathAccent{\widearcarrow}{\mathord}{largesymbols}{140}
+\DeclareMathAccent{\wideOarc}{\mathord}{largesymbols}{140}
+\DeclareMathAccent{\wideparen}{\mathord}{largesymbols}{146}
+
+\newcommand{\widering}[1]{\overset{\smash{\vbox to .2ex{%
+ \hbox{$\mathring{}$}}}}{\wideparen{#1}}}
+
+\renewcommand{\int}{\intop\kp@ilimits}
+\renewcommand{\oint}{\ointop\kp@ilimits}
+
+\re@DeclareMathSymbol{\coprodop}{\mathop}{largesymbols}{96}
+ \def\coprod{\coprodop\kp@slimits}
+\re@DeclareMathSymbol{\bigveeop}{\mathop}{largesymbols}{87}
+ \def\bigvee{\bigveeop\kp@slimits}
+\re@DeclareMathSymbol{\bigwedgeop}{\mathop}{largesymbols}{86}
+ \def\bigwedge{\bigwedgeop\kp@slimits}
+\re@DeclareMathSymbol{\biguplusop}{\mathop}{largesymbols}{85}
+ \def\biguplus{\biguplusop\kp@slimits}
+\re@DeclareMathSymbol{\bigcapop}{\mathop}{largesymbols}{84}
+ \def\bigcap{\bigcapop\kp@slimits}
+\re@DeclareMathSymbol{\bigcupop}{\mathop}{largesymbols}{83}
+ \def\bigcup{\bigcupop\kp@slimits}
+\re@DeclareMathSymbol{\prodop}{\mathop}{largesymbols}{81}
+ \def\prod{\prodop\kp@slimits}
+\re@DeclareMathSymbol{\sumop}{\mathop}{largesymbols}{80}
+ \def\sum{\sumop\kp@slimits}
+\re@DeclareMathSymbol{\bigotimesop}{\mathop}{largesymbols}{78}
+ \def\bigotimes{\bigotimesop\kp@slimits}
+\re@DeclareMathSymbol{\bigoplusop}{\mathop}{largesymbols}{76}
+ \def\bigoplus{\bigoplusop\kp@slimits}
+\re@DeclareMathSymbol{\bigodotop}{\mathop}{largesymbols}{74}
+ \def\bigodot{\bigodotop\kp@slimits}
+\re@DeclareMathSymbol{\bigsqcupop}{\mathop}{largesymbols}{70}
+ \def\bigsqcup{\bigsqcupop\kp@slimits}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Math Extension A (jkpexa) Definition % largesymbolsA
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\re@DeclareMathSymbol{\bignplusop}{\mathop}{largesymbolsA}{0}
+ \def\bignplus{\bignplusop\kp@slimits}
+\re@DeclareMathSymbol{\bigsqcupplusop}{\mathop}{largesymbolsA}{2}
+ \def\bigsqcupplus{\bigsqcupplusop\kp@slimits}
+\re@DeclareMathSymbol{\bigsqcapplusop}{\mathop}{largesymbolsA}{4}
+ \def\bigsqcapplus{\bigsqcapplusop\kp@slimits}
+\re@DeclareMathSymbol{\bigsqcapop}{\mathop}{largesymbolsA}{6}
+ \def\bigsqcap{\bigsqcapop\kp@slimits}
+
+\def\narrowiints{\ifkp@narrowiints10\else0\fi}
+
+\re@DeclareMathSymbol{\oiintop}{\mathop}{largesymbolsA}{\narrowiints8}
+ \def\oiint{\oiintop\kp@ilimits}
+
+\def\narrowiints{\ifkp@narrowiints1\else0\fi}
+
+\re@DeclareMathSymbol{\ointctrclockwiseop}{\mathop}{largesymbolsA}{10}
+ \def\ointctrclockwise{\ointctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\ointclockwiseop}{\mathop}{largesymbolsA}{12}
+ \def\ointclockwise{\ointclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\sqintop}{\mathop}{largesymbolsA}{14}
+ \def\sqint{\sqintop\kp@ilimits}
+\re@DeclareMathSymbol{\varprod}{\mathop}{largesymbolsA}{16}
+%\re@DeclareMathDelimiter{\llbracket}{\mathopen}{symbolsC}{126}{largesymbolsA}{18}
+%\re@DeclareMathDelimiter{\rrbracket}{\mathclose}{symbolsC}{127}{largesymbolsA}{19}
+\re@DeclareMathSymbol{\br@cext}{\mathord}{largesymbolsA}{32}
+\re@DeclareMathSymbol{\iintop}{\mathop}{largesymbolsA}{\narrowiints33}
+ \def\iint{\iintop\kp@ilimits}
+\re@DeclareMathSymbol{\iiintop}{\mathop}{largesymbolsA}{\narrowiints35}
+ \def\iiint{\iiintop\kp@ilimits}
+\re@DeclareMathSymbol{\iiiintop}{\mathop}{largesymbolsA}{\narrowiints37}
+ \def\iiiint{\iiiintop\kp@ilimits}
+\re@DeclareMathSymbol{\idotsintop}{\mathop}{largesymbolsA}{\narrowiints39}
+ \def\idotsint{\idotsintop\kp@ilimits}
+\re@DeclareMathSymbol{\oiiintop}{\mathop}{largesymbolsA}{\narrowiints41}
+ \def\oiiint{\oiiintop\kp@ilimits}
+\re@DeclareMathSymbol{\varointctrclockwiseop}{\mathop}{largesymbolsA}{43}
+ \def\varointctrclockwise{\varointctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\varointclockwiseop}{\mathop}{largesymbolsA}{45}
+ \def\varointclockwise{\varointclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\fintop}{\mathop}{largesymbolsA}{62}
+ \def\fint{\fintop\kp@ilimits}
+\re@DeclareMathSymbol{\oiintctrclockwiseop}{\mathop}{largesymbolsA}{\narrowiints64}
+ \def\oiintctrclockwise{\oiintctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\varoiintclockwiseop}{\mathop}{largesymbolsA}{\narrowiints66}
+ \def\varoiintclockwise{\varoiintclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\oiiintctrclockwiseop}{\mathop}{largesymbolsA}{\narrowiints68}
+ \def\oiiintctrclockwise{\oiiintctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\varoiiintclockwiseop}{\mathop}{largesymbolsA}{\narrowiints70}
+ \def\varoiiintclockwise{\varoiiintclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\oiintclockwiseop}{\mathop}{largesymbolsA}{\narrowiints72}
+ \def\oiintclockwise{\oiintclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\varoiintctrclockwiseop}{\mathop}{largesymbolsA}{\narrowiints74}
+ \def\varoiintctrclockwise{\varoiintctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\oiiintclockwiseop}{\mathop}{largesymbolsA}{\narrowiints76}
+ \def\oiiintclockwise{\oiiintclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\varoiiintctrclockwiseop}{\mathop}{largesymbolsA}{\narrowiints78}
+ \def\varoiiintctrclockwise{\varoiiintctrclockwiseop\kp@ilimits}
+\re@DeclareMathSymbol{\sqiintop}{\mathop}{largesymbolsA}{\narrowiints80}
+ \def\sqiint{\sqiintop\kp@ilimits}
+\re@DeclareMathSymbol{\sqiiintop}{\mathop}{largesymbolsA}{\narrowiints82}
+ \def\sqiiint{\sqiiintop\kp@ilimits}
+\re@DeclareMathSymbol{\varintop}{\mathop}{largesymbolsA}{84}
+ \def\varint{\varintop\kp@ilimits}
+\re@DeclareMathSymbol{\variintop}{\mathop}{largesymbolsA}{\narrowiints86}
+ \def\variint{\variintop\kp@ilimits}
+\re@DeclareMathSymbol{\variiintop}{\mathop}{largesymbolsA}{\narrowiints88}
+ \def\variiint{\variiintop\kp@ilimits}
+\re@DeclareMathSymbol{\variiiintop}{\mathop}{largesymbolsA}{\narrowiints90}
+ \def\variiiint{\variiiintop\kp@ilimits}
+\re@DeclareMathSymbol{\varidotsintop}{\mathop}{largesymbolsA}{\narrowiints92}
+ \def\varidotsint{\varidotsintop\kp@ilimits}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Common Macros, too
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% Use math italic, not text, version of dot, in \vdots and \ddots definitions
+\def\vdots{\vbox{\baselineskip4\p@ \lineskiplimit\z@
+ \kern6\p@\hbox{$\m@th.$}\hbox{$\m@th.$}\hbox{$\m@th.$}}}
+\def\ddots{\mathinner{\mkern1mu\raise7\p@
+ \vbox{\kern7\p@\hbox{$\m@th.$}}\mkern2mu
+ \raise4\p@\hbox{$\m@th.$}\mkern2mu\raise\p@\hbox{$\m@th.$}\mkern1mu}}
+
+
+%%% For \underbrace and \overbrace:
+%%% use brace extenstion bar (in "20 of jkpexa) instead of vrule (Acroread Bug...)
+\re@DeclareMathSymbol{\br@cext}{\mathord}{largesymbolsA}{32}
+\def\downbracefill{$\m@th%
+ \braceld\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu%
+ \braceru\bracelu%
+ \mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\bracerd$}
+\def\upbracefill{$\m@th%
+ \bracelu\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu%
+ \bracerd\braceld%
+ \mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\braceru$}
+
+%%% \not redefined:
+%%% \not= becomes \ne
+%%% \not< becomes \nless
+%%% \not> becomes \ngtr
+%%% if \notXXX is defined, \not\XXX becomes \notXXX;
+%%% if \nXXX is defined, \not\XXX becomes \nXXX;
+%%% otherwise, \not\XXX is done in the usual way.
+\DeclareMathSymbol{\n@tch@r}{\mathrel}{symbols}{54}
+
+\DeclareRobustCommand*{\not}[1]{%
+ \ifx #1=\ne\else
+ \ifx #1<\nless\else
+ \ifx #1>\ngtr\else
+ \n@t@@n{#1}\fi\fi\fi}
+
+\def\n@t@@n#1{%
+ \begingroup \escapechar\m@ne\xdef\@gtempa{not\string#1}\endgroup%
+ \expandafter\@ifundefined{\@gtempa}%
+ {\not@n@{#1}}%
+ {\@nameuse{\@gtempa}}}
+\def\not@n@#1{%
+ \begingroup \escapechar\m@ne\xdef\@gtempa{n\string#1}\endgroup%
+ \expandafter\@ifundefined{\@gtempa}%
+ {\n@tch@r #1}%
+ {\@nameuse{\@gtempa}}}
+
+%%%%%%%%%%%%%%%%%%%
+% \D close integral
+%%%%%%%%%%%%%%%%%%%
+
+\ifkp@Dcommand
+ \DeclareMathSymbol{\kp@D}{\mathord}{operators}{100}
+ \def\D#1{\mathclose{\,\ifkp@upRm\kp@D%
+ \else\mathit{d}%
+ \fi}#1}
+\fi
+
+%%%%%%%%%%%%
+% new arrows
+%%%%%%%%%%%%
+
+\let\kp@ora\overrightarrow
+\def\overrightarrow#1{\,\kp@ora{#1\:}}
+
+\let\kp@ura\underrightarrow
+\def\underrightarrow#1{\,\kp@ura{#1\,}}
+
+\let\kp@ola\overleftarrow
+\def\overleftarrow#1{\kp@ola{\:#1}\,}
+
+\let\kp@ula\underleftarrow
+\def\underleftarrow#1{\kp@ula{\,#1}\,}
+
+%%%
+\fi %%% End of no-math option
+%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \classicstylenums and \olstylenums
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\classicstylenums#1{{\fontfamily{jkp\kp@stylemath\kp@famillem}\selectfont #1}}
+
+%%%
+
+\let\kp@osn\oldstylenums
+
+\ifkp@os
+ \ifkp@osm % fulloldstyle
+ \def\oldstylenums#1{#1}
+ \else
+ \ifkp@vosm % oldstyle and veryoldstylemath
+ \def\oldstylenums#1{#1}
+ \else % oldstyle
+ \def\oldstylenums#1{%
+ \relax\ifmmode\kp@osn{#1}%
+ \else#1\fi}
+ \fi
+ \fi
+\else
+ \ifkp@vos
+ \ifkp@vosm % fullveryoldstyle
+ \def\oldstylenums#1{#1}
+ \else
+ \ifkp@osm % veryoldstyle and oldstylemath
+ \def\oldstylenums#1{#1}
+ \else % veryoldstyle
+ \def\oldstylenums#1{%
+ \relax\ifmmode\kp@osn{#1}%
+ \else#1\fi}
+ \fi
+ \fi
+ \else
+ \ifkp@osm % oldstylemath
+ \def\oldstylenums#1{%
+ \relax\ifmmode#1%
+ \else\kp@osn{#1}\fi}
+ \else
+ \ifkp@vosm % veryoldstylemath
+ \def\oldstylenums#1{%
+ \relax\ifmmode#1%
+ \else\kp@osn{#1}\fi}
+ \fi
+ \fi
+ \fi
+\fi
+
+\endinput
+
+ \ No newline at end of file
diff --git a/Report/report/notation.tex b/Report/report/notation.tex
new file mode 100644
index 0000000..42fe734
--- /dev/null
+++ b/Report/report/notation.tex
@@ -0,0 +1,77 @@
+% quick way of adding a figure
+\newcommand{\fig}[3]{
+ \begin{center}
+ \scalebox{#3}{\includegraphics[#2]{#1}}
+ \end{center}
+}
+
+%\newcommand*{\point}[1]{\vec{\mkern0mu#1}}
+\newcommand{\ci}[0]{\perp\!\!\!\!\!\perp} % conditional independence
+\newcommand{\point}[1]{{#1}} % points
+\renewcommand{\vec}[1]{{\boldsymbol{{#1}}}} % vector
+\newcommand{\mat}[1]{{\boldsymbol{{#1}}}} % matrix
+\newcommand{\R}[0]{\mathds{R}} % real numbers
+\newcommand{\Z}[0]{\mathds{Z}} % integers
+\newcommand{\N}[0]{\mathds{N}} % natural numbers
+\newcommand{\nat}[0]{\mathds{N}} % natural numbers
+\newcommand{\Q}[0]{\mathds{Q}} % rational numbers
+\ifxetex
+\newcommand{\C}[0]{\mathds{C}} % complex numbers
+\else
+\newcommand{\C}[0]{\mathds{C}} % complex numbers
+\fi
+\newcommand{\tr}[0]{\text{tr}} % trace
+\renewcommand{\d}[0]{\mathrm{d}} % total derivative
+\newcommand{\inv}{^{-1}} % inverse
+\newcommand{\id}{\mathrm{id}} % identity mapping
+\renewcommand{\dim}{\mathrm{dim}} % dimension
+\newcommand{\rank}[0]{\mathrm{rk}} % rank
+\newcommand{\determ}[1]{\mathrm{det}(#1)} % determinant
+\newcommand{\scp}[2]{\langle #1 , #2 \rangle}
+\newcommand{\kernel}[0]{\mathrm{ker}} % kernel/nullspace
+\newcommand{\img}[0]{\mathrm{Im}} % image
+\newcommand{\idx}[1]{{(#1)}}
+\DeclareMathOperator*{\diag}{diag}
+\newcommand{\E}{\mathds{E}} % expectation
+\newcommand{\var}{\mathds{V}} % variance
+\newcommand{\gauss}[2]{\mathcal{N}\big(#1,\,#2\big)} % gaussian distribution N(.,.)
+\newcommand{\gaussx}[3]{\mathcal{N}\big(#1\,|\,#2,\,#3\big)} % gaussian distribution N(.|.,.)
+\newcommand{\gaussBig}[2]{\mathcal{N}\left(#1,\,#2\right)} % see above, but with brackets that adjust to the height of the arguments
+\newcommand{\gaussxBig}[3]{\mathcal{N}\left(#1\,|\,#2,\,#3\right)} % see above, but with brackets that adjust to the height of the arguments
+\DeclareMathOperator{\cov}{Cov} % covariance (matrix)
+\ifxetex
+\renewcommand{\T}[0]{^\top} % transpose
+\else
+\newcommand{\T}[0]{^\top}
+\fi
+% matrix determinant
+\newcommand{\matdet}[1]{
+\left|
+\begin{matrix}
+#1
+\end{matrix}
+\right|
+}
+
+
+
+%%% various color definitions
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+
+\newcommand{\blue}[1]{{\color{blue}#1}}
+\newcommand{\red}[1]{{\color{red}#1}}
+\newcommand{\green}[1]{{\color{darkgreen}#1}}
+\newcommand{\orange}[1]{{\color{orange}#1}}
+\newcommand{\magenta}[1]{{\color{magenta}#1}}
+\newcommand{\cyan}[1]{{\color{cyan}#1}}
+
+
+% redefine emph
+\renewcommand{\emph}[1]{\blue{\bf{#1}}}
+
+% place a colored box around a character
+\gdef\colchar#1#2{%
+ \tikz[baseline]{%
+ \node[anchor=base,inner sep=2pt,outer sep=0pt,fill = #2!20] {#1};
+ }%
+}%
diff --git a/Report/report/titlepage.tex b/Report/report/titlepage.tex
new file mode 100644
index 0000000..87077f1
--- /dev/null
+++ b/Report/report/titlepage.tex
@@ -0,0 +1,54 @@
+% Last modification: 2016-09-29 (Marc Deisenroth)
+\begin{titlepage}
+
+\newcommand{\HRule}{\rule{\linewidth}{0.5mm}} % Defines a new command for the horizontal lines, change thickness here
+
+
+%----------------------------------------------------------------------------------------
+% LOGO SECTION
+%----------------------------------------------------------------------------------------
+
+\includegraphics[width = 4cm]{./figures/imperial}\\[0.5cm]
+
+\begin{center} % Center remainder of the page
+
+%----------------------------------------------------------------------------------------
+% HEADING SECTIONS
+%----------------------------------------------------------------------------------------
+\textsc{\LARGE \reporttype}\\[1.5cm]
+\textsc{\Large Imperial College London}\\[0.5cm]
+\textsc{\large Department of Electrical and Electronic Engineering}\\[0.5cm]
+%----------------------------------------------------------------------------------------
+% TITLE SECTION
+%----------------------------------------------------------------------------------------
+
+\HRule \\[0.4cm]
+{ \huge \bfseries \reporttitle}\\ % Title of your document
+\HRule \\[1.5cm]
+\end{center}
+%----------------------------------------------------------------------------------------
+% AUTHOR SECTION
+%----------------------------------------------------------------------------------------
+
+%\begin{minipage}{0.4\hsize}
+\begin{flushleft} \large
+\textit{Authors:}\\
+\reportauthor~(email: \email) \\% Your name
+\reportauthora~(email: \emaila) \\% Your name
+\reportauthorb~(email: \emailb) \\% Your name
+\reportauthorc~(email: \emailc) \\% Your name
+\reportauthord~(email: \emaild) % Your name
+\end{flushleft}
+\vspace{2cm}
+\makeatletter
+Date: \@date
+
+\vfill % Fill the rest of the page with whitespace
+
+
+
+\makeatother
+
+
+\end{titlepage}
+
generated by cgit (git 2.34.1) at 2024-05-15 04:21:33 +0000