new latex package frege (15jul12)

git-svn-id: svn://tug.org/texlive/trunk@27106 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 787 insertions, 0 deletions

diff --git a/Master/texmf-dist/doc/latex/frege/GNU.txt b/Master/texmf-dist/doc/latex/frege/GNU.txt
new file mode 100644
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--- /dev/null
+++ b/Master/texmf-dist/doc/latex/frege/GNU.txt
@@ -0,0 +1,340 @@
+		    GNU GENERAL PUBLIC LICENSE
+		       Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
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diff --git a/Master/texmf-dist/doc/latex/frege/README b/Master/texmf-dist/doc/latex/frege/README
new file mode 100644
index 00000000000..cac3957a85e
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+frege.sty - a LaTeX2e package for typesetting begriffsschrift
+
+This package is based on begriff.sty released under the GNU General Public License. 
+Copyright (C) 2003 by Josh Parsons <josh@coombs.anu.edu.au>
+
+Changes with respect to begriff.sty
+
+correct relative lengths of the content stroke with respect to other strokes attached 
+to it;
+content strokes point at the middle of the following symbols, rather than the bottom;
+greater width for the assertion stroke as compared to the content stroke;
+a more intuitive structure for the conditional (arguments are now given in the same 
+order as they appear on the left of a completed formula);
+the command for the conditional with empty arguments now results in a vertical line 
+(conditional stroke) on it's own the other strokes are added as the arguments;
+the linewidth is properly accounted for so that things remain properly centered when 
+scaled;
+
+frege.sty defines the following basic commands:
+\Fcontent[1]       - plain content stroke
+\Fncontent[1]      - negated content stroke
+\Fnncontent[1]     - twice negated content stroke
+\Faconten[1]       - asserted content stroke
+\Fancontent[1]     - asserted negated content stroke
+\Fanncontent[1]    - asserted twice negated content stroke
+\Fquant[1]{a}      - content stroke with quantifier
+\Fnquant[1]{a}     - negated quantifier
+\Fnnquant[1]{a}    - twice negated quantifier
+\Fquantn[1]{a}     - quantifier with negated content
+\Fquantnn[1]{a}    - quantifier with twice negated content
+\Fnquantn[1]{a}    - negated quantifier with negated content
+\Fnquantnn[1]{a}   - negated quantifier with twice negated content
+\Fnnquantn[1]{a}   - twice negated quantifier with negated content
+\Fnnquantnn[1]{a}  - twice negated quantifier with twice negated content
+\Faquant[1]{a}     - asserted content stroke with quantifier
+\Fanquant[1]{a}    - asserted negated quantifier
+\Fannquant[1]{a}   - asserted twice negated quantifier
+\Faquantn[1]{a}    - asserted quantifier with negated content
+\Faquantnn[1]{a}   - asserted quantifier with twice negated content
+\Fanquantn[1]{a}   - asserted negated quantifier with negated content
+\Fanquantnn[1]{a}  - asserted negated quantifier with twice negated content
+\Fannquantn[1]{a}  - asserted twice negated quantifier with negated content
+\Fannquantnn[1]{a} - asserted twice negated quantifier with twice negated content
+
+while this may look like a daunting list think of it as just two commands:
+\Fcontent[1]       - generates a content stroke
+\Fquant[1]{a}      - generates a quantifier with variable a
+
+Adding an "a" after the "\F" adds an assertion stroke to the front of the command, 
+this may be followed by one two or no "n" to add one two or no negations to the 
+stroke. Next comes the name of the command either "content" or "quant". "quant" may 
+then be followed by another one two or no "n" which will add one two or no negations 
+after the quantifier to it's content stroke. All commands may be used in either text 
+or math mode. All the above commands produce output of the same length and may be 
+arbitrarly combined to produce longer composite formulas. Since version 1.1 each of 
+the basic strokes also has an optional argument with default value one, that scales 
+the total length of the stroke (\Fbaselength), so that an optional argument of [.5] 
+will produce a stroke half as long. Warning: setting a length shorter than what is 
+needed to fit all the options of a stroke leads to negative lengths and hence 
+unpredictable results.
+
+frege.sty defines the following more complex commands:
+\Fconditional[<option>]{<consequent>}{<antecedent>}
+\Fbox{<begriffsschrift formula with at least one conditional>}
+\Fbracket{<begriffsschrift formula with at least one conditional>}
+\Fargument[<premise 0>]{<premise 1>}{<premise 2>}{<conclusion>}
+\Fstrut[1]
+
+The final two have been added in version 1.2.
+
+The "Fconditional" command requires a mixture of the commands defined by frege.sty 
+and normal mathmode input to produce begriffsschrift. A implies B would be written 
+like this: 
+
+\Fconditional[\Facontent]{\Fcontent B}{\Fcontent A}
+
+This produces the two dimensional fregean conditional symbol with B lined up above A. 
+In addition the "Fconditional" command may be arbitrarily nested to produce any 
+begriffsschrift formula possible. Only the unnested conditional requires the optional 
+argument.
+
+"Fbracket" is just the same as "\left(\Fbox\right)" everything said about "Fbox" 
+applies equally to "Fbracket". A completed formula of begriffsschrift that includes 
+at least one conditional, should always be placed in an "Fbox" this ensures it is 
+given enough space in the output behaves correctly with respect to the text around it 
+and works correctly within environments such as align*.
+
+"Fargument" arranges two begriffsschrift formulas above each other and seperates them 
+from a third by a horizontal line. The option is for the name of a premise written 
+elsewhere and will outout (name): to the left of the horizontal line.
+
+"Fstrut" is like a invisible content stroke. Like all other basic strokes, it may be 
+scaled using it's optional argument. Fstrut is to be used in conjunction with 
+Fargument to ensure the formulas line up properly.
+
+The final result may also be modified by changing the following lengths using the 
+\setlength{<lengthname>}{<value>} command. The lengths and there default values are 
+given as follows:
+
+length:         default value:  description:
+\Fbaselength    20pt            the length of a single basic stroke
+\Flinewidth     0.5pt           the width of all lines other than the assert stroke
+\Fspace         2pt             seperation between begriffsschrift and text/formula
+\Fassertwidth   3\Flinewidth    the width of the assert stroke
+\Fraiseheight   1ex-\Flinewidth the height of content strokes above the baseline
+\Fnegsep        3\Flinewidth    the sepparation between a double negation
+\Fnegshort      2\Flinewidth    the space between negation stroke and baseline
+\Fquantwidth    6pt             width of the semi circular quantifier depression
+
+For more examples see accompanying manual (Frege.pdf or Frege.tex)
+Everything released under GNU General Public License.
diff --git a/Master/texmf-dist/doc/latex/frege/frege.pdf b/Master/texmf-dist/doc/latex/frege/frege.pdf
new file mode 100644
index 00000000000..276ae09e2c9
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/frege/frege.pdf
diff --git a/Master/texmf-dist/doc/latex/frege/frege.tex b/Master/texmf-dist/doc/latex/frege/frege.tex
new file mode 100644
index 00000000000..36b0041286f
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/frege/frege.tex
@@ -0,0 +1,336 @@
+\documentclass[12pt]{article}
+\usepackage{frege}
+\usepackage{amsmath}
+
+%% For condensed itemize:
+\newcommand{\squishlist}{
+  \begin{list}{$\bullet$}{
+    \setlength{\itemsep}{0pt}
+    \setlength{\parsep}{0pt}
+    \setlength{\topsep}{0pt}
+    \setlength{\partopsep}{0pt}
+    \setlength{\leftmargin}{1em}
+    \setlength{\labelwidth}{1em}
+    \setlength{\parskip}{0pt}
+    \setlength{\partopsep}{0pt}
+    \setlength{\rightmargin}{0pt}
+    \setlength{\labelsep}{0.5em}}}
+\newcommand{\squishlistend}{\end{list}}
+
+\title{frege.sty \\ A \LaTeXe Package for Typesetting Begriffsschrift}
+\author{Quirin Pamp \\ \texttt{Quirin.Pamp.2009@my.bristol.ac.uk}}
+
+\begin{document}
+\maketitle
+\section{Background}
+\subsection{begriff.sty}
+  This package is based on begriff.sty released under the GNU General Public 
+  License. 
+  Copyright (C) 2003 by Josh Parsons (josh@coombs.anu.edu.au) with changes made in 
+  October 2004 by Richard Heck (heck@fas.harvard.edu) and minor changes by Josh 
+  Parsons to fix a problem with linespacing made in May 2005.
+
+  While I could not have done so without the aforementioned work, I have reworked the 
+  package from the ground up, to the point where some of the underlying approaches 
+  have changed. On the downside this means there is no simple way of converting 
+  anything typeset using begriff.sty to use this package instead. I felt this was 
+  necessary to achieve a end result I was happy with.
+
+\subsection{GNU General Public License}
+  This package and all accompanying documentation is released under the GNU General 
+  Public License. It is free software; you can redistribute it and/or modify it under 
+  the terms of the GNU General Public License as published by the Free Software 
+  Foundation; either version 2 of the License, or (at your option) any later version.
+
+  This program is distributed in the hope that it will be useful, but WITHOUT ANY 
+  WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A 
+  PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License along with this 
+  program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - 
+  Suite 330, Boston, MA 02111, USA. (or just search for it online... Seriously.)
+
+\subsection{Changes as Compared to begriff.sty}
+  \squishlist
+    \item correct relative lengths of the content stroke with respect to other 
+      strokes attached to it;
+    \item content strokes point at the middle of the followint symbols, rather 
+      than the bottom;
+    \item greater width for the assertion stroke as compared to the content stroke;
+    \item a more intuitive structure for the conditional (arguments are now given in 
+      the same order as they appear on the left of a completed formula);
+    \item the command for the conditional with empty arguments now results in a 
+      vertical line (conditional stroke) on it's own the other strokes are added as   
+      the arguments;
+    \item the linewidth is properly accounted for so that things remain properly 
+      centered when scaled;
+  \squishlistend
+
+\subsection{Changes in Version 1.1}
+  \squishlist
+    \item added a optional scale factor to all basic strokes;
+    \item simplified the code for Fbracket in terms of that for Fbox;
+    \item rearranged the code in the style file in a more logical way;
+  \squishlistend
+
+\subsection{Changes in Version 1.2}
+  \squishlist
+    \item added a new command ``Fargument'' for typesetting arguments;
+    \item added a new command ``Fstrut'' to be used in conjunction with Fargument;
+    \item changed Fbaselength to be equal to the full length of a basi stroke (20pt);
+    \item fixed a bug where the scale factor introduced in version 1.1 does not reset 
+      after all uses;
+  \squishlistend
+
+\subsection{Changes and Features yet to come}
+  \squishlist
+    \item incorporation of other frege related material such as fge.sty so as to put 
+      all frege related material in a single package;
+    \item a vertical shorthand stroke such as used by Frege for typesetting arguments 
+      in ``Begriffsschrift'';
+  \squishlistend
+
+\section{Features and Usage}
+\subsection{Commands}
+\subsubsection{Basic Commands}
+  The following is a list of the basic commands provided by this package along with 
+  accompanying output. The conditional is treated sepperately.
+  \begin{flalign*}
+    &\mbox{\textbackslash Fcontent[1]} & &\Fcontent & & &\\
+    &\mbox{\textbackslash Fncontent[1]} & &\Fncontent\\
+    &\mbox{\textbackslash Fnncontent[1]} & &\Fnncontent\\
+    &\mbox{\textbackslash Facontent[1]} & &\Facontent\\
+    &\mbox{\textbackslash Fancontent[1]} & &\Fancontent\\
+    &\mbox{\textbackslash Fanncontent[1]} & &\Fanncontent\\
+    &\mbox{\textbackslash Fquant[1]\{a\}} & &\Fquant{a}\\
+    &\mbox{\textbackslash Fnquant[1]\{a\}} & &\Fnquant{a}\\
+    &\mbox{\textbackslash Fnnquant[1]\{a\}} & &\Fnnquant{a}\\
+    &\mbox{\textbackslash Fquantn[1]\{a\}} & &\Fquantn{a}\\
+    &\mbox{\textbackslash Fquantnn[1]\{a\}} & &\Fquantnn{a}\\
+    &\mbox{\textbackslash Fnquantn[1]\{a\}} & &\Fnquantn{a}\\
+    &\mbox{\textbackslash Fnquantnn[1]\{a\}} & &\Fnquantnn{a}\\
+    &\mbox{\textbackslash Fnnquantn[1]\{a\}} & &\Fnnquantn{a}\\
+    &\mbox{\textbackslash Fnnquantnn[1]\{a\}} & &\Fnnquantnn{a}\\
+    &\mbox{\textbackslash Faquant[1]\{a\}} & &\Faquant{a}\\
+    &\mbox{\textbackslash Fanquant[1]\{a\}} & &\Fanquant{a}\\
+    &\mbox{\textbackslash Fannquant[1]\{a\}} & &\Fannquant{a}\\
+    &\mbox{\textbackslash Faquantn[1]\{a\}} & &\Faquantn{a}\\
+    &\mbox{\textbackslash Faquantnn[1]\{a\}} & &\Faquantnn{a}\\
+    &\mbox{\textbackslash Fanquantn[1]\{a\}} & &\Fanquantn{a}\\
+    &\mbox{\textbackslash Fanquantnn[1]\{a\}} & &\Fanquantnn{a}\\
+    &\mbox{\textbackslash Fannquantn[1]\{a\}} & &\Fannquantn{a}\\
+    &\mbox{\textbackslash Fannquantnn[1]\{a\}} & &\Fannquantnn{a}\\
+  \end{flalign*}
+  This may seem like a daunting list, but there is an exceedingly simple way to think 
+  about it. In a sense there are only two commands \textbackslash Fcontent[1] and 
+  \textbackslash Fquant[1]\{\}. These two commands can be augmented with a 
+  combination of as and ns so as to add assertion and negation strokes respectively. 
+  Any stroke that is asserted (has a fat vertical line at the start) starts with 
+  `\textbackslash Fa'. This may be followed by either one or two or no `n' to add one 
+  or two or no negation strokes (the small vertical lines below the assertion 
+  stroke). Next comes the name of the main command, either `quant' or `content'. 
+  Finally the quantifiers may be followed by either one or two `n' to add one or two 
+  negation strokes to the content stroke after the quantifier's depression.
+
+  Consider also that many of these commands are only really present for completeness 
+  sake. It is difficult to imagine a situation where a twice negated quantifier with 
+  twice negated content would ever be needed.
+
+  Since version 1.1 all basic strokes also have an optional scaling factor. A command 
+  followed by [.5], for example would produce a stroke exactly half the default 
+  length while [2] produces a stroke twice the default length. (The default length 
+  is given by \textbackslash Fbaselength which is set to 20pt. Scaling allows for 
+  greater control in the total length of formula as well as for a shorter syntax. 
+  (We can replace expressions like \textbackslash Facontent \textbackslash Fcontent 
+  with \textbackslash Facontent[2].) Care must be taken not to set a length that is 
+  shorter than what is needed to fit all the parts of some basic stroke. This will 
+  lead to negative lengths and hence unpredictable output.
+
+  All quantifiers also have a mandatory argument that specifies the variable 
+  associated with the quantifier. (Mandatory arguments are contained in a set of 
+  curly brackets \{ and \}). This argument should be a single small letter and 
+  will be typeset above the semi circular depression in the assertion stroke in 
+  mathfrak font which is provided by tha amssymb package. This font can be used in 
+  maths mode by using the command `\textbackslash mathfrak\{\}'. Note that all the 
+  commands provided by this package may be used in both math and text mode. (Though 
+  math mode usually results in better formatting.)
+
+  Finally one may combine the above commands in arbitrary combinations which will 
+  result in gapless longer strokes. (Eg.: $\Faquant[0.6]{a}\Fnquantn[1.4]{b}A$) 
+  which may be roughly translated into english as ``for all $\mathfrak{a}$ there 
+  exists a $\mathfrak{b}$ such that $A$''. (The commands I used for this expression 
+  are \$\textbackslash Faquant\{a\}\textbackslash Fnquantn\{b\}A\$).
+
+\subsubsection{Conditional}
+  The conditional is the most important command in this package since it gives 
+  Frege's Begriffsschrift it's two dimensional structure.\\
+  The syntax for the Fconditional command is as follows:
+  
+  \textbackslash Fconditional[\textless option\textgreater]
+  \{\textless consequent\textgreater\}\{\textless antecedent\textgreater\}\\
+  The arguments may in principle be anything, but you will only get a begriffschrift 
+  formula if the arguments are themselves given by appropriate commands from the list 
+  of basic commands given earlier. As an example, an asserted conjunction between $A$ 
+  and $B$ would be given as follows:
+
+  \$\textbackslash Fconditional[\textbackslash Fancontent]\{\textbackslash Fncontent 
+  A\}\{\textbackslash Fcontent B\}\$ \\
+  and produce the following output: 
+  \begin{align*}
+    \Fbox{\Fconditional[\Fancontent]{\Fncontent A}{\Fcontent B}}
+  \end{align*}
+  In addition Fconditional may be nested as it's own argument to arbitrary depth. 
+  Nesting in the option is not recommended. \\
+  A conditional with nested consequent may be given as follows:
+
+  \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash 
+  Fcontent\textbackslash Fconditional\{\textbackslash Fcontent A\}\{\textbackslash 
+  Fcontent B\}\}\{\textbackslash Fcontent\textbackslash Fcontent C\}\$\\
+  and produces the following output:
+  \begin{align*}
+    \Fbox{\Fconditional[\Facontent]{\Fcontent\Fconditional{\Fcontent A}
+    {\Fcontent B}}{\Fcontent[2] C}}
+  \end{align*}
+  A conditional with nested antecedent may be given as follows:
+
+  \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash Fcontent 
+  \textbackslash Fcontent A\}\{\textbackslash Fcontent\textbackslash Fconditional 
+  \{\textbackslash Fcontent B\}\{\textbackslash Fcontent C\}\}\$\\
+  and produces the following output:
+  \begin{align*}
+    \Fbox{\Fconditional[\Facontent]{\Fcontent[2] A}{\Fcontent\Fconditional%
+    {\Fcontent B}{\Fcontent C}}}
+  \end{align*}
+  Each section of a content stroke may thus be replaced with any of the strokes given 
+  by the list of basic commands. Note that it is up to the user to place the 
+  appropriate number of strokes in each argument to ensure that the content strokes 
+  all line up on the right hand side.
+
+\subsubsection{Brackets and Boxes}
+  There are two more commands to be considered: 
+
+  \textbackslash Fbracket\{\textless complex expression\textgreater\}
+
+  \textbackslash Fbox\{\textless complex expression\textgreater\}\\
+  Both Fbox and Fbracket take what I have called a `complex expression' for their 
+  argument. A `complex expression' is any formula in begriffsschrift that has at 
+  least one conditional in it. It is generally a good idea to put all complex 
+  expressions into either a Fbox or a Fbracket. It is never necessary to place a 
+  complex expressions into both an Fbox and an Fbracket since an Fbox simply is a 
+  Fbracket without the actual brackets. Fbracket exists only for convenience with 
+  the same effect being achieved by \textbackslash left(\textbackslash Fbox\{\} 
+  \textbackslash right).
+
+  The reason why the Fbox is a good idea, is that the baseline is very near the top of
+  a complex expression of Begriffsschrift, which can make for some odd formatting 
+  effects. In addition to placing the baseline at the middel of a complex expression 
+  an Fbox ensures the expression is treated by LaTeX as a single object and given 
+  enough space.
+
+  Finally a complex expression may not format correctly in some environments (like 
+  the align* environment for example) unless it is placed in an Fbox. In short, 
+  always use an Fbox (or Fbracket).
+
+\subsection{Arguments and Struts}
+  Since version 1.2 two arguments have been added that allow for the typesetting of 
+  arguments. The syntax for the argument command is as follows:
+
+  \textbackslash Fargument[\textless absent premise\textgreater]\{\textless premise 
+  1\textgreater\}\{\textless premise 2\textgreater\}\{\textless conclusion
+  \textgreater\}\\
+  In the following esample the optional argument for the absent premise takes the 
+  value `$X$' the premises are the two formulas above the therfore line and the 
+  conclusion is the formula below the therefore line. The Begriffschrift expressions 
+  in the arguments of the Fargument command do not need to be placed in an Fbox, 
+  since the Fargument command works by boxing it's arguments allready.
+  \begin{align*}
+    \Fargument[X]
+      {\Fconditional[\Facontent]
+        {\Fcontent[2] A}
+        {\Fcontent\Fconditional{\Fcontent B}{\Fcontent C}}}
+      {\Fstrut[2]\Facontent C}
+      {\Fstrut[2]\Facontent A}
+  \end{align*}
+  where $X=\Facontent B$; (this is typeset seperately from the Fargument command);
+
+  The three begriffsschrift formulas above are in fact aligned leftbound. To make 
+  them appear rightbound no matter what the relative lengths of $A$, $B$, and $C$, 
+  the command ``Fstrut'' has been used in front of $\Facontent C$ and $\Facontent A$. 
+  The command \textbackslash Fstrut[1] works exactly like an invisible content 
+  stroke, that is it inserts space of length Fbaselength. Like all basic strokes it 
+  can be scaled via an optional scale factor.
+
+\subsection{Lengths}
+  In theory all the dimensions in this package can be changed with the command 
+  \textbackslash setlength\{\textless name of length\textgreater\}\{\textless new 
+  value\textgreater\}, though I have not done a great deal of testing and recommend 
+  sticking to the default values. The following then is a table of all lengths: \\
+  \begin{tabular}{|l|l|l|}
+    \hline
+    name & default value & description \\
+    \hline
+    \textbackslash Fbaselength & 20pt & the length of the basic strokes \\
+    \textbackslash Flinewidth & 0.5pt & the line width \\
+    \textbackslash Fspace & 2pt & seperation between lines and text/formula \\
+    \textbackslash Fassertwidth & 3\textbackslash Flinewidth & width of assert 
+    stroke \\
+    \textbackslash Fraiseheight & 1ex-\textbackslash Flinewidth & height of content 
+    lines above baseline \\
+    \textbackslash Fnegsep & 3\textbackslash Flinewidth & seperation between a 
+    double negation \\
+    \textbackslash Fnegshort & 2\textbackslash Flinewidth & space between negation 
+    stroke and baseline \\
+    \textbackslash Fquantwidth & 6pt & width of the semi-circular quantifier 
+    depression \\
+    \hline
+  \end{tabular}
+  the height of the conditional stroke is determined by the size of the contents of 
+  the conditionals argument, as well as the baselineskip of the surrounding text. It 
+  cannot be changed manually.
+
+\subsection{Final Example}
+  The Geach-Kaplan sentance (with thanks to Marcus Rossberg):
+  \begin{align*}
+    \Fbox%
+    {%
+      \Fconditional[{\Facontent[.2]\Fnquant{F}\Fcontent[.2]}]%
+      {%
+        \Fcontent%
+        \Fconditional%
+        {%
+          \Fcontent[3]%
+          \Fbox%
+          {%
+            f\Fbracket%
+            {%
+              \Fconditional[\Faquant{a}]%
+                {\Fcontent C\mathfrak{(a)}}%
+                {\Fcontent \mathfrak{F(a)}}%
+            }%
+          }%
+        }%
+        {\Fcontent\Fnquantn{b}\Fcontent\mathfrak{F(b)}}%
+      }%
+      {%
+        \Fcontent[0.4]%
+        \Fquant[0.6]{c}%
+        \Fquant[0.6]{d}%
+        \Fcontent[0.4]%
+        \Fconditional%
+        {%
+          \Fncontent%
+          \Fconditional{\Fcontent\mathfrak{c=d}}{\Fcontent\mathfrak{F(d)}}%
+        }%
+        {%
+          \Fncontent%
+          \Fconditional{\Fncontent\mathfrak{F(c)}}{\Fcontent A\mathfrak{(c,d)}}%
+        }%
+      }%
+    }%
+  \end{align*}
+  And that is all. \\ 
+  For comments, suggestions, identified errors, email me at \\
+  \textless Q.Pamp.2009 at my.bristol.ac.uk\textgreater.
+  % don't like storing my full email in a text file on the interneti,
+  % so I replaced the @ with " at ";
+\end{document}