\title{Package \textsc{accentbx}: some problems with accents
in \TeX{} and how to solve them}
\author{A.S. Berdnikov}
\affiliation{Institute of Analytical Instrumentation\\
             Rizskii pr. 26\\
             198103 St.Petersburg\\
             Russia\\
             \texttt{berd@ianin.spb.su} or \\
             \texttt{berdn@ptslab.ioffe.rssi.ru}}
\authorhead{A.S.Berdnikov}
\titlehead{Package \textsc{accentbx}}
\maketitle
\date{}
\def\AmS{$\cal AMS$}

\chardef\bs=`\\
\chardef\bh=`\^

\font\cyrfont=wncyr10
\font\cmfont=cmr10

\def\TA#1{\upaccent{{\tiny a}}{#1}}
\def\tA#1{\upaccent{\aboxsplitup{\tiny a}}{#1}}
\def\burg{b\upaccent{\Aboxshift{\char"15}}{\markchar}g}
\def\BURG{B\upaccent{\Aboxshift{\char"15}}{\MARKCHAR}G}
\def\Burg{b\upaccent{\Aboxshift{\char"15}}{\marktwochar bg}g}
\def\Tcomma#1{\upaccent{,}{#1}}
\def\tcomma#1{\upaccent{\Aboxsplit{\Aboxbase{,}}}{#1}}

\makeatletter
\def\hackersmile{\@ifnextchar[{\@hackersmile}{\@hackersmile[8]}}
\def\@hackersmile[#1]{\hbox{%
   \unitlength=1pt\relax
   \unitlength=#1\unitlength
   \divide\unitlength by 10\relax
   \thicklines
   \raise -3\unitlength \hbox{%
   \begin{picture}(12,12)(-6,-6)
   \put(0,0){\circle{10}}
   \put(-2,1.75){\circle*{1}}
   \put(2,1.75){\circle*{1}}
   \thicklines
   \put(-2.75,3){\line(1,0){1.5}}
   \put(2.75,3){\line(-1,0){1.5}}
   \put(0,-1){\line(0,1){3}}
   \put(-2.5,-2.5){\line(1,0){5}}
   \put(-2.5,-2.5){\line(0,1){1}}
   \put(2.5,-2.5){\line(0,1){1}}
   \end{picture}%
}}}
\makeatother


\begin{abstract}
Weak points of \TeX{} internal command \verb?\accent?
are investigated. It appears that some features of \verb?\accent?
prevent to construct specific letters
which require several accents simultaneously.
Special macro which emulates the work of \verb?\accent?,
additional macro for fine tuning of accents,
\textsf{if-then-else} structures which enable to put correct accents
depending on uppercase/lowercase state and font family conditions, etc.,
are described.
Closely related to it are the accents for I/i and J/j which are different
for uppercase and lowercase letters, and similar
problem occurs for so-called \textit{title letters}.
The whole package is coded in such a way
that in works for {\sl Plain},
\AmS\TeX, etc., as well, not only for \LaTeXe.
\end{abstract}

\section{Introduction\label{S-Intro}}

The nearly inevitable feature of cyrillic encodings is that some cyrillic
letters (for example, the majority of accented letters) should be assembled
from pieces~--- accents, modifiers, composite elements, etc.
There are the cases (not too rare) where {\em several} elements should be
attached to the same base character. The typical examples are the stresses
over accented letters, some specific characters from Nivh language,
multi-level accents specific for Saam language, stroke-type modifiers
added to some letters, and so on~--- some of these constructions
are shown here:
\begin{center}
{\cmfont
  \upaccent{\aboxshift{\char"13}}%
           {\upaccent{\aboxshift{\char"7F}}%
                     {\cyrfont E}%
           }%
},\qquad
{\cmfont
  \upaccent{\aboxshift{\char"13}}%
           {\upaccent{\aboxshift{\char"16}}%
                     {\cyrfont I}%
           }%
},\qquad
{\cmfont
  \upaccent{\aboxshift{\char"7D}}%
       {\baseaccent{\aboxjoindn[0.1ex]{\kern-0.05ex\char"18}}%
               {\makeaccent[Cs]<,,0.15em,>{\aboxrule{0.3em}}%
                           {\cyrfont G}%
               }%
       }%
},\qquad
{\cmfont
  \upaccent{\aboxsplit{.}}%
           {\makeaccent[Cs]<,,0.03em,>{\aboxrule{0.4em}}%
                       {\cyrfont H}%
           }%
},\qquad
{\cmfont
  \upaccent{\aboxshift{\char"16}}%
           {\upaccent{\aboxshift{\char"7F}}%
                     {\cyrfont O}%
           }%
},\qquad
{\cmfont
  \upaccentbar{\upaccent{\aboxshift{\char"7F}}{\cyrfont \char3}{\cyrfont A}}%
},\qquad
\dots
\end{center}

In addition there are the cases
where the accent is positioned {\em between} two characters~---
for example, in German \cite{DC} there is the abbreviation
\textit{-\burg} which substitutes \textit{-burg}
when necessary\footnote{In first version of this paper
published in Proceedings of Euro\TeX-97 there was an error:
it states that sometimes in Serbian language
the accents {\em acute}, {\em grave}, {\em double-grave}
and {\em frown} (reverted breve) which are the specific
Serbian stresses, may be positioned in a similar manner:
{\cmfont
{\cyrfont b}\upaccent{\aboxshift{\char"13}}{\markchar}{\cyrfont rvno}%
},
{\cmfont
{\cyrfont mr}\upaccent{\aboxshift{\char"12}}{\markchar}{\cyrfont tvats}%
},
{\cmfont
{\cyrfont mr}\upaccent{\aboxshift{\char"12\kern-0.35em\char"12}}{\markchar}{\cyrfont kva}%
},
{\cmfont
{\cyrfont zr}\upaccent{\aboxshift{\char"15}}{\markchar}{\cyrfont tva}%
},
\dots
More detailed investigation shows that in such cases
corresponding stresses are placed strictly over the letter
`{\cyrfont r}'. But in Church Slavonic and Old Slavonic
the accents {\em paerok} and {\em titlo-in-letters}
placed between two letters are not a rare case.}.
Such effect could be simulated by a special invisible character
with zero width and corresponding height
as it is described in the documentation for DC/EC fonts \cite{DC},
but invisible rule with zero width or
\verb?\phantom? command are better for this purpose~---
unfortunately \verb?\accent? cannot place accents over them.

Another problem arises when we need the accent above the letters
I/i or J/j~--- these letters contain dots for the lowercase form
but do not contain it for the uppercase form. It is not a problem
when there is no automatic uppercase and lowercase conversion
of the user defined text since {\em dottless} lowercase forms
are available in Computer Modern typefaces~---
but, for example, the Khakassian uppercase `\.I'
could be unexpectedly transformed into
double-dotted `i' after {\tt\bs{}lowercase} used somethere:
\begin{center}
\begin{tabular}{c@{ = }cc@{ = }cc@{ = }c}
{\tt\bs{}.I} &  \.I
&
{\tt\bs{}uppercase\{\bs{}.I\}} & \uppercase{\.I}
&
{\tt\bs{}lowercase\{\bs{}.I\}} & \lowercase{\.I}
\end{tabular}
\end{center}

Summary: the primitive \verb?\accent? command cannot
be used for such constructions
(it cannot analyze uppercase/lowercase characters,
it puts accents only over the letters
and atomic symbols ignoring the composite characters
like \verb?\hbox? or \verb?\vrule? and it cannot
put accent over already accented characters).
To overcome these restrictions and to support inside one encoding
as much cyrillic writing systems as possible, it is necessary
to simulate the work of the command \verb?\accent?
by some other \TeX{} tools.

Finally, there is some problem which does not relate directly
to accents~--- This is the problem of so-called \textit{title letters}
which are not supported by \TeX{} when
the commands \verb?\lowercase? and \verb?\uppercase? work.
Although it is not the problem with \verb?\accent?
(and hence corresponding macro are not included into \textsc{accentbx}),
it closely relates to the problem with accented I/i and J/j~--- so,
this problem and its solution is discussed in section~\ref{S-title}.

\section{How {\tt\bs{}accent} works\label{S-accent}}

Before we proceed to simulate the work of \verb?\accent? it may be a good
idea to see what particular operations are performed by this internal
\TeX{} command. Its syntaxis is specified as \cite{TEXB,TOPIC}:
\begin{center}
{\tt\bs{}accent}$\left<\hbox{\em 8-bit number}\right>
                \left<\hbox{\em optional assignments}\right>
                \left<\hbox{\em character}\right>$%
\end{center}
{\em Character} is a letter over which the accent should be placed.
The 8-bit number is the code from the current font which corresponds
to the character used as the accent.
The optional assignments between the {\em 8-bit number} and
the {\em character} could contain, in particular, the font switching
commands which enable to take the accent defined by
{\em 8-bit number} and the accented object defined by {\em character}
from different fonts
(although it cannot contain {\tt\bs{}setbox} assignments).

If the assignments are not followed by a {\em character}
(where {\em character} is the token with {\tt\bs{}catcode=11}
or {\tt\bs{}catcode=12}, command {\tt\bs{}char}, \TeX{} command
created through {\tt\bs{}chardef}, {\tt\bs{}noboundary}
command), \TeX{} considers {\tt\bs{}accent} as the equivalent
to {\tt\bs{}char$\left<\hbox{\em 8-bit number}\right>$} command.
Otherwise the character which follows the
assignment is accented by the character that corresponds to
{\em 8-bit number}. The accenting algorithm is the
following\footnote{This description with minor corrections
belongs to Bernd Raichle and
was extracted by him through investigation of the original Web
code for \TeX.}:
\begin{enumerate}
\item If the {\em character} has a height equal to
      \verb?\fontdimen5? for the font where the accent is selected
      (which is {\tt 1ex} for this font), the accent is
      centered horizontally over the box corresponding
      to the {\em character} and no additional vertical
      shift is inserted.
\item
      If the {\em character} has a height unequal to {\tt 1ex} and the
      font is not slanted, i.e., the slant \verb?\fontdimen1?
      for the font where the accent is selected
      is equal to {\tt 0pt}, the accent \verb?\char?{\em 8-bit number}
      is placed in a \verb?\hbox? which is vertically shifted by the
      difference of the height of the {\em character} and {\tt 1ex}.
      The accent box is shifted up, if the {\em character} is
      heigher than {\tt 1ex}, otherwise it is shifted down.
      It is also centered horizontally to the {\em character} box.
\item
      If the {\em character}  has a height unequal to {\tt 1ex} and the
      font is slanted, i.e., the value \verb?\fontdimen1?
      for the font where the accent is selected is not equal to {\tt 0pt},
      the accent \verb?\char?{\em 8-bit number} is placed in a
      \verb?\hbox? and vertically shifted as described
      under 2.

      Horizontally the center of the accent box is
      displaced from the center of the {\em character} by the
      absolute amount of the horizontal shift amount multiplied
      by the font slant \verb?\fontdimen1?
      (which is given as {\em slant-per-pt}).
      It is displaced to the right, either if the box is shifted up and
      the font slant is positive (i.e., the glyphs of the font
      are slanted to the right), or if the box is shifted down
      and the font slant is negative, otherwise the accent box is
      moved to the left.

      Such additional horizontal shift
      proportional to slant value is an essential component of
      \TeX{} accenting algorithm since it enables to position the
      accent properly over the slanted character
      proportionally to its height.

\end{enumerate}

The proper positioning of the accent box over the accented character
is performed by the explicit kerns inserted by \TeX. Kerns
are inserted in such a manner that the horizontal size of
the accented character is not affected.
On the contrary, the vertical size of the accented character is
corrected following the height of the resulting construction.

The fact that the command \verb?\accent? inserts explicit kerns
prevents \TeX{} from using its automatic hyphenation
algorithm, as it usually happens for the words with explicitly inserted
kerns.
It is essential that the commands for the correct alignment of the accent
with respect to the accented character are inserted by \TeX{} in the output
stream at first~--- i.e, {\em before} the main character.
If the italic correction command  \verb?\/? is placed after
the accented character and if it is separated from the main character
by some kerns, \verb?\hbox? command, etc., it fails to define properly
the {\em italic correction} shift.

\section{How new {\tt\bs{}accent} may be implemented\label{S-acentI}}

By definition the command \verb?\accent? can put accents only over
the atomic letters and symbols. In particular, it cannot put an
accent over already accented character (at least in text mode).
The other disadvantage is that accent and accented character should
be taken usually from the same font. Although the syntaxis of
\verb?\accent? enables to use the font switching commands,
this possibility is realized not in a comfortable mode.
Usually we would like to select the accent from a special font, and
the main character~--- from the current font. Inspite of it
the \verb?\accent? syntaxis forces to store and to reconstruct
explicitly the current font status when the accent is selected
not from the current font.

Some simple macro emulating the work of \verb?\accent? and enabling
to overcome its restrictions are suggested in \cite{SOL}%
   \footnote{The original commands are modified a little
             to fit the purposes of this paper.}:
\begin{verbatim}
\def\ifnnull#1{\def\inner{#1}\ifx\inner\empty\else}
\def\genaccent#1#2#3{%
   \leavevmode\setbox0=\hbox{#3}%
   \vbox{\offinterlineskip
         \ifnnull{#1}\hbox to \wd0{\hss#1\hss}\kern 0.2ex\fi
         \vbox to \ht0{\copy0\vss}%
         \vtop{\null\vbox to \dp0{\vss}%
           \ifnnull{#2}\kern 0.2ex \hbox to \wd0{\hss#2\hss}\fi
         }%
   }%
}
\end{verbatim}
It enables to put above and below an arbitrary \TeX{} object
as many accents as you wish (defined as \verb?\hbox? if it is necessary).
It is also not a problem to select the accents used for this purpose
from a separate font without taking care about the current font status.
Unfortunately these commands do not take into account the
fine accent tuning for slanted fonts, and they also
break down the work of italic correction \verb?\/?
(the main character is deeply hidden inside \verb?\vbox?).

This scheme could be modified. Suppose the accent is defined as the first
parameter of some macro, and the main symbol to be accented -- as its
second parameter. The following commands
\begin{itemize}
\item[]\begin{verbatim}
\setbox0=\hbox{#2}
\setbox2=\hbox to \wd0{\hss#1\hss}
\raise\ht0\box2\kern-\wd0 \unhbox0
\end{verbatim}
\end{itemize}
do the necessary work:\footnote{Here the command {\tt\bs{}unhbox}
is used instead of {\tt\#2} following the recommendations
by Bernd Raichle to avoid the side effects if there are
assignments inside the argument {\tt\#2}.}
\begin{itemize}
\item put the accent above the main character,
\item align it properly in horizontal direction
      (at least for straight fonts),
\item does not change the width of the
      main character while the height of the composite construction
      is corrected properly,
\item leaves the main character as the last object in the output stream
      so that the italic correction command \verb?\/? can have a free
      access to it,
\item enables to use arbitrary \TeX{} constructions for accents and
      accented characters,
\item conserves the kerning with the characters followed after
      the accented character (unfortunately the kerning with the
      {\em previous} character is destroyed irreversibly).
\end{itemize}

The only thing to do is to add the fine horizontal tuning
which is not a problem as soon as we can calculate it.
But the calculation of the horizontal shift necessary
for slanted fonts {\em is} a problem and requires additional
tricks! It is necessary to multiply slant value \verb?\fontdimen1?
by the vertical shift of the accent,
but the problem is that \TeX{} contains {\em no} primitive
tools to multiply {\tt 2pt} by {\tt 2pt} and to get
{\tt 4pt} as a result (at least if the multiplied values
are the \verb?\dimen? registers).

\begin{figure}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Case 1: & Case 2: \\
\hline
\begin{minipage}{0.45\hsize}
\begin{verbatim}

\dimenA=...
\dimenB=...
\dimenC=\dimenA
\countX=\dimenB
\multiply\dimenC by \countX
\divide\dimenC by 65536

\end{verbatim}
\end{minipage}
&
\begin{minipage}{0.45\hsize}
\begin{verbatim}

\dimenA=...
\dimenB=...
\dimenC=\dimenA
\countX=\dimenB
\divide\dimenC by 65536
\multiply\dimenC by \countX

\end{verbatim}
\end{minipage}
\\
\hline
\end{tabular}
\end{center}
\caption{How to multiply $ 2pt\times2pt\to4pt$ in \TeX\label{S-Fig1}}
\end{figure}

One way to do such operation is to convert one value to
an integer (assuming 1{\em pt}=65536) and perform multiplication
as it is shown on Fig.~\ref{S-Fig1}. Unfortunately the accuracy of such
algorithm is very low: in the first case the overflow could
occur after \verb?\multiply\dimenC by \countX? if \verb?\dimenA?
is too big; in the second case the result after
\verb?\divide\dimenC? by 65536 could be zero id \verb?\dimenA?
is too small. Some special macro exist \cite{DRATEX,Calc,FP,Real}
which perform floating point calculations in \TeX{}
with high accuracy. Hopefully we do not need such intensive
calculations. The macro \verb?\slant@value?
which converts the \verb?\fontdimen1? specified for the current font
into numerical string (like \verb?\the? command, but without the
suffix {\tt pt} at its end) would be enough for our purpose:
\begin{verbatim}
\setbox0=\hbox{#2}
\setbox2=\hbox to \wd0{\hss#1\hss}
\dimen2=\slant@value\ht0
\kern\dimen2
   \raise\ht0\box2\kern-\wd0
\kern-\dimen2 #2
\end{verbatim}
The macro which converts the \verb?\fontdimen1? of the current font
into text string without the suffix {\tt pt} at its end
can be coded, for example, as
\begin{verbatim}
\begingroup\catcode`P=12 \catcode`T=12
           \lowercase{\endgroup\def\strip@pt#1PT}{#1}}
\def\slant@value{\expandafter\strip@pt\the\fontdimen1\font}
\end{verbatim}
(This trick is suggested by Bernd Raichle and is based
on {\tt\bs{}kslant} shown on p.375 of \TeX{}book.)

Other operations require a standard \TeX{}nical work
with boxws and does not cause serious problems
from the designer. Unfortunately, such operations destroy
automatic kerning and prevents automatic hyphenations (like ordinary
command \verb?\accent? does).

\section{General remarks about accent commands\label{S-general}}

To create the ``universal'' set of accenting commants it is necessary
to take into account the following factors:
\begin{enumerate}
\item
Symbol used as accent could be (and should be)
an ordinary \verb?\hbox?~--- i.e., the User does not align it in
advance with respect to the height of \textsf{1ex} as it is done
for accent characters in CM fonts.
\item
Since typical accents in CM fonts
are shifted in advance verically by \textsf{1ex} and horizontally by
corresponding slant correction, before we use these characters
as accents we should compensate these shifts backward. Hence,
the User should have at his/her disposal necessary macro.
\item
Although typically accents are placed above the characters,
there are cases where the modifiers are placed below the character,
at the baseline of the character and over the character to make
special composite objects. Hence, a variety of accenting commands
is necessary.
\item
Accents which are placed above the character or below the character
may have additional vertical space between the accent and the character
for fine tuning.
\item
Accents which are the modifiers joined without
space with the character may require to shift it closer to
the character to make intersection well expressed.
\item
Symbol like comma may require to raise it above the baseline
before it can be used as the upper accent.
\item
Accents can be placed before the letter at the beginning
of the word, after the letter at the end of the word,
or between two letters in the middle of the word,
as in it explained in section \ref{S-Intro}.
\item
Accents ``{\em overline}'' ({\em macron})
and ``{\em underline}'' may be longer than the width
of one letter\footnote{The Saam (Lappish) writing system is the only
           known up to now which has such modificators.}.
\item
Accents may be justified with respect to the character
in non-standard way~--- say, it can be aligned to the left corner
or to the right corner of the character.
\item
Pseudo accents like strokes, ets., artificially added to already existing
characters, may require fine tuning of their position with respect
to the body of the character. In particular, such tuning
can depend on font style (italic, slanted, etc.).
\item
It is necessary to take into account that the composite characters may
be influenced by the commands \verb?\uppercase? and \verb?\lowercase?
(or by equivalent \LaTeXe{} commands \verb?\MakeUppercase?
and \verb?\MakeLowercase?). Accents should be stable (since these
operations change the height and the width of the character) and
robust (since accented characters may be placed inside section
headers, etc., where~--- at least for \LaTeXe{}~--- fragile commands
are not welcome).
\item
Closely related to it is the problem with the accents for I/i and
J/j: when converted by \verb?\uppercase? and \verb?\lowercase?
these letters can get or loose the upper dot accent.
\end{enumerate}

\section{Some examples\label{S-example}}

Before we proceed further let me demonstrate some simple examples.
(Although the commands included into \textsc{accentbx} are rather lengthy,
it is done intensionally: these commands are mainly designed for creating
your own accent commands and specific characters available through macros,
not for ``everyday usage'' inside your text.)

Suppose we would like to put a tiny letter `a' as the accent over
some character. Using the package \textsc{accentbx}
we create special command
\begin{itemize}
\item[]\verb?\def\tA#1{\upaccent{\tiny a}{#1}}?
\end{itemize}
(\verb?\upaccent? places one box as the accent over the second box).
Now we can see how it works:
\begin{center}
\begin{tabular}{c@{ = }lc@{ = }l}
 \tA{X} & {\tt\bs{}tA\{X\}}
&
 \tA X & {\tt\bs{}tA X}
\\
 \tA{x} & {\tt\bs{}tA\{x\}}
&
\lowercase{\tA X} & {\tt\bs{}lowercase\{\bs{}tA X\}}
\\
{\bf \tA{X}} & {\tt\bs{}bf\bs{}tA\{X\}}
&
{\it \tA{X}} & {\tt\bs{}it\bs{}tA\{X\}}
\\
\tA{\tA X} & {\tt\bs{}tA\{\bs{}tA X\}}
&
\tA{\tA{\tA X}} & {\tt\bs{}tA\{\bs{}tA\{\bs{}tA X\}\}}
\\
{\it\tA{\tA X}} & {\tt\bs{}it\bs{}tA\{\bs{}tA X\}}
&
{\it\tA{\tA{\tA X}}} & {\tt\bs{}it\bs{}tA\{\bs{}tA\{\bs{}tA X\}\}}
\\
\end{tabular}
\end{center}

If you would like to reproduce exactly what is typed above,
you'll discover that the result is a little bit different:
\verb?\it\tA{\tA{X}}? gives {\it\TA{\TA{X}}}, not {\it\tA{\tA{X}}}.
Yes, actually the previous example was defined as
\begin{itemize}
\item[]\verb?\def\tA#1{\upaccent{\aboxsplit{\tiny a}}{#1}}?
\end{itemize}
--- since \verb?\upaccent? just places a box over box, it is necessary
to add some space around tiny `a' to separate these boxes, and this is
just what macro \verb?\aboxsplit? does.

If you try to make ordinary \TeX{} accents with
\verb?\upaccent?, you'll discover another essential feature:
\begin{itemize}
\item[]
\verb?\upaccent{\char"13}{X}?=\upaccent{\char"13}{X}
\end{itemize}
while you would like to have {\accent"13 X}
--- the space is too big because the character \verb?\char"13?
in \textsl{Computer Modern} typeface is shifted in advance
to fit the letter `x' without further adjustments.
To correct this artificial shift typical for
\TeX{} accents special macro \verb?\aboxshift? should be used:
\begin{itemize}
\item[]
\verb?\upaccent{\aboxshift{\char"13}}{X}?=\upaccent{\aboxshift{\char"13}}{X}.
\end{itemize}
This macro subtracts the height \textsf{1ex} in vertical direction
and corresponding slant correction in horizontal direction.

Similar effect is when you try to put \textit{comma} as the accent without
preliminary adjustment:
\begin{itemize}
\item[]
\verb?\def\tcomma#1{\upaccent{,}{#1}}?\\
\verb?\tcomma{X}?=\Tcomma{X}
\end{itemize}
Since \verb?\upaccent? alignes the boxes with respect to the baseline
and comma has non-zero depth, its descender overlaps with the
character to be accented. To correct it we should use this macro:
\begin{itemize}
\item[]
\verb?\def\tcomma#1{\upaccent{\aboxsplit{\aboxbase{,}}}{#1}}?\\
\verb?\tcomma{X}?=\tcomma{X}
\end{itemize}
Macro \verb?\aboxbase? raises the character by its depth so that
the baseline of the result corresponds to its geometrical bottom, and
macro \verb?\aboxsplit? adds some extra space above and below it.

Finally, let us show how the interletter accents
shown in section~\ref{S-Intro} can be created:
\begin{itemize}
\item[]
\verb?\def\burg{b\upaccent{\aboxshift{\char"15}}{\markchar}g}?
\\
\verb?St.~Peters\burg?=St.~Peters\burg
\end{itemize}
Here macro \verb?\markchar? creates invisible rule with zero width and
the height corresponding to that of letter `x'. Since \verb?\upaccent?
adjusts the height and the depth of the accented character but not its
width, the result is the object with zero width (from \TeX' point of view)
placed between characters \textit{b} and \textit{g}.

If we would like
to make our macro case-sensitive, it can be defined as
\begin{itemize}
\item[]
\verb?\def\burg{b\upaccent{\Aboxshift{\char"15}}{\markchar}g}?
\\
\verb?\def\BURG{B\upaccent{\Aboxshift{\char"15}}{\MARKCHAR}G}?
\end{itemize}
This results to:
\begin{itemize}
\item[]
\verb?St.~Peters\burg?=St.~Peters\burg
\\
\verb?ST.~PETERS\BURG?=ST.~PETERS\BURG
\\
\verb?\MakeUppercase{st.~peters\burg}?=\MakeUppercase{st.~peters\burg}
\\
\verb?\MakeLowercase{ST.~PETERS\BURG}?=\MakeLowercase{ST.~PETERS\BURG}
\end{itemize}
(Here macro \verb?\MARKCHAR? creates the invisible rule
with the height of capital letter `X',
macro \verb?\markchar? and \verb?\MARKCHAR?
operate in such a way that they are transformed into each other
after uppercasing and lowercasing,
macro \verb?\Aboxshift? is the robust version of \verb?\aboxshift?
which is not destroyed by the \LaTeXe{} macro
\verb?\MakeUppercase? and \verb?\MakeLowercase?.)

\section{Commands for accents\label{S-commands}}

\paragraph{Important note.}
In most cases the symbol used as the accent or modifier
should be adjusted in advance~--- see examples in
the previous section and section~\ref{S-commandsI}
for more details.

\bigskip

\noindent
The style file {\sc accentbx}
contains the following commands used to make accents:
\begin{description}
\item[] \verb?\upaccent{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   put {\em accent} above {\em main-symbol}
\item[] \verb?\dnaccent{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   put {\em accent} below {\em main-symbol}
\item[] \verb?\baseaccent{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   put {\em accent} at the baseline below symbol {\em main-symbol}
\item[] \verb?\nullaccent{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   the {\em accent} (i.e., some character modifier like stroke, etc.,
   attached to the main character)
   is centered with respect to the height of the
   {\em main-symbol}
\item[] \verb?\upaccentC{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   synonim for \verb?\upaccent?.
\item[] \verb?\upaccentL{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   put {\em accent} above {\em main-symbol} like
   the command \verb?\upaccent? does,
   but aligns it over the left corner of the character.
\item[] \verb?\upaccentR{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   put {\em accent} above {\em main-symbol} like
   the command \verb?\upaccent? does,
   but aligns it over the right corner of the character.
\item[] \verb?\dnaccentC{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,
        \verb?\dnaccentL{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,\\
        \verb?\dnaccentR{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   corresponding modifications of the command \verb?\dnaccent?.
\item[] \verb?\baseaccentC{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,
        \verb?\baseaccentL{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,\\
        \verb?\baseaccentR{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   corresponding modifications of the command  \verb?\baseaccent?.
\item[] \verb?\nullaccentC{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,
        \verb?\nullaccentL{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?,\\
        \verb?\nullaccentR{?{\em accent}\verb?}{?{\em main-symbol}\verb?}?~---
   corresponding modifications of the command  \verb?\nullaccent?.
\item[] \verb?\upaccentbar[?{\em height}\verb?]{?{\em main-symbol}\verb?}?~---
   place the horizontal bar above the {\em character}
   taking into account its width (i.e., it can place the bar over
   more than one character). Optional parameter {\em height}
   specifies additional space which is placed around the bar.
   Default value of additional space is~\textsf{0.2ex}.
\item[] \verb?\dnaccentbar[?{\em height}\verb?]{?{\em main-symbol}\verb?}?~---
   put the horizontal bar below the {\em character}
   taking into account its width (i.e., it can place the bar under
   more than one character). Optional parameter {\em height}
   specifies additional space which is placed around the bar.
   Default value of additional space is~\textsf{0.2ex}.
\end{description}
You can use a variety of \TeX{} constructions as the {\em accent}
and {\em main-symbol}~--- mainly those that can be used inside
\verb?\hbox?. In particular, the accented letter can be used as the main
symbol (i.e., the multiple commands
\verb?\upaccent?, \verb?\dnaccent?, \verb?\baseaccent?, etc.,
could be used).
It is essential to note that if the final symbol in a chain
of accenting commands is the symbol with \verb?\catcode?
11 or 12, the italic correction command \verb?\/? will work
correctly if it follows the whole construction.

\section{Commands which create and correct accent
         characters\label{S-commandsI}}

The special objects useful if they are used
as the {\em accents} can be created using the following
commands:
\begin{description}
\item[] \verb?\aboxshift[?{\em height}\verb?]{?{\em character}\verb?}?~---
   lower by {\em height} the character
   (which is usually the accent from Computer Modern font family).
   Default value for {\em height} is  \textsf{1ex}.
   Except the height the additional horizontal shift
   typical to slanted fonts is subtracted as well.
\item[] \verb?\aboxbase[?{\em height}\verb?]{?{\em character}\verb?}?~---
   raise the character by the specified {\em height} and, if
   there is still some depth of the result, by the residue depth.
   Default value for {\em height} is  \textsf{0pt}
   which means that the character is just raised if some its
   elements are below the baseline.
\item[] \verb?\aboxbaseline{?{\em character}\verb?}?~---
   raise or lower the character so that its bottom becomes
   the baseline (i.e., if the depth of the character is positive,
   the character is raised, if the depth is negative~---
   the character is lowered).
\item[] \verb?\aboxsplit[?{\em height}\verb?]{?{\em character}\verb?}?~---
   insert above and below the {\em character} the
   white space with the specified {\em height}. Default value
   for the {\em height} is \textsf{0.2ex}.
\item[] \verb?\aboxjoin[?{\em height}\verb?]{?{\em character}\verb?}?~---
   subtract above the {\em character} and below it the
   specified {\em height}.  Default value
   for the {\em height} is \textsf{0.1ex}.
\item[] \verb?\aboxsplitup[?{\em height}\verb?]{?{\em character}\verb?}?~---
   insert below the {\em character} the
   white space with the specified {\em height} (it adds white space
   \textit{below} the accent because the accent created by \verb?\upaccent?
   is supposed to be \textit{above} the character). Default value
   for the {\em height} is \textsf{0.2ex}.
\item[] \verb?\aboxsplitdn[?{\em height}\verb?]{?{\em character}\verb?}?~---
   insert above the {\em character} the
   white space with the specified {\em height} (it adds white space
   \textit{above} the accent because the accent created by \verb?\dnaccent?
   is supposed to be \textit{below} the character). Default value
   for the {\em height} is \textsf{0.2ex}.
\item[] \verb?\aboxsplitup[?{\em height}\verb?]{?{\em character}\verb?}?~---
   subtract below the {\em character} the
   white space with the specified {\em height} (it subtracts white space
   \textit{below} the accent because the accent created by \verb?\upaccent?
   is supposed to be \textit{above} the character). Default value
   for the {\em height} is \textsf{0.1ex}.
\item[] \verb?\aboxsplitdn[?{\em height}\verb?]{?{\em character}\verb?}?~---
   subtract above the {\em character} the
   white space with the specified {\em height} (it subtracts white space
   \textit{above} the accent because the accent created by \verb?\dnaccent?
   is supposed to be \textit{below} the character). Default value
   for the {\em height} is \textsf{0.1ex}.
\item[] \verb?\markchar?~--- make the invisible rule with
    the height equal to {\tt 1ex}. After \verb?\uppercase?
    and \verb?\MakeUppercase? it is converted into \verb?\MARKCHAR?.
\item[] \verb?\MARKCHAR?~--- make the invisible rule with
    the height equal to the height of the capital letter \textit{X}.
    After \verb?\lowercase?
    and \verb?\MakeLowercase? it is converted into \verb?\markchar?.
\item[] \verb?\marktwochar{?{\em char$_1$}\verb?}{?{\em char$_2$}\verb?}?~---
    make the invisible rule with zero width, with
    height equal to the maximal height of two characters
    and with corresponding depth. Can be substituted by
    \verb?\aboxmarker? but is conserved for compatibility reasons.
\item[] \verb?\aboxmarker{?{\em character}\verb?}?~---
    make the invisible rule with zero width,
    with height equal to the height of the box
    and with corresponding depth.
\item[] \verb?\aboxnull{?{\em character}\verb?}?~---
   makes an artificial box with zero height and zero
   depth but with the same the contents as
   the source. The width and the baseline are conserved as well.
\item[] \verb?\akern{?{\em char$_1$}\verb?}{?{\em char$_2$}\verb?}?~---
    make the kern corresponding to the pair of characters.
    It is useful if you would like to reconstruct kerning
    destroyed by accents. Example:
    \begin{itemize}
    \item[]
    \begin{tabular}{lcr}
    {\tt\bs{}upaccent\{.\}\{A\}\bs{}upaccent\{.\}\{W\}} &=&
    \upaccent{\aboxsplit.}{A}\upaccent{\aboxsplit.}{W}
    \\
    {\tt\bs{}upaccent\{.\}\{A\}\bs{}akern AW\bs{}upaccent\{.\}\{W\}} &=&
    \upaccent{\aboxsplit.}{A}\akern AW\upaccent{\aboxsplit.}{W}
    \end{tabular}
    \end{itemize}
\item[] \verb?\aboxbar{?{\em character}\verb?}?~---
   create the horizontal bar which is as wide as necessary
   to overline or to underline the {\em character}.
   The commands \verb?\upaccentbar? and \verb?\dnaccentbar?
   described in the previous section are defined with its help as:
{\begin{verbatim}
\def\upaccentbar#1{\upaccent{\aboxsplit{\aboxbar{#1}}}{#1}}
\def\dnaccentbar#1{\dnaccent{\aboxsplit{\aboxbar{#1}}}{#1}}
\end{verbatim}}
   The width of the bar is scaled with respect to the nominal
   width of the character by factor \verb?\accentwidthfactor?
   (default value 0.9). The thickness of the bar is the height
   of the dot selected from currect font and scaled
   twice by factor \verb?\accentthickness? (default value is 0.1)~--- so
   by default the bar thickness is in 5 times less than
   the thickness of the dot (i.e., the character~`.' of the current font).
\item[] \verb?\aboxrule{?{\em width}\verb?}?~--- just the same as
   \verb?\aboxbar? but the width of the object to be covered by the bar
   is specified explicitly and the width is not scaled by
   \verb?\accentwidthfactor?.

\end{description}

\section{General accent {\tt\bs{}makeaccent}
        and general frame {\tt\bs{}aboxframed},{\tt\bs{}aboxtuning}%
        \label{S-genmacro}}

Macro listed above are enough for 99\% of applications. But for
extremely exotic accent constructions and for cases which require
fine tuning of the accent and the main character
\textsc{accentbx} contains three additional commands:
\begin{itemize}
\item \verb?\makeaccent?~--- for fine tuning of the accent
      and the main character (both could be some \verb?\hbox?
      constructions!) with respect to each other,
\item \verb?\aboxframed?~--- for fine tuning of the frame and the baseline
      of the character used as the accent,
\item \verb?aboxtuning?~--- for explicit specification
      of frame and baseline of the box.
\end{itemize}

\subsection{Macro {\tt\bs{}aboxframed} and {\tt\bs{}aboxtuning}}

Macro \verb?\aboxframed? enables to control white spaces
around the character used as the accent and the position
of its baseline. It has the syntaxis:
\begin{itemize}
\item[]\verb?\aboxframed[?{\em options}\verb?]{?{\em object}\verb?}?
\end{itemize}
where {\em object} is the \verb?\hbox?-object to be adjusted,
and {\em options} is the list of letters describing the operations:
\begin{itemize}
\item[\texttt{r}]~--- increase right boundary by one step,
\item[\texttt{u}]~--- increase upper boundary by one step,
\item[\texttt{l}]~--- increase left boundary by one step,
\item[\texttt{d}]~--- increase lower boundary by one step,
\item[\texttt{b}]~--- increase baseline position by one step,
\item[\texttt{R}]~--- decrease right boundary by one step,
\item[\texttt{U}]~--- decrease upper boundary by one step,
\item[\texttt{L}]~--- decrease left boundary by one step,
\item[\texttt{D}]~--- decrease lower boundary by one step,
\item[\texttt{B}]~--- decrease baseline position by one step.
\end{itemize}
You can use as much lettwers as you wish, and each letter
performs an independent increment or decrememt of corresponding value.
The step values are defined by macro:
\begin{description}
\item[]\verb?\aboxframestepV?~--- step in vertical direction
       (i.e., for upper and lowerr boundaries and for baseline position),
       default value is~\textsf{0.2ex},
\item[]\verb?\aboxframestepH?~--- step in horizontal direction
       (i.e., for right and left boundaries),
       default value is~\textsf{0.08em}.
\end{description}
The algorithm behaves like following:
\begin{enumerate}
\item All five increments (right boundary, upper boundary,
      left boundary, lower boundary and baseline position)
      are collected and stored in corresponding variables.
\item The height and the depth of the object are corrected
      by corresponding values without any changes inside the object.
\item Left and right spaces (may be, negative) are added
      to the object.
\item The object is shifted (raised) by the value corresponding
      to the shift of the specified shift of the baseline.
\end{enumerate}

To make life easier, there is the macro \verb?\aboxtuning?
which performs just the same operation in one step. Its syntaxis is:
\begin{itemize}
\item[]\verb?\aboxtuning{?{\tt $\Delta r$,$\Delta h$,$\Delta l$,$\Delta d$,$\Delta b$}\verb?}{?{\em object}\verb?}?
\end{itemize}
where $\Delta r$ shows the shift of the right boundary,
$\Delta h$~--- the shift of the upper boundary,
$\Delta l$~--- the shift of the left boundary,
$\Delta d$~--- the shift of the lower boundary,
$\Delta b$~--- the shift of the baseline. Some values can be omitted
(in this case they are assumed to be zero), trailing commas
can be omitted also if there are no more values in a list.

\subsection{Macro {\tt\bs{}makeaccent}}

Macro \verb?\makeaccent? enables to control mutial alignment
of the accent and the main character in more details.
It has the syntaxis:
\begin{itemize}
\item[]\verb?\makeaccent[?{\em options}\verb?]<?{\em shifts}%
       \verb?>{?{\em accent-character}\verb?}{?{\em main-character}\verb?}?
\end{itemize}
where
\begin{itemize}
\item
{\em accent-character} is the \textsf{hbox}-object used as the accent,
\item
{\em main-character} is the \textsf{hbox}-object to be accented,
\item
{\em options} is the list of letters describing roughly
what base points of the accent and
the main character are joined when these two object are overlapped,
\item
{\em shifts} is the list of four numeric values which control fine tuning
of the base points of the accent and
the main character.
\end{itemize}

Macro \verb?\makeaccent? overlaps the {\em main character}
and the {\em accent character} so that their base points coinside
with each other. When the accent character is lowered or raised, the
corresponding slant correction is added to is horizontal shift.
By default the accent and
the main character are aligned so that the accent
is centered above the main character and its baseline is placed on top
of the main character (see below the defasult value
for the parameter {\em options}).
Parameters {\em options} and {\em shifts} are optional~---
they may be omitted together with surrounding angular and square
braces.

Following letters can be used in {\em options}
to specify the base points of
the {\em accent-character} and the {\em main-character}
which should be overlapped by \TeX{} when composing the accented
character:
\begin{itemize}
\item[\texttt{r}]~--- right side of the main character,
\item[\texttt{l}]~--- left side of the main character,
\item[\texttt{o}]~--- center between left and right boundaries
                      of the main character,
\item[\texttt{t}]~--- top of the main character,
\item[\texttt{d}]~--- bottom of the main character (including its depth),
\item[\texttt{b}]~--- baseline of the main character,
\item[\texttt{c}]~--- vertical center of the main character
                      (the middle between its top and bottom
                      boundaties including its depth),
\item[\texttt{s}]~--- $1/2$ of the height of the main character,
\item[\texttt{z}]~--- $1/2$ of the depth of the main character.
\item[\texttt{R}]~--- right side of the accent,
\item[\texttt{L}]~--- left side of the accent,
\item[\texttt{O}]~--- center between left and right boundaries
                      of the accent,
\item[\texttt{T}]~--- top of the accent,
\item[\texttt{D}]~--- bottom of the accent (including its depth),
\item[\texttt{B}]~--- baseline of the accent,
\item[\texttt{C}]~--- vertical center of the accent,
\item[\texttt{S}]~--- $1/2$ of the height of the accent,
\item[\texttt{Z}]~--- $1/2$ of the depth of the accent.
\end{itemize}
For example, the combination {\tt rt} means that the right top
point of the main character is selected as the base point,
and the combination {\tt OD} means that the center of the lower
boundary of the accent is selected as its base point.
By default {\em options}={\tt [tBoO]}
which means that the accent and
the main character are aligned horizontally so that their
vertical middle lines coinside, and that the top of the main character
and the baseline of the accent counside as well.

In addition to rough specification of the base points of the main character
and the accent character by {\em options}, the User may perform fine
tuning of their positions using {\em shifts}. Namely,
this parameter is the list of four values (lengths) separated by commas
which are added to the coordinates of the base points specified by
{\em options}. First value corresponds to $x$-shift of the base point
of the main character, second value~--- to $y$-shift of the base point
of the main character, third value~--- to $x$-shift of the base point
of the accent character, forth value~--- to $y$-shift of the base point
of the accent character. If some values are equal to zero,
they can be omitted. If there are no more non-zero values in a list,
trailing commas can be omitted as well. By default parameter
{\em shift} consistes of four zero values.

To illustrate the power of macro \verb?\makeaccent? let us see how the
accent macro described in section~\ref{S-commands} can be
specified:
\begin{center}
\small
\begin{verbatim}
\def\upaccentC#1#2{\makeaccent[BtOo]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\upaccentR#1#2{\makeaccent[BtRr]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\upaccentL#1#2{\makeaccent[BtLl]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\dnaccentC#1#2{\makeaccent[TdOo]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\dnaccentR#1#2{\makeaccent[TdRr]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\dnaccentL#1#2{\makeaccent[TdLl]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\baseaccentC#1#2{\makeaccent[TbOo]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\baseaccentR#1#2{\makeaccent[TbRr]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\baseaccentL#1#2{\makeaccent[TbLl]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\nullaccentC#1#2{\makeaccent[SsOo]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\nullaccentR#1#2{\makeaccent[SsRr]<0pt,0pt,0pt,0pt>{#1}{#2}}
\def\nullaccentL#1#2{\makeaccent[SsLl]<0pt,0pt,0pt,0pt>{#1}{#2}}
\end{verbatim}
\end{center}


\section{Robust versions of some commands\label{S-robust}}

Since \LaTeXe{} macro \verb?\@ifnextchar? is fragile and is
destroyed by some \LaTeXe{} commands (for example,
by \verb?\MakeUppercase? and \verb?\MakeLowercase?),
commands with optional arguments
have similar robust versions which do not have options but which
are not destroyed inside \LaTeXe{} stomach.
The list of fragile commands is the following:
\begin{itemize}
\item \verb?\aboxshift[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxshift{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{1ex},
        \item
        \verb?\AboxShift{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxbase[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxbase{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0pt},
        \item
        \verb?\AboxBase{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxsplit[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxsplit{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.2ex},
        \item
        \verb?\AboxSplit{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxsplitup[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxsplitup{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.2ex},
        \item
        \verb?\AboxSplitup{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxsplitdn[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxsplitdn{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.2ex},
        \item
        \verb?\AboxSplitdn{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxjoin[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxjoin{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.1ex},
        \item
        \verb?\AboxJoin{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxjoinup[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxjoinup{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.1ex},
        \item
        \verb?\AboxJoinup{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxjoindn[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxjoindn{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.1ex},
        \item
        \verb?\AboxJoindn{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\upaccentbar[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Upaccentbar{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.2ex},
        \item
        \verb?\UpaccentBar{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\dnaccentbar[?{\em height}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Dnaccentbar{?{\em character}\verb?}?
        assumes that {\em height}=\textsf{0.2ex},
        \item
        \verb?\DnaccentBar{?{\em height}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\aboxframed[?{\em options}\verb?]{?{\em character}\verb?}?:
        \begin{itemize}
        \item
        \verb?\Aboxframed{?{\em character}\verb?}?
        assumes that {\em options}=\textsf{ud},
        \item
        \verb?\AboxFramed{?{\em options}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\item \verb?\makeaccent[?{\em options}\verb?]<?%
             {\em shifts}\verb?>{?%
             {\em accent}\verb?}{?{\em character}\verb?}?~:
        \begin{itemize}
        \item
        \verb?\Makeaccent{?%
             {\em accent}\verb?}{?{\em character}\verb?}?
        assumes that the parameters
        {\em options} and {\em shifts} are empty,
        \item
        \verb?\MakeAccent{?{\em options}\verb?}{?%
             {\em shifts}\verb?}{?%
             {\em accent}\verb?}{?{\em character}\verb?}?
        is robust.
        \end{itemize}
\end{itemize}

\section{Case-sensitive accents for {\sl I}
         and {\sl J}\label{S-IJ}}

The letters {\sl I} and {\sl J} should be separated in a
specific class among all the letters used with accents.
The essential difference is that the lowercase form contains the
{\em dot} accent while the uppercase form does not have such modifiers.
To make correct accented versions of lowercase {\sl i} and {\sl j}
\TeX{} contains special characters {\sl dotless-i} and
{\sl dottless-j}, usually defined by the commands \verb?\i? and \verb?\j?.
As a result the correctly working command {\tt\bs{}accent} should
analyze the uppercase and lowercase forms of these letters and select
proper glyph to produce correct forms of letters even after
{\tt\bs{}uppercase} and {\tt\bs{}lowercase}.

As soon as we consider the cyrillic writing systems, the capital
{\sl Ukranian I} ({\sl \"I}) should be produced by \verb?\"I?,
while the lowercase {\sl ukranian i} ({\sl \"\i}) uses the command
\verb?\"\i?. Contrary to that example, the Khakassian letter
{\sl dotted-I}, which has a dot in uppercase form as well as
in lowercase one, requires \verb?\.I? to produce the uppercase variant
{\sl \.I}, and an ordinary \verb?i? to produce the lowercase
variant {\sl i}.
Since it is assumed that {\it Mr.\space User} or {\it Mrs.\space User}
can distinguish what letter does he/she want and to separate uppercase
and lowercaee variants explicitly, it seems that the existance
of two various types for specification of lowercase and uppercase
forms does not produce any troubles. Unfortunately it is so before
the commands \verb?\uppercase? and \verb?\lowercase? starts their work:
\begin{center}
\begin{tabular}{c@{ = }cc@{ = }cc@{ = }c}
 \.I & {\tt\bs{}.I}
&
{\tt\bs{}uppercase\{\bs{}.I\}} & \uppercase{\.I}
&
{\tt\bs{}lowercase\{\bs{}.I\}} & \lowercase{\.I}
\\
 i & {\tt i}
&
{\tt\bs{}uppercase\{i\}} & \uppercase{i}
&
{\tt\bs{}lowercase\{i\}} & \lowercase{i}
\\
 \"I & {\tt\bs{}"I}
&
{\tt\bs{}uppercase\{\bs{}"I\}} & \uppercase{\"I}
&
{\tt\bs{}lowercase\{\bs{}"I\}} & \lowercase{\"I}
\\
\"\i & {\tt\bs{}"\bs{}i}
&
{\tt\bs{}uppercase\{\bs{}"\bs{}i\}} & \uppercase{\"\i}
&
{\tt\bs{}lowercase\{\bs{}"\bs{}i\}} & \lowercase{\"\i}
\end{tabular}
\end{center}

Although in principle {\tt\bs{}uppercase} and {\tt\bs{}lowercase}
can be encountered at any place, in practice only the {\tt\bs{}uppercase}
and only in \LaTeX{} headers is used outside explicit User's control
(although, for example, to create the headers using {\sc small capitals}
font one could insert in some style the macro containing
the construction like {\tt\bs{}lowercase\{\bs{}sc ....\}}).
Roughly the \LaTeX{} mechanism for automatically
created headers works as follows:
\begin{enumerate}
\item The header text {\em some-header-text} containing the text
      and \TeX{} commands is created elsewhere.
\item The object {\em some-header-text} is expanded into non-expandable
      tokens.
\item The uppercase transformation over the list of
      non-expandable tokens is performed.
      The latter means that the characters
      are substituted by their {\tt\bs{}uccode} values while the \TeX{}
      primitive commands remain unchangable.
\item The result is substituted into the header of the page and
      the list of tokens is processed by \TeX{} as usually.
\end{enumerate}
(The detailed investigation of \LaTeX{} source code shows that it
is not actually true, but the result of `true' macro is close
to this description.)

The behaviour of \verb?\uppercase? and \verb?\lowerrcase? is different in
such formats as {\sl Plain}, \AmS\/\TeX{} and \LaTeX{} 2.09,
and \LaTeXe. The transformation of the characters in old formats
uses only the values \verb?\uccode? and \verb?\lccode?, while
\LaTeXe{} uses additional list \verb?\@uclclist? of characters
which use their own rule different from \verb?\lccode?--\verb?\uccode?.
In particular, for old formats and \LaTeX$2_{\varepsilon}$ in
OT1 with encoding the symbols \verb?\i? and \verb?\j? are not
affected by the commands \verb?\uppercase?
and \verb?\lowercase?, which means that the page header
ctreated automatically by \verb?\uppercase? will be wrong.

In this respect the behaviour of \LaTeXe{}
in T1 encoding is quite different.
The letter {\sl dotless-i} remains constant after
\verb?\lowercase?, and is transformed into capital {\sl I}
after \verb?\uppercase?. The letter {\sl I} after
\verb?\uppercase? remais the same, but \verb?\lowercase?
transforms it into ordinary {\sl i}.
Finally, the letter {\sl i} is transformed into {\sl I}
after \verb?\uppercase?, and conserves its form after
\verb?\lowercase?. Similar transformations happen with
$\hbox{\sl \j} \longleftrightarrow \hbox{\sl J}
\longleftrightarrow\hbox{\sl j}$.
This property enables to create headers and footers
properly as soon as only one \verb?\uppercase? is used for it,
but creates funny errors when the User tries to apply
\verb?\uppercase?--\verb?\lowercase? by himself%
   \footnote{The problem becomes even more complex taking into account
             that there is also the letter {\sl \.I} in encoding T1.
             It is transferred to ordinary {\sl i} by {\tt\bs{}lowercase},
             and into {\sl I} after subsequent {\tt\bs{}uppercase}.}.
The optional variant where the stress is put above some of these
letters makes the life even more unhappy.

The following macro enables to analyze
if the text is transformed by some \verb?\uppercase? or
\verb?\lowercase? commands and put correct form of the letters.
The commands \verb?\i? and \verb?\I? create the letters
{\sl \i}/{\sl I}, which are correctly processed by
\verb?\uppercase?--\verb?\lowercase?,
commands \verb?\ii? and \verb?\II? create the letters
{\sl i}/{\sl \.I} with corresponding properties:
\begin{itemize}\item[]\begin{verbatim}
\edef\temp{\the\i} \chardef\idotless=\temp\relax
\def\i{\ifnum`i=`\i \idotless \else I\fi}
\def\I{\ifnum`I=`\I I\else \idotless \fi}
\def\ii{\ifnum`i=`\i i\else \.I\fi}
\def\II{\ifnum`I=`\I \.I\else i\fi}
\end{verbatim}\end{itemize}
Finally, the ordinary letters \verb?i? and \verb?I?
correspond to the case where the lowercase form has
a dot while the uppercase form does not.
These macro work due to the fact that the name of the macro \verb?\I?
and \verb?\i? is conserved after \verb?\uppercase?--\verb?\lowercase?
transformation, while in expressions
\verb?`i? and \verb?`I? it is coverted appropriately.
It is worth to note that although {\em then} and {\em else}
parts of the macro are also affected by {\tt\bs{}uppercase}
and {\tt\bs{}lowercase}, the results are correct:
\begin{center}
\begin{tabular}{r@{=}lr@{=}l}
{\tt\bs{}uppercase\bs{}expandafter\{\bs{}i\}} & \uppercase\expandafter{\i}
&
{\tt\bs{}uppercase\bs{}expandafter\{\bs{}ii\}} & \uppercase\expandafter{\ii}
\\
{\tt\bs{}lowercase\bs{}expandafter\{\bs{}i\}} & \lowercase\expandafter{\i}
&
{\tt\bs{}lowercase\bs{}expandafter\{\bs{}ii\}} & \lowercase\expandafter{\ii}
\\
{\tt\bs{}uppercase\bs{}expandafter\{\bs{}I\}} & \uppercase\expandafter{\I}
&
{\tt\bs{}uppercase\bs{}expandafter\{\bs{}II\}} & \uppercase\expandafter{\II}
\\
{\tt\bs{}lowercase\bs{}expandafter\{\bs{}I\}} & \lowercase\expandafter{\I}
&
{\tt\bs{}lowercase\bs{}expandafter\{\bs{}II\}} & \lowercase\expandafter{\II}
\end{tabular}
\end{center}
It is more or less evident that the combination
``lowercase-i-without-dot'' + ``uppercase-I-with-dot''
is of no interest, although corresponding macro could be created
as well.

Similar commands are intoduced for  {\sl \j/j} and {\sl J/\.J}.
\begin{itemize}\item[]\begin{verbatim}
\edef\temp{\the\j} \chardef\jdotless=\temp\relax
\def\j{\ifnum`j=`\j \jdotless \else J\fi}
\def\J{\ifnum`J=`\J J\else \jdotless \fi}
\def\jj{\ifnum`j=`\j j\else \.J\fi}
\def\JJ{\ifnum`J=`\J \.J\else j\fi}
\end{verbatim}\end{itemize}

It is essential that the commands \verb?\i? and \verb?\I?,
\verb?\ii? and \verb?\II?, \verb?\j? and \verb?\J?,
\verb?\jj? and \verb?\JJ? creates the correct forms
when the commands \verb?\uppercase? and \verb?\lowercase?
or \verb?\MakeUppercase? and \verb?\MakeLowercase?
affect them. They also work correctly when there are
additional upper and lower accents created by the commands from
the section~\ref{S-commands}. It is worth to note that
the invisible characters created by the commands {\tt\bs{}markchar}
and {\tt\bs{}MARKCHAR} described in section~\ref{S-commandsI}
are also transformed into each other
after transformation by {\tt\bs{}uppercase}
and {\tt\bs{}lowercase}.

\subsection{Title letters `L+soft-sign' and `N+soft-sign'\label{S-title}}

Similar problem of case-sensitivity exists
in the writing systems for Serbian, Makedonian,
Itelmen and Nganasan languages which use the ligatures
`{\sl L+soft-sign}' and `{\sl N+soft-sign}':
{\cyrfont \char1}, {\cyrfont \char9},
{\cyrfont \char0}, {\cyrfont \char8}.
Except the uppercase and the lowercase variants shown above
there is also the `title' variant%
     \footnote{The Dutch ligature {\sl IJ}
               also have the title form.}
which is composed from the uppercase {\cyrfont L} and {\cyrfont N}
and the bowl from the {\em lowercase} soft-sign {\cyrfont \char126}.
Such ligature is useful for titles where the first letter is the
uppercase variant while the rest of the test is composed from
the lowercase letters.

The command {\tt\bs{}uppercase} applied to the title letter
should transfer it into the normal uppercase form,
and {\tt\bs{}lowercase}~--- into normal lowercase form.
Changing {\tt\bs{}lccode}--{\tt\bs{}uccode} values
for the title letters (which could help in this case)
is not allowed in \LaTeXe{}, and
the list {\tt\bs{}@uclclist} used in \LaTeXe{}
to make lower/uppercase conversion is of no
usage since different assignments are necessary
for {\tt\bs{}uppercase} and {\tt\bs{}lowercase}.

The following macro uses the same idea
to distinguish {\tt\bs{}uppercase} and {\tt\bs{}lowercase}
modes and to produce correct letter as the output:
\begin{verbatim}
\def\makeCYRlje{%
   \ifnum`x=`\X        \CYRLJE  % there was \uppercase
   \else \ifnum `X=`\x \cyrlje  % there was \lowercase
   \else               \CYRlje  % natural title form
   \fi\fi
}
\end{verbatim}
Here {\tt \bs{}CYRLJE} corresponds to the uppercase form
{\cyrfont \char1}, {\tt \bs{}cyrlje}~--- to the lowercase form
{\cyrfont \char9}, and {\tt \bs{}CYRlje}~--- to the title
form. Similar commands can be defined for the letter `N+soft-sign'.

\section{Conditional operators \textsf{if-then-else}\label{S-ifthen}}

Fine tuning of main characters and accents (modifiers) may require
the analysis of the font style used for the composite construction.
To make it easier, \textsc{accentbx} contains special
\textsf{if-then-else} macro:
\begin{description}

\item[] \verb?\ifupper{?{\em character}\verb?}{?%
              {\em if-upper}\verb?}{?{\em if-lower}\verb?}?~---
        checks that you deal with the uppercase character:
        first parameter is the character to be checked,
        second~--- commands which are executed for {\em true},
        third~--- commands to be executed for {\em false}.

\item[] \verb?\iflower{?{\em character}\verb?}{?%
              {\em if-upper}\verb?}{?{\em if-lower}\verb?}?~---
        checks that you deal with the lowercase character:
        first parameter is the character to be checked,
        second~--- commands which are executed for {\em true},
        third~--- commands to be executed for {\em false}.

\item[]  \verb?\ifcaseupper{?%
              {\em uppercase-or-none}\verb?}{?{\em lowercase}\verb?}?~---
        checks that your construction was influenced by \verb?\lowercase?:
        first group of commands is executed
        if there was \verb?\uppercase? conversion or no conversion,
        and second group of commands is executed
        if there was \verb?\lowercase? conversion.

\item[] \verb?\ifcaselower{?%
              {\em lowercase-or-none}\verb?}{?{\em uppercase}\verb?}?~---
        checks that your construction was influenced by \verb?\uppercase?:
        first group of commands is executed
        if there was \verb?\lowercase? conversion or no conversion,
        and second group of commands is executed
        if there was \verb?\uppercase? conversion.

\item[] \verb?\ifcasetitle{?{\em no-case}\verb?}{?%
              {\em uppercase}\verb?}{?{\em lowercase}\verb?}?~---
        checks allthree variants:
        first group of commands is executed if there is no conversion,
        second~--- for  \verb?\uppercase? conversion, third~---
        for \verb?\lowercase? conversion.

\item[] \verb?\ifwide{?{\em character}\verb?}{?%
              {\em if-wide}\verb?}{?{\em if-narrow}\verb?}?~---
        checks that you deal with wide character (character
        is considetred as wide if its width
        is more than the value \verb?\accentwidefactor?
        (default value for it is~\textsf{0.65em})).

\item[] \verb?\ifwidth{?{\em character}\verb?}{?{\em width}\verb?}{?%
              {\em if-wide}\verb?}{?{\em if-narrow}\verb?}?~---
        just the same as \verb?\ifwide?, but the width for comparison
        is specified explicitly as the second parameter.

\item[] \textsf{if-then-else} operators for font families:
       command
       \verb?\ifrm{#1}{#2}? checks that you are in normal (upright roman) mode,
       command
       \verb?\ifit{#1}{#2}?~--- that you are in {\it italic} mode,
       command
       \verb?\ifsl{#1}{#2}?~--- that you are in {\sl slanted} mode,
       command
       \verb?\ifbf{#1}{#2}?~--- that you are in {\bf boldface} mode,
       command
       \verb?\ifsf{#1}{#2}?~--- that you are in {\sf sans serif} mode,
       command
       \verb?\ifsc{#1}{#2}?~--- that you are in {\sc small caps} mode,
       command
       \verb?\iftt{#1}{#2}?~--- that you are in {\tt typewriter} mode.
There are also the commands \verb?\ifmit{#1}{#2}? and \verb?\ifsym{#1}{#2}?
which checks that by some mistake you are in mathematical mode
and are working with mathematical letters or mathematical symbols~---
but these should never used in practice \hackersmile.

\end{description}

\section{Changes in version 1.4\label{S-new}}

Version 1.4 is actually the first version which is uploaded to CTAN
for wide distribution among \TeX-users. Previous version 1.3
was distributed only between restricted set of people as a result
of private communications. Nevertheless, the changes are
the following:

\begin{itemize}
\item \verb?\aboxadjust? is renamed into \verb?\aboxshift?,
\item \verb?\makeaccent?, \verb?\aboxframed? and \verb?\aboxtuning?
      are added,
\item commands \verb?\akern? and \verb?aboxmarker? appear,
\item thickness and width od \verb?\aboxbar? is controlled now
      by the User; macro \verb?\aboxrule? appeared,
\item optional arguments are introduced for some commands
      (by default, i.e., without such arguments, these commands
      behave as it was in previous version),
\item robust versions of the commands with optional arguments are included,
\item family of \verb?\nullaccent...? commands is reviewed and
      modified (it was safe because in the previous version
      these commands were not documented and hence were not available
      for the User),
\item behaviour of \verb?\aboxbase? is changed~--- now it shifts
      the character only if it has positive depthy value; for compatibility
      with older application macro \verb?\aboxbaseline? which shifts
      the character to its baseline always, is added,
\item compatibility with {\sl Plain}, \AmS\TeX, etc., is checked
      and some errors are corrected,
\item internal macro \verb?\slant@value? is renamed and macro
      \verb?\strip@pt? is deleted (since \LaTeXe{} also has such macro),
\item \textsf{if-then-else} structures now have two or three
      parameters~--- groups of commands to be executed when
      corresponding condition is satisfied are specified explicitly,
\item \textsf{if-then-else} structures for uppercase/lowercase
      conversion and for title letters are added,
\item Now you have more or less detailed documentation \hackersmile.
\end{itemize}

\section*{Acknowledgements}

I am grateful to Olga Lapko, Mikhail Kolodin and Andrew Janishevskii
for numerous useful discussions which result
to the appearance of the style file {\sc accentbx}.
The examples of \TeX{} programming demonstrated
by Kees van der Laan helped to make the package {\sc accentbx}
more effective and compact. The discussions with J\"org Knappen
helped to understand better the base ideology of accents in T1 and EC/DC fonts.
The extensive comments and recommendations of the first referee
of this paper, Bernd Raichle, enabled to improve greatly the description
of the {\tt\bs{}accent} algorithm in section~\ref{S-accent}
and to correct numerous errors in suggested macro.
Robin Fairbairns spent a lot of his time
polishing the text of the first variant of this paper.
I express my warmest thanks to all these \TeX{}nicians and \TeX{}perts.

And I would like to thank separately
Aaldert Compagner from Delft University of Technology for his
long-term friendship and patient attention as a teacher~--- not
necessarily relating to some \TeX{} or \LaTeX{} joint works.

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\bibitem{TEXB}
        Donald E.\ Knuth.
        The \TeX{}book.
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\bibitem{TOPIC}
        Victor Eijkhout.
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\bibitem{SOL}
        D.Salomon.
        NTG's Advanced \TeX{} course: Insights \& Hindsights.
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\bibitem{DRATEX}
        Eitan M.\ Gurari. \TeX{} \& \LaTeX: drawing \&
        literate programming. McGraw-Hill, Inc., 1994.
\bibitem{Calc}
        Kresten Krab Thorup and Frank Jensen,
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        arithmetic in \LaTeX, version 4.0c).
\bibitem{FP}
        Michael Mehlich,
        The package {\sl FP.sty} ({\em Fixed Point Package}),
        version 0.8 (April 1995).
\bibitem{Real}
        Frank Buchholz,
        The style file {\sc RealCalc.sty},
        dated January 1993.
\end{thebibliography}
\endinput