Low-level command for controlling left superscript spacing

Question

This question has led to a new package: leftindex

It is a well-known problem that there seems to be no automatic way of getting nice spacing for left indices, particularly left superscripts. The most standard choice of command seems to be \prescript from mathtools, but superscripts suffer from the same problem as with other options:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\[
    \prescript{a}{b}{f},
    \qquad
    \prescript{a}{b}{\int}
\]

\end{document}

What I would like is a low-level, manual solution to this problem: A command

\manualprescript{<height>}{<superscript indentation>}{<subscript indentation>}
        {<superscript>}{<subscript>}{<symbol>}

where I can manually specify the height and the indentation of the indices. This could be either using TeX dimensions (e.g. .3em) or as tokens to be plugged into \vphantom and \hphantom. Either solution will be fine by me (or both, if you have the time). I could probably come up with some (very) bad solution to this myself using boxes and \phantom’s, which is why I am asking in here in order to obtain the right solution. (If possible, I would prefer a solution in LaTeX3 syntax since this is usually more readable and future-proof).

Answer 1

You can do it automatically.

\documentclass{article}
\usepackage{amsmath,mathtools,xparse}

\makeatletter
\NewDocumentCommand{\preint}{e{^_}}{\mathpalette\pre@int{{#1}{#2}}\!\int}
\newcommand{\pre@int}[2]{\pre@@int#1#2}
\newcommand{\pre@@int}[3]{%
  \sbox0{$#1\int\sb{xxxxxx}$}%
  \sbox2{$#1{\int}\sb{xxxxxx}$}%
  \setlength{\dimen4}{\dimexpr\wd2-\wd0\relax}%
  % compute the spacing
  \settowidth{\dimen0}{$\m@th#1^{\IfValueT{#2}{#2}}$}%
  \addtolength{\dimen0}{-\dimen4}%
  \settowidth{\dimen2}{$\m@th#1_{\IfValueT{#3}{#3}}$}%
  % start the business
  \mathop{}\!%
  \ifdim\dimen0>\dimen2 \kern\dimen0\else\kern\dimen2\fi
  % print the scripts
  {\mbox{$#1\vphantom{\int}$}}
  ^{\mathmakebox[0pt][l]{\mathmakebox[\dimen4][r]{\IfValueT{#2}{#2}\mspace{-1mu}}}}
  _{\mathmakebox[0pt][r]{\IfValueT{#3}{#3}}}
 }
\makeatother

\begin{document}

\[
x\preint_a^b f(x)\,dx + \preint_a^{b+c+d} f(x)\,dx
\]
\begin{center}
$x\preint_a^b$
\end{center}

\end{document}

Answer 2

This solution is now available as a package: leftindex

I tried adjusting egreg’s answer to the general case. It is not built specifically for \int and therefore does not produce quite as perfect an output for that particular symbol. The benefit is that it provides relatively nice results in the general case. I provide the command

\leftindex^{<left superscript>}_{<left subscript>} {<symbol>}

This will indent the left superscript with the same value as the negative indentation of the right subscript. Sometimes, this yields wrong results. Therefore, the command takes two additional, optional arguments:

\leftindex[<slanting phantom>][<height phantom>]
    ^{<left superscript>}_{<left subscript>} {<symbol>}

This one will instead calculate the left superscript indentation using the <slanting phantom>. If provided, it will calculate the height based on the <height phantom>.

There is also another, underlying command

\manualleftindex
    {<height phantom>}
    {<slanting phantom>}
    {<subscript>}
    {<superscript>}

which is mainly intended for use in other commands (or packages).

\documentclass{article}

\usepackage{expl3,mathtools,kpfonts}

\ExplSyntaxOn

\DeclareDocumentCommand\manualleftindex { mmmm }
{
    % #1 = height phantom
    % #2 = slanting phantom
    % #3 = left superscript
    % #4 = left subscript
    \mathpalette \__leftindex_auxiliary_mathpalette_command:nn { {#1}{#2}{#3}{#4} }
}

\ExplSyntaxOff

\DeclareDocumentCommand\leftindex { o o E{^_}{{}{}} m }
{
    % #1 = slanting phantom
    % #2 = height phantom
    % #3 = left superscript
    % #4 = left subscript
    % #5 = symbol
    \IfValueTF {#1}
    {
        \IfValueTF{#2}
        {
            \manualleftindex { #2 } { #1 } { #3 } { #4 }
        }
        {
            \manualleftindex { #1 } { #1 } { #3 } { #4 }
        }
    }
    {
        \manualleftindex { #5 } { #5 } { #3 } { #4 }
    }
    #5
}

\DeclareDocumentCommand\LeftIndex { o o E{^_}{{}{}} }
{
    % #1 = slanting phantom
    % #2 = height phantom
    % #3 = left superscript
    % #4 = left subscript
    \IfValueTF {#1}
    {
        \IfValueTF{#2}
        {
            \manualleftindex { #2 } { #1 } { #3 } { #4 }
        }
        {
            \manualleftindex { #1 } { #1 } { #3 } { #4 }
        }
    }
    {
        \manualleftindex { } { } { #3 } { #4 }
    }
}

\ExplSyntaxOn

\cs_new_protected:Npn\leftindex_kern_horizontal:n#1
{
    \kern #1 \relax
}

\cs_new_protected:Npn\leftindex_set_mathsurround_to_zero:
{
     % This is equivalent to "\m@th"
    \dim_set:Nn \mathsurround { 0pt }
}

\cs_new_protected:Npn\__leftindex_auxiliary_mathpalette_command:nn#1#2
{
    \__leftindex_auxiliary:nnnnn { #1 } #2
}

\dim_new:N\l__leftindex_phantom_height_dim

\box_new:N \l__leftindex_slanting_phantom_with_subscript_box
\dim_new:N \l__leftindex_slanting_phantom_with_subscript_dim

\box_new:N \l__leftindex_slanting_phantom_with_subscript_without_indentation_box
\dim_new:N \l__leftindex_slanting_phantom_with_subscript_without_indentation_dim

\dim_new:N \l__leftindex_indentation_of_slanting_phantom_subscript

\box_new:N \l__leftindex_superscript_temp_box
\dim_new:N \l__leftindex_width_of_superscript_dim

\box_new:N \l__leftindex_subscript_temp_box
\dim_new:N \l__leftindex_width_of_subscript_dim

\cs_new_protected:Npn\__leftindex_auxiliary:nnnnn#1#2#3#4#5
{
    \group_begin:
        \hbox_set:Nn \l__leftindex_slanting_phantom_with_subscript_box
            { $ #1 #3 \sb{xxxxxx} $ }
        \dim_set:Nn \l__leftindex_slanting_phantom_with_subscript_dim
            { \box_wd:N \l__leftindex_slanting_phantom_with_subscript_box }
        \hbox_set:Nn \l__leftindex_slanting_phantom_with_subscript_without_indentation_box
            { $ #1 \hbox:n {$ #1 #3 $} \sb{xxxxxx} $ }
        \dim_set:Nn \l__leftindex_slanting_phantom_with_subscript_without_indentation_dim
            { \box_wd:N \l__leftindex_slanting_phantom_with_subscript_without_indentation_box }
        \dim_set:Nn \l__leftindex_indentation_of_slanting_phantom_subscript
        {
            \l__leftindex_slanting_phantom_with_subscript_without_indentation_dim
            -
            \l__leftindex_slanting_phantom_with_subscript_dim
        }
        \tl_if_blank:nTF { #4 }
        {
            \dim_zero:N \l__leftindex_width_of_superscript_dim
        }
        {
            \hbox_set:Nn \l__leftindex_superscript_temp_box
            {
                $
                \leftindex_set_mathsurround_to_zero:
                #1 \sp { #4 }
                $
            }
            \dim_set:Nn \l__leftindex_width_of_superscript_dim
            {
                \box_wd:N \l__leftindex_superscript_temp_box
                -
                \l__leftindex_indentation_of_slanting_phantom_subscript
            }
        }
        \tl_if_blank:nTF { #5 }
        {
            \dim_zero:N \l__leftindex_width_of_subscript_dim
        }
        {
            \hbox_set:Nn \l__leftindex_subscript_temp_box
            {
                $
                \leftindex_set_mathsurround_to_zero:
                #1 \sb { #5 }
                $
            }
            \dim_set:Nn \l__leftindex_width_of_subscript_dim
            {
                \box_wd:N \l__leftindex_subscript_temp_box
            }
        }
        \mathop{}
        \leftindex_kern_horizontal:n
        {
            \dim_max:nn
                { \l__leftindex_width_of_superscript_dim }
                { \l__leftindex_width_of_subscript_dim }
        }
        \mathopen{ \vphantom { #2 } }
        \tl_if_blank:nF { #4 }
        {
            \sp {
                \mathmakebox[0pt][l]{
                    \mathmakebox[ \l__leftindex_indentation_of_slanting_phantom_subscript ][r]{ #4 }
                }
            }
        }
        \tl_if_blank:nF { #5 }
        {
            \sb {
                \mathmakebox[0pt][r]{ #5 }
            }
        }
    \group_end:
}

\ExplSyntaxOff

\begin{document}

\[
    x \leftindex^{a+b}_{c+d} {\int} f(x)\, dx
\]


\[
    \leftindex^{1}_{0} {f}^u_v
    \neq
    \leftindex^{pq}_{0} {H}^u_v
\]

\[
    \leftindex^{a}_{b} {\Gamma}^c_d
    \neq
    \leftindex[]^{a}_{b} {\Gamma}^c_d
\]


\end{document}