%This file contains all the macros used
%in the LaTeX port of the document cheat.pdf available
%in the TeX showcase.
%This boolean is true when output is DVI and false otherwise
\newtoggle{DVIOutput}
\togglefalse{DVIOutput}
\ifx\pdfoutput\@undefined
% no pdfTeX
\togglefalse{DVIOutput}
\else\ifnum\pdfoutput<1
%pdfTeX is outputting a .dvi file
\toggletrue{DVIOutput}
\else
%pdfTeX is outputting a .pdf file
\togglefalse{DVIOutput}
\fi\fi
%These lengths are used to specify the dimentions of the different columns
%of the tabular environment. These are useful to write code working on many
%page after the specific dimentions for the page have been assigned to them.
%Normally no page of the document has more than three columns even
%the page 2 but for the ease of typesetting it is useful
%to split the first logical column in three. Thus it is
%possible to have until 5 columns.
\newlength{\ColOne}
\newlength{\ColTwo}
\newlength{\ColThree}
\newlength{\ColFour}
\newlength{\ColFive}
%Theses length are mainly used to save the current similar
%values which can be locally modified.
\newlength{\BeforeFormulaSpace} % Will contain the space before a formula when it is displayed.
\newlength{\InterFormulaSpace} %Space between two lines of formulae displayed
%inside the 'DisplayFormulae' environment
\newlength{\DisLeftSkip}
\newlength{\DisParFillSkip}
\newlength{\DisParIndent}
%The length '\CurrentLineWidth' is the current width of a line.
%It is useful when a lot of data (like when writing
%formulae with "\Fm" macros) should be put on a line to
%know when inserting a break.
%
%This variable is mainly used in the macro "\LongEquation"
%and "\Fm" which have to put a maximum amount of text on a line.
\newlength{\CurrentLineWidth}
%The length \MathContentSize is used to setup the size of the parboxes
%containing the different mathematical elements of the page
\newlength{\MathContentSize}
%This length is useful to manipulate horizontal space
\newlength{\HSpace}
%This length is useful to manipulate vertical space at different
%place
\newlength{\VSpace}
%This is a temporary length usable for computation inside macro
\newlength{\TmpLengthA}
%A temporary counter for a local usage
\newcounter{tmpCountA}
%A counter used to contain the number of blank lines
%to add in a table from the 'nicematrix' package.
\newcounter{NbBlankLines}
%Some new counters are usefuls to number equations and formulaes
%The counter 'DisplayFormulaNb' is the number of the current displayed formulae
\newcounter{DisplayFormulaNb}
%The enumerated type describing the style to display the number
%of the formulae. The values are:
% 0 without number
% 1 regular
% 2 bold
\chardef\StyleWithoutNumber=0
\chardef\StyleRegular=1
\chardef\StyleBold=2
\chardef\DisNumberStyle=\StyleWithoutNumber
%Enumerated type to indicate if the formula should be typeset
%in display style (with bigger characters) or without change
\chardef\SmallChar=1
\chardef\BigChar=0
\chardef\DisDisplay=\BigChar
%This box is useful to store a formula which can
%be moved after composition.
\newsavebox\FormulaBox
%Three temporary boxes (for use in a macro)
\newsavebox\TmpBoxA
\newsavebox\TmpBoxB
\newsavebox\TmpBoxC
%This box contains the Escher's impossible brick on page 10
\newsavebox\ImpossibleBrick
%------------------------------------------------------------------------------
%
% Macros definition
%
%------------------------------------------------------------------------------
%This TeX (and not LaTeX) macro does nothing but it can be used
%inside other macro to achieve some effects. It is declared here just
%to be certain that the name will be unique.
\def\cheatTmpMacro{\relax}
%This command define the separator of thousands (this one is different in differents
%regions/country)
\newcommand\SepMillier{\,}
%Similary the decimal separator is different in different country.
\newcommand\SepDecimal{{,}}
%The following macros modify the space typeset by LaTeX before and after
%a formula in display math.
%
%The command has two parameter
% 1) the new space to use in normal mode (symmetric for above and below)
% 2) the new space to use for short mode (the mode is short when
% the line of text before is shorter than the width of formula).
\newcommand\DisplaySpace[2]{%
\deflength{\abovedisplayskip}{#1}%
\deflength{\belowdisplayskip}{#1}%
\deflength{\abovedisplayshortskip}{#2}%
\deflength{\belowdisplayshortskip}{#2}%
}
%Define a new environment useful to typeset formulae in a more or less free
%style.
%
%This environment has 5 parameters:
% 1) The number to use when displaying the first formula
% (generally 1 except when a sequence of formula should
% be continued)
% 2) The horizontal space to let before a formula.
% 3) The dimention which should separate two formulae
% 4) An enumerated value to define the style of displaying
% the formula (standard mode, display mode etc.)
% 5) An enumerated type to specify the style (bold, regular...) of the number of the
% formula.
\newenvironment{DisplayFormulae}[5]{%Begin definitions
\newbool{FirstFormula}%
\booltrue{FirstFormula}%
\newbool{PrintEquation}% true if the formula should be typeset
% and printed, when fals it is only typeset
% (useful to know its width)
\booltrue{PrintEquation}%
\newbool{Inline}%When true, the formula is not typeset in a box
%but simply typed inline. Rarely used but useful
%if the formula is surrounded by some text.
\boolfalse{Inline}%
\deflength\CurrentLineWidth{0pt}%
\defcounter{DisplayFormulaNb}{#1}%
% Since this counter is automatically incremented before
% to typeset a formula
\defcounter{DisplayFormulaNb}{\value{DisplayFormulaNb}-1}%
\deflength{\BeforeFormulaSpace}{#2}%
\deflength{\InterFormulaSpace}{#3}%
\chardef\DisDisplay=#4%
\chardef\DisNumberStyle=#5%
\deflength{\DisLeftSkip}{\leftskip}%
\deflength{\DisParFillSkip}{\parfillskip}%
\deflength{\DisParIndent}{\parindent}%
\deflength{\parindent}{0pt}%
\deflength{\leftskip}{0pt}%
\deflength{\parfillskip}{0pt}%
\par\unskip
\begin{sloppypar}\raggedright\noindent\unskip
}{%End definitions
\par\end{sloppypar}\noindent
\setlength{\leftskip}{\DisLeftSkip}%
\setlength{\parfillskip}{\DisParFillSkip}%
}
%This macro put a new line when writing formulae with the
%\Fm family of macro inside an environment 'DisplayFormulae'
%The macro has one parameter
% 1)The height to force at the begining of a paragraph
% This forces an interline with a rule. This parameter
% is optionnal and its default value is '\InterFormulaSpace'
%
%This macro uses the global (to itself) length
%'\CurrentLineWidth'
\newcommand\NewParFormulae[1][\InterFormulaSpace]{%
\par
%To force the desired space between formulae
\rule{0pt}{#1}%
\unskip\noindent\unskip}
%This macro is the separator of formulae. Normally
%it is empty but it can be redefined to set a specific
%separator if needed.
%
%This macro is executed in math mode
\newcommand\FmSep{\relax}
%This macro is used to display a formula inside an environment
%"DisplayFormulae". It will work correctly only in that
%environement which provide a way to use global variables (to this
%macro) to keep some states between its different calls.
%
%It has two parameters:
% 1) A boolean value which, when it is true, indicates
% that the formula should be printed inline
% with some other text (but the formula is still
% typeset in LR box). For this to work correctly,
% it is sufficient that the length '\CurrentLineWidth'
% being set to a length of 0pt. This is like the
% first equation on a line and the equation is simply
% printed without adding anything.
% This parameter is optionnal and its default value is 'false'.
% 2) The formula to display. The formula
% is typeset in math mode.
%
%This macro uses and update the global (to the macro)
%length "\CurrentLineWidth" (which indicate the next point
%where to put text on the current line).
%
%The global variable (defined inside the
%'DisplayFormulae' environment) '\DisNumberStyle' is used too,
%to determine how the equation should be typeset (with or without
%numbering for instance).
%
%!! Be careful !!
%When not in inline mode, this macro skips all the blanks
%before it. This is useful to avoid spurious blanks introduced
%somewhere before the call to this macro.
\newcommand\Fm[2][false]{%
\setbool{Inline}{#1}%
\ifbool{Inline}{\deflength{\CurrentLineWidth}{0pt}}{%
%Not Inline:
\unskip\noindent\unskip
}%
\defcounter{DisplayFormulaNb}{\value{DisplayFormulaNb}+1}%
\WriteFormula{\the\CurrentLineWidth}{\CurrentLineWidth}{#2}{true}%
%Since a formula is written, we are no more on the first formula.
\boolfalse{FirstFormula}%
}%
%This command do really the job of typesetting the formula
%It has 5 parameters:
% 1) A white space to be put before the equation.
% If this value is greater than 0pt, the equation is
% considered to be part of a multipart equation
% (but it is not its first part).
%
% This means that a space of that dimention is simply added
% before the equation and the equation is printed.
% If the width of the text with the added space before
% the equation is wider than the available space, the equation
% is simply typeset right justified.
%
% This parameter is optionnal and its value is 0pt.
% 2) The current position on the line
% 3) A variable of type dimen to contain the new
% point of insertion in the printed line (where
% the next equation could be typesetted).
% 4) The formula to type
% 5) A boolean value which when it is true indicates that
% the equation should be printed. Otherwise the equation
% is typesetted but not printed. This is useful to
% know the width of the printed equation, but without
% printing it in the text.
\newcommand\WriteFormula[5][0pt]{%
\begingroup%To protect the global boxes and variables used
%in this macro.
\deflength{\CurrentLineWidth}{#2}%The current position on the line
\setbool{PrintEquation}{#5}%
\ifdimequal{#1}{0pt}%
{%Normal case when one has to print a std equation
\ifdimgreater{\CurrentLineWidth}{0pt}{%Already some text on the line
%we add the space between the formula.
\ifbool{PrintEquation}{%
\hspace{\InterFormulaeSkip}%
\deflength{\CurrentLineWidth}{\CurrentLineWidth+\InterFormulaeSkip}%
}{}%
}{}%
\savebox\FormulaBox{%
\hspace*{\BeforeFormulaSpace}%
\ifnum\DisNumberStyle=\StyleBold
\textbf{\arabic{DisplayFormulaNb}.~}%
\else
\ifnum\DisNumberStyle=\StyleRegular
\arabic{DisplayFormulaNb}.~%
\fi
\fi
\ensuremath{%
\ifnum\DisDisplay=\BigChar\displaystyle\fi
%Typeset the equation and call the macro to
%add a separator between the equations.
#4\FmSep}%
}%
\settowidth{\HSpace}{\usebox\FormulaBox}%
\deflength\CurrentLineWidth{\CurrentLineWidth+\HSpace}%
\ifdimgreater{\CurrentLineWidth}{\linewidth}%
{%Force a new paragraph
\ifbool{PrintEquation}{\NewParFormulae}{}%
\deflength{\CurrentLineWidth}{\HSpace}%Since the formula is the only text on the line
}{}%
}{%The second part of the equation should be printed
\savebox\FormulaBox{%
\ensuremath{%
\ifnum\DisDisplay=\BigChar\displaystyle\fi
%Typeset the second part of the equation
%but add the white space before it.
\makebox[#1][l]{}#4\FmSep\relax
}%
}%
\settowidth{\HSpace}{\usebox\FormulaBox}%
\deflength{\CurrentLineWidth}{\HSpace}%
\ifdimgreater{\CurrentLineWidth}{\linewidth}%
{%With the space added before it,
%the second part of the equation is wider
%than the available space. We simply put
%the equation right aligned
\savebox\FormulaBox{%
\makebox[\linewidth][l]{%
\ensuremath{%
\ifnum\DisDisplay=\BigChar\displaystyle\fi
%Typeset the second part of the equation without
%the preceding blank space and force the right alignment
\hfill #4\FmSep\relax
}%
}%
}%
\settowidth{\HSpace}{\usebox\FormulaBox}%
%Since the line is pushed to the right of space, the line
%is full.
\deflength{\CurrentLineWidth}{\linewidth}%
}{}%
}%
\ifbool{PrintEquation}{\usebox\FormulaBox}{}%Print the formula in the document
%\HSpace is the width of the box containing the typeseted formula.
\ifdimgreater{\HSpace}{\linewidth}%
{\typeout{^^J==Info The text of this equation:^^J#4^^J%
is wider than the width of the text. Please split it manually.}%
}{}%
\edef\mytemp{\endgroup
\noexpand\deflength{#3}{\the\CurrentLineWidth}%
}%
\mytemp %Close the group and set the value of the
%insertion point of the next equation.
}
%The following macro is similar to '\Fm' but write only
%the first part of an equation. When an equation is spiltted in two parts,
%the first part starts always on a new line (except if this is
%the first equation of a group of equations, to avoid extra blank
%space).
%
%The macro has one parameter:
% 1) The first part of the equation
% The formula is typeset in math mode.
\newcommand\FmPartA[1]{%
\begingroup
%A group can be used since this command should always be used
%with '\FmPartB' and the fact that the \CurrentLineWidth is not
%updated (due to the group) is without importance since the next
%text will be the second part of the equation on a new line.
%Force equation on a new line except if this is the first equation.
\ifbool{FirstFormula}{%First formula
}{%No more the first formula, a new line is forced
\NewParFormulae%
}%
\deflength{\CurrentLineWidth}{0pt}%Since this equation starts
%on a new line
%There must be no separator of equation between the two part of
%a splitted equation
\def\FmSep{\relax}%
\Fm{#1}%
\endgroup
}
%The following macro is similar to '\Fm' but write only
%the second part of an equation
%
%The macro has two parameters:
% 1) Some text which will be used to determine the horizontal
% offset to let before writing the second part of the equation
% 2) The second part of the equation
%The formulae are typeset in math mode.
\newcommand\FmPartB[2]{%
%Start on a new line.
\NewParFormulae
%Typeset the first part of the equation without printing it
%to get the length of the first part in \TmpLengthA
\WriteFormula{0pt}{\TmpLengthA}{#1}{false}%
%Print the second (or following) part of the equation by
%adding a blank space corresponding to the width of the
%first part. The parameter with a length of 0pt
%reflects the fact that the equation start at the beginning
%of the line (after the \NewParFormulae}.
\WriteFormula[\TmpLengthA]{0pt}{\CurrentLineWidth}{#2}{true}%
%A blank character seems to be present, it is suppressed
%now
\unskip
}
%This macro is useful to indicate that no specific typeseting
%should be done (and the default typesetting should be used instead)
\newcommand\DoNothing{}
%This macro is made to display the long equations (where 2 equal signs are used
%to separate part of equation)
%The macro has 5 parameters
% 1) Any parameter expanding to something prevents
% the addition of space before equation. Otherwise
% a space of "\SpaceBeforeLongEq" is added
% 2) The formula until the first equal sign
% 3) The formula beteween the two equal sign
% 4) The formula after the last equal sign
% 5) The width of the line where the long equation should be typeset.
%
%If for some reason there is less than 2 equal signs, the corresponding
%parameters should be empty.
%
%This macro uses the global boxes "\TmpBoxA" and \TmpBoxB".
%This macro uses the global length "\CurrentLineWidth" and "\HSpace"
%
\newcommand\LongEquation[5][{\DoNothing}]{%
\begingroup
\deflength{\CurrentLineWidth}{#5}%
\par
\ifdefempty{#1}{\AdjustSpace{\SpaceBeforeLongEq}}{}%
\noindent
\def\temp{#3}%
\ifx\temp\empty
%Second parameter empty, the first part of equation is simply printed.
$#2$%
\else
%Second parameter not empty
\savebox\TmpBoxA{$#2=#3$}%
\settowidth\HSpace{\usebox\TmpBoxA}%
\ifnum\HSpace>\CurrentLineWidth
$#2=$\\\mbox{}\hfill
\savebox\TmpBoxA{$#3$}%
\fi
\def\temp{#4}%
\ifx\temp\empty
%Third parameter empty the formula until this parameter is typeset
\usebox\TmpBoxA
\else
%Third parameter not empty
\savebox\TmpBoxB{$#2=#3=#4$}%
\settowidth{\HSpace}{\usebox\TmpBoxB}%
\ifnum\HSpace>\CurrentLineWidth
\usebox\TmpBoxA=\\\mbox{}\hfill
$#4$%
\else
\usebox\TmpBoxB
\fi
\fi
\fi
\endgroup
}
%This command add or remove vertical space
%
%The command has 1 parameter
% 1) The length for the space to add or remove
\newcommand\AdjustSpace[1]{\par %to force vertical mode
\vspace{#1}\noindent\ignorespaces\par}
%This command assign a counter with the biggest of three numbers.
%
%The macro has 4parameters:
% 1) The name of the resulting counter.
% This parameter is optionnal and its name is
% 'NbBlankLines'
% 2-4) The three values to check
\newcommand\BiggestNbLines[4][NbBlankLines]{%
\defcounter{#1}{#2}%The biggest is the first
\ifnumless{\value{#1}}{#3}{%first < second
%The biggest is the second number
\defcounter{#1}{#3}%
}{}
\ifnumless{\value{#1}}{#4}{%The current biggest < third
%the biggest is the third number
\defcounter{#1}{#4}%
}{}
}
%This command adds few blank lines in a table. It is particularly useful
%with the 'nicematrix' package where it is often necessary to add few lines
%to be able to use block on many lines.
%
%The macro has two parameters:
% 1) The number of lines to add
% 2) A macro to add the lines
%
%This command uses the global counter 'NbBlankLines' and the macro
%'\cheatTmpMacro'.
\newcommand\AddBlankLines[2]{%
\defcounter{NbBlankLines}{#1}%
\def\cheatTmpMacro{\relax}%
\whileboolexpr{test {\ifnumcomp{\value{NbBlankLines}}{>}{0}}}%
{\defcounter{NbBlankLines}{\value{NbBlankLines}-1}%
\edef\cheatTmpMacro{\cheatTmpMacro #2}}%
\cheatTmpMacro
}
%This command is used to setup the style of the numerous
%small titles used in the page.
%
%The command has one parameter
% 1) The text of the intertitle
\newcommand\IntertitleShape[1]{%
\textit{#1}%
}
%This command add some remarks about a math formula.
%It is very useful to add some text like "a>0"
%
%The macro has two parameters
% 1) The separator to typeset before the remark. This parameter
% is optionnal and has the value of '\text{,}\enspace'
% 2) The text of the remark, which will be typeset
% in math mode. One has to use the AMS command
% '\text' to typeset in text mode
\newcommand\MathRemark[2][\text{,}\enspace]{\unskip\ensuremath{#1#2}}
%This command add the infinitesimal difference after a math expression
%It is very useful to have consistent spacing
%before the 'dx'.
%The command has one parameter:
% 1) The letter to use. This parameter is typeset
% in math mode and it is optionnal. Its
% default value is 'x'
\newcommand\dx[1][x]{\unskip\ensuremath{\,d#1}}
%This command is used to typeset a variable followed
%by the infinitesimal difference dx
%
%This command has one parameter
% 1) The letter to use for the variable.
% This text is typeset in math mode This parameter
% is optional and its value is 'x'
\newcommand\xdx[1][x]{\ensuremath{#1\dx}}
%
%This command is intended to stack two characters
%with some vertical space between them.
%
%The command has 4 parameters:
% 1) a left delimiter (might be empty)
% 2) a right delimiter (might be empty)
% 3) the "numerator" character
% 4) the "denominator" character
%
%The idea is taken from here:
%https://tex.stackexchange.com/questions/119096/on-atop-again-how-to-obtain-the-same-result-without-warning
%
%The syntax of \genfrac macro is:
%\genfrac{<left-delim>}{<right-delim>}{<thickness>}{<mathstyle>}{<numerator>}{<denominator>}
\newcommand\Empile[4]{%
\genfrac{#1}{#2}{\z@}{}{#3}{#4}%
}
%Macros defined in the original document
\newcommand\titleTable{\textbf{\rule[-2ex]{0pt}{6ex}\large Mathematical formul�� and facts}}
\newcommand\Real{\iftutex\BbbR\else\mathbb{R}\fi} %���
\newcommand\Natural{\iftutex\BbbN\else\mathbb{N}\fi} %���
\newcommand\Z{\iftutex\BbbZ\else\mathbb{Z}\fi} %���
\newcommand\Par{\par\vskip 3pt}
\newcommand\centertwo[2]{\line {\hss #1\hss #2\hss}}
\newcommand\centerthree[3]{\line {\hss #1\hss #2\hss #3\hss}}
\newcommand\sign{\hbox{\rm sign}}
\newcommand\etc{$\ldots$}
\newcommand\Ldots{,\ldots,}
\newcommand\Hrule{\vskip 3pt\hrule\vskip 3pt}
\newcommand\Or{\vee}
\newcommand\E{\iftutex\BbbE\else\mathbb{E}\fi} %Expectation (in probabilities)
\newcommand\abs{\mathop{\rm abs}\nolimits}
\newcommand\perm{\mathop{\rm perm}\nolimits}
\newcommand\sech{\mathop{\rm sech}\nolimits}
\newcommand\csch{\mathop{\rm csch}\nolimits}
\newcommand\arccot{\mathop{\rm arccot}\nolimits}
\newcommand\arcsec{\mathop{\rm arcsec}\nolimits}
\newcommand\arccsc{\mathop{\rm arccsc}\nolimits}
\newcommand\arcsinh{\mathop{\rm arcsinh}\nolimits}
\newcommand\arccosh{\mathop{\rm arccosh}\nolimits}
\newcommand\arctanh{\mathop{\rm arctanh}\nolimits}
\newcommand\arccoth{\mathop{\rm arccoth}\nolimits}
\newcommand\arcsech{\mathop{\rm arcsech}\nolimits}
\newcommand\arccsch{\mathop{\rm arccsch}\nolimits}
\iftutex %16bits TeX
%lAngle,rAngle are defined in unicode-math
\newcommand\Euls[2]{\ensuremath{\Empile{\lAngle}{\rAngle}{#1}{#2}}}
%but not in Lucida
\ifnum\PoliceDocument=\PoliceLucida
\renewcommand\Euls[2]{\bigg\langle\!\!\!\bigg\langle{#1 \atop #2} \bigg\rangle\!\!\!\bigg\rangle}
%and dejavusans
\else
\ifnum\PoliceDocument=\PoliceDejavuSans
\renewcommand\Euls[2]{\bigg\langle\!\!\!\bigg\langle{#1 \atop #2} \bigg\rangle\!\!\!\bigg\rangle}
\fi
\fi
\else %8 bits TeX.
%Use of the TeX definition.
\newcommand\Euls[2]{\bigg\langle\!\!\!\bigg\langle{#1 \atop #2} \bigg\rangle\!\!\!\bigg\rangle}
\fi
\newcommand\ramsey{\mathop{\rm r}\nolimits}
\newcommand\Var{\mathop{\rm Var}\nolimits} %variance (prob and stat)
\newcommand\SousEnsemble[2]{\ensuremath{\Empile{\{}{\}}{#1}{#2}}}
\newcommand\Cycle[2]{\cycle{#1}{#2}}
\newcommand\cycle[2]{\ensuremath{\Empile{[}{]}{#1}{#2}}}
\newcommand\Eul[2]{\eul{#1}{#2}}
\newcommand\eul[2]{\ensuremath{\Empile{\langle}{\rangle}{#1}{#2}}}
\newcommand\fivrm{}
\newcommand\euls[2]{\Euls{#1}{#2}}
\newcommand\ValAbs[1]{\lvert#1\rvert} %absolute value
%Commands used to make the title page.
%This document could be typeset many times with each time a different
%font. Then each produced document will be merged into one.
%This is useful to show a large set of fonts.
%
%In this latter case, it is important to be able to deactivate
%some parts of the title which will be otherwise redundant.
\newbool{FullTitle}
\booltrue{FullTitle}%When true all the title is typeset, otherwise
%only the name of the used font is displayed
%The font to use for the name of the package (this font should be adapted,
%if possible, to a very big character used a title).
\newcommand\TitleFontFile{QTHelvet-BoldOutline.otf}
\IfFontExistsTF{\TitleFontFile}%
{\newfontface\PackageNameFnt{\TitleFontFile}}{\newcommand\PackageNameFnt{\relax}}
%This command typeset the main title and the full name of the package
%The command has no parameter
\newcommand\PackageName{%
\ifbool{FullTitle}%
{%
\par\centerline{\PackageNameFnt\fontsize{50pt}{55pt}\selectfont MathTrip}\par
}{}%
}
%A short quote to go with the package name (and the main title)
\newcommand\TitleQuote{%
\ifbool{FullTitle}%
{%
\begin{flushright}%
\parbox[t]{20em}{%
%\fontsize{20pt}{24pt}\selectfont
La pente, d��j�� verticale, se redressait encore.
\par
%\fontsize{16pt}{18pt}\selectfont\itshape
\textit{\small The slope, already vertical, was still rising.}
\begin{flushright}
Georges Livanos (french alpinist)
\end{flushright}%
}%
\end{flushright}%
}{}%
}
%The version of the document
\newcommand\Version{2.8}