# How can I redefine \int to put a negative space after the integral sign, but keep the limits properly set?

I'd like to modify the \int command such that it adds an automatic negative space, e.g. \! after the integral sign. Preferentially, I'd like to be able to not edit any of my code, so cleverly redefining \int seems like my best option. Unfortunately, naive implementations get the limits wrong:

\documentclass{article}
\usepackage[intlimits]{amsmath}
\usepackage{ifthen}

\newcommand{\diff}[2][]{
\ifthenelse { \equal {#1} {} }
{\ensuremath{\mathop{\mathrm{d} #2}}}
{\ensuremath{\mathop{\mathrm{d}^#1 #2}}}
}

\begin{document}

This is what I would want:
$$\int_0^\infty \mspace{-4mu}\diff[3]{\boldsymbol r} f(\boldsymbol r),$$
but with this user code", containing no negative spacing explicitly:
\begin{verbatim}
\int_0^\infty \diff[3]{\boldsymbol r} f(\boldsymbol r),
\end{verbatim}
which for comparison with the above gives:
$$\int_0^\infty \diff[3]{\boldsymbol r} f(\boldsymbol r),$$

mostly because this gives me the option to remove it or change the spacing when I see fit.
\end{document}


Which results in:

• Note I can't put it in \diff because that command is used everywhere, and sometimes the integral sign is followed by a fraction containing the \diff... Mar 18 '15 at 15:10
• Are you open to a wrapper command \Integral or something like this?
– user31729
Mar 18 '15 at 15:24
• @SoundsOfSilence Hmm that would take a lot of user code modification. I can write that myself, but asked here to see if there was a nice/hackish way to push that into \int. Mar 18 '15 at 15:26
• The problem is the implicit \limits command which must be done first and then then negative spacing added
– user31729
Mar 18 '15 at 15:28
• If you always add limits to the integral, it's easy, \def\int_#1^#2{\oldint_{#1}^{#2} \mspace{-4mu}}. In case you don't always have limits, it's a bit more trickier. In any case, let's see if someone comes with an “official” solution. Mar 18 '15 at 15:29

With this code

\usepackage{etoolbox}

\newcommand*\diff[2][]{\mathop{\mathrm{d}\ifblank{#1}{}{^{#1}}{#2}}}
\let\originalint\int
\def\int_#1^#2{\originalint_{#1}^{#2}\mathopen{}}


you remove space after the \int but your code must be written always with \int_{..}^{..} with limits and in that specific order. You could write some trickery so that if the limits are blank they are not added to the code. Or you could do some trickery with \@ifnextchar so that one checks for both limits in any order and the result is more clean. If it's wanted, I can add that. Here's the code (thanks to @kyle_the_hacker):

\usepackage{etoolbox}
\makeatletter
\newcommand*\diff[2][]{\mathop{\mathrm{d}\ifblank{#1}{}{^{#1}}{#2}}}
\let\int@original\int
\def\int{\int@checkfirstsb}
\def\int@checkfirstsb{\@ifnextchar_{\int@checksecondsp}{\int@checkfirstsp}}
\def\int@checkfirstsp{\@ifnextchar^{\int@checksecondsb}{\int@{}{}}}
\def\int@checksecondsp_#1{\@ifnextchar^{\int@grabsp{#1}}{\int@{#1}{}}}
\def\int@checksecondsb^#1{\@ifnextchar_{\int@grabsb{#1}}{\int@{}{#1}}}
\def\int@grabsb#1_#2{\int@{#2}{#1}}
\def\int@grabsp#1^#2{\int@{#1}{#2}}
\def\int@#1#2{\int@original\ifblank{#1}{}{_{#1}}\ifblank{#2}{}{^{#2}}\mathopen{}}
\makeatother


In any case, here's an oportunity to add a bit of code I wrote some time ago to add new kind of arguments to xparse.

\documentclass{scrartcl}
\usepackage[intlimits]{amsmath}
\usepackage{etoolbox,xparse}

\ExplSyntaxOn
\cs_new_protected:Npn \__xparse_count_type_k:w #1
{
\__xparse_single_token_check:n { #1 }
\__xparse_count_mandatory:N
}
\cs_new_protected:Npn \__xparse_count_type_K:w #1 #2
{
\__xparse_single_token_check:n { #1 }
\quark_if_recursion_tail_stop_do:nn { #2 } { \__xparse_bad_arg_spec:wn }
\__xparse_count_mandatory:N
}
{ \exp_args:NNo \__xparse_add_type_K:w #1 { \c__xparse_no_value_tl } }
{
\__xparse_flush_m_args:
\tl_put_right:Nn \l__xparse_signature_tl { #1 { #2 } }
\__xparse_prepare_signature:N
}
{
\exp_args:NNo \__xparse_add_expandable_type_K:w #1 { \c__xparse_no_value_tl }
}
{
\__msg_kernel_error:nnx { xparse } { invalid-expandable-argument-type } { K }
\__xparse_add_expandable_type_m:w % May be create this?
}
\cs_new_protected:Npn \__xparse_grab_K:w #1 #2 #3 \l__xparse_args_tl
{
\__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected_nopar:Npn
{ _ignore_spaces }
}
\cs_new_protected:Npn \__xparse_grab_K_long:w #1 #2 #3 \l__xparse_args_tl
{
\__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected:Npn
{ _ignore_spaces }
}
\cs_new_protected:Npn \__xparse_grab_K_trailing:w #1 #2 #3 \l__xparse_args_tl
{
\__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected_nopar:Npn
{ _ignore_spaces }
}
\cs_new_protected:Npn \__xparse_grab_K_long_trailing:w #1 #2 #3 \l__xparse_args_tl
{
\__xparse_grab_K_aux:NnnNn #1 { #2 } { #3 } \cs_set_protected:Npn
{ _ignore_spaces }
}
\cs_new_protected:Npn \__xparse_grab_K_aux:NnnNn #1 #2 #3 #4 #5
{
\exp_after:wN #4 \l__xparse_fn_tl ##1
{
#3 \l__xparse_args_tl
}
\use:c { peek_meaning_remove #5 :NTF } #1
{ \l__xparse_fn_tl }
{
#3 \l__xparse_args_tl
}
}

\prop_put:Nnn \c__xparse_shorthands_prop { a } { k \sb }
\prop_put:Nnn \c__xparse_shorthands_prop { b } { k \sp }
\prop_put:Nnn \c__xparse_shorthands_prop { A } { K \sb }
\prop_put:Nnn \c__xparse_shorthands_prop { B } { K \sp }

\NewDocumentCommand \diff { o m }
{\mathop{\mathrm{d}\IfValueT{#1}{^{#1}}{#2}}}
\ExplSyntaxOff

\let\originalint\int
\RenewDocumentCommand \int { a b }
{\originalint\IfValueT{#1}{_{#1}}\IfValueT{#2}{^{#2}}\mathopen{}}

\begin{document}

$$\int_0^\infty \diff[3]{\boldsymbol r} f(\boldsymbol r)$$

\end{document}


And it may be even better to check if \diff follows and in case it doesn't just have the original behaviour, just change the definition to this (it's a pity that spaces aren't skipped, so we need to explicitly check for a space and then check for \diff after that)

\makeatletter
\RenewDocumentCommand \int { a b t\@sptoken t\diff }
{\originalint\IfValueT{#1}{_{#1}}\IfValueT{#2}{^{#2}}%
\IfBooleanT{#4}{\mathopen{}\diff}}
\makeatother


# After a few thoughts

Completed rethink code that I would use for a complete flexibility. This adds all possible combinations of sub-superscripts for the \int plus the natural input for differentials \dd x, \dd{\bm x}, \dd^2 x, \dd^{a_1}{x_1}.

\usepackage{mathtools,bm}
\usepackage{etoolbox}
\makeatletter
\def\dd{\@ifnextchar^{\dd@grabsp}{\dd@{}}}
\def\dd@grabsp^#1#2{\dd@{#1}{#2}}
\def\dd@#1#2{\mathop{d\ifblank{#1}{}{^{#1}}{#2}}}
\let\int@original\int
\def\int{\int@checkfirstsb}
\def\int@checkfirstsb{\@ifnextchar_{\int@checksecondsp}{\int@checkfirstsp}}
\def\int@checkfirstsp{\@ifnextchar^{\int@checksecondsb}{\int@{}{}}}
\def\int@checksecondsp_#1{\@ifnextchar^{\int@grabsp{#1}}{\int@{#1}{}}}
\def\int@checksecondsb^#1{\@ifnextchar_{\int@grabsb{#1}}{\int@{}{#1}}}
\def\int@grabsb#1_#2{\int@{#2}{#1}}
\def\int@grabsp#1^#2{\int@{#1}{#2}}
\def\int@#1#2{\int@original\ifblank{#1}{}{_{#1}}\ifblank{#2}{}{^{#2}}\mathopen{}}
\makeatother


that with the xparse code from before it would become

\NewDocumentCommand\dd{bm}{\mathop{d\IfValueT{#1}{^{#1}}{#2}}}
\let\originalint\int
\RenewDocumentCommand\int{ab}{\originalint\IfValueT{#1}{_{#1}}\IfValueT{#2}{^{#2}}\mathopen{}}

• I tried something like: \makeatletter \let\originalint\int \def\int\@ifnextchar_{\@int}{\@int_{}^{}} \def\@int_#1^#2{\originalint_{#1}^{#2}\mathopen{}} \makeatother but it don't work, could you add the correct way to do it to you answer? Thanks. Feb 9 '16 at 20:55
• \def\int{\@ifnextchar_{\@int}{\@int_{}^{}}} at least there you got a missing pair of {..}. Feb 9 '16 at 21:22
• Yeah, ok. That's because I tried a lot of stuff. I still become the error: You can't use \spacefactor' in display math mode. (so obviously a problem with the @) Feb 9 '16 at 22:01
• You are not using \makeatletter. This should compile fine \makeatletter \let\originalint\int \def\int{\@ifnextchar_{\@int}{\@int_{}^{}}} \def\@int_#1^#2{\originalint_{#1}^{#2}\mathopen{}} \makeatother Feb 9 '16 at 22:03
• You are right, they were mispositioned. Edited your answer. Feb 9 '16 at 22:07

This has become really easy with the newest release of xparse:

\documentclass{article}
\usepackage[intlimits]{amsmath}
\usepackage{bm}
\usepackage{xparse}

\let\oldint\int % for the comparison

\RenewDocumentCommand{\int}{e{_^}}{%
\DOTSI
\intop_{\IfValueT{#1}{#1}}^{\IfValueT{#2}{#2}}%
\mspace{-4mu}%
}

\NewDocumentCommand{\diff}{om}{% equivalent, but easier with xparse
\mathop{\mathrm{d}\IfValueT{#1}{^{#1}}#2}
}

\begin{document}

This is the normal typesetting
$$\oldint_0^\infty \diff[3]{\bm{r}} f(\bm{r}),$$
This is what I would want:
$$\oldint_0^\infty \mspace{-4mu}\diff[3]{\bm{r}} f(\bm{r}),$$
and this is what we get
$$\int_0^\infty \diff[3]{\bm{r}} f(\bm{r}),$$

\end{document}


However, this is a false problem, mainly due to the spurious space inserted by the faulty definition of \diff.

Indeed, compare with

\documentclass{article}
\usepackage[intlimits]{amsmath}
\usepackage{bm}
\usepackage{xparse}

\NewDocumentCommand{\diff}{om}{% note \!
\mathop{\!\mathrm{d}\IfValueT{#1}{^{#1}}#2}
}

\begin{document}

This is the normal typesetting
$$\int_0^\infty \diff[3]{\bm{r}} f(\bm{r}),$$

\end{document}


With the previously posted answer being HUGE and has complex dependencies, I tried to come up with a more compact solution, and arrived at the following:

## Code

Drop this anywhere in the document, before the first use of \int.

\makeatletter
\let\MyIntOrig\int
\def\MyIntSpace{\hspace{-.5em}} %% Configure as needed.
\def\int{\MyInt}
\def\MyInt{\MyIntOrig\MyIntSkipMaybe}
\def\MyIntSkipMaybe{
\@ifnextchar_{\MyIntSkipScript}{%
\@ifnextchar^{\MyIntSkipScript}{%
\@ifnextchar\limits{\MyIntSkipTok}{%
\@ifnextchar\nolimits{\MyIntSkipTok}{%
%% Add more cases here as needed. Keep in mind to close the braces.
\MyIntSpace}}}}%
}
\def\MyIntSkipScript#1#2{#1{#2}\MyIntSkipMaybe}
\def\MyIntSkipTok#1{#1\MyIntSkipMaybe}
\makeatother


## Minimal working document

\documentclass[12pt]{article}
\usepackage{amsmath}

\begin{document}

\makeatletter
\let\MyIntOrig\int
\def\MyIntSpace{\hspace{-.5em}} %% Configure as needed.
\def\int{\MyInt}
\def\MyInt{\MyIntOrig\MyIntSkipMaybe}
\def\MyIntSkipMaybe{
\@ifnextchar_{\MyIntSkipScript}{%
\@ifnextchar^{\MyIntSkipScript}{%
\@ifnextchar\limits{\MyIntSkipTok}{%
\@ifnextchar\nolimits{\MyIntSkipTok}{%
%% Add more cases here as needed. Keep in mind to close the braces.
\MyIntSpace}}}}%
}
\def\MyIntSkipScript#1#2{#1{#2}\MyIntSkipMaybe}
\def\MyIntSkipTok#1{#1\MyIntSkipMaybe}
\makeatother

\def\MyTry#1{%
& {\let\int\MyIntOrig #1} &
& #1 &
& \text{\ttfamily\detokenize{#1}}&
}
\begin{align*}
& \text{Original} && \text{Redefined} && \text{Source} &\\
\MyTry{\int }\\
\MyTry{\int \int }\\
\MyTry{\int a\,dx}\\
\MyTry{\int _b a\,dx}\\
\MyTry{\int ^c a\,dx}\\
\MyTry{\int _b^c a\,dx}\\
\MyTry{\int _{from}^{to} a\,dx}\\
\MyTry{\int \limits_{from}^{to} a\,dx}\\
\MyTry{\int \nolimits_{from}^{to} a\,dx}\\
\MyTry{\int a_b x}
\end{align*}

\end{document}
`