Second kind of Surface Integral with P,Q,R optional

Question

I want to use \dss[\Sigma][P][Q][R] or \dss[\Sigma]{P,Q,R} or \dss{\Sigma,P,Q,R} to generate

\[
\iint_{\Sigma} P\mathrm{d}y\mathrm{d}z+Q\mathrm{d}z\mathrm{d}x+R\mathrm{d}x\mathrm{d}y
\]

---

\documentclass{article}
%\usepackage{xparse,expl3}
\usepackage{amsmath}
%\ExplSyntaxOn
\NewDocumentCommand{\dss}{O{\Sigma}ooo}{\iint_{#1}%
    \IfValueT{#2}{#2\,\mathrm{d}y\mathrm{d}z}%
    \IfValueT{#3}{+#3\,\mathrm{d}z\mathrm{d}x}%
    \IfValueT{#4}{+#4\,\mathrm{d}x\mathrm{d}y}%
}
%\ExplSyntaxOff
\begin{document}
$\dss[D][(x+y+z)][xy][(x-y-z)]$

$\dss[D][][xy][(x-y-z)]$

$\dss[D][][][x-y-z]$

$\dss[D][(x+y+z)][][]$

%or $\dss{D,x+y+z,xy,x-y-z}$.
\end{document}

But if we only have Q and R, then there is no + sign with Q. However, there are many situations and I don't know how to deal with it.

\dss[D][][][x-y-z] indicates P and Q empty but actually those are T under the test of \IfValueTF. But I can't use \dss[D][x-y-z] since x-y-z will presents P instead of R.

Answer 1

I suggest a key-value approach.

\documentclass{article}
\usepackage{amsmath}

% swap the comments if you really want an upright d
\newcommand{\diff}{\mathop{}\!d}
%\newcommand{\diff}{\mathop{}\!\mathrm{d}}

\ExplSyntaxOn
\NewDocumentCommand{\dss}{O{\Sigma}m}
 {
  \iint\sb{#1}%
  \helen_dss:n {#2}
 }

\keys_define:nn { helen/dss }
 {
  P .tl_set:N = \l_helen_dss_p_tl,
  Q .tl_set:N = \l_helen_dss_q_tl,
  R .tl_set:N = \l_helen_dss_r_tl,
 }
\bool_new:N \l__helen_dss_check_bool

\cs_new_protected:Nn \helen_dss:n
 {
  \group_begin:
  % populate the token lists
  \keys_set:nn { helen/dss } {#1}
  % add the parts
  \bool_set_true:N \l__helen_dss_check_bool
  \tl_if_blank:VTF \l_helen_dss_p_tl
   {% no P part
    \bool_set_false:N \l__helen_dss_check_bool
   }
   {% P part
    \tl_use:N \l_helen_dss_p_tl \diff y \diff z
   }
  \tl_if_blank:VF \l_helen_dss_q_tl
   {
    \bool_if:NT \l__helen_dss_check_bool
     {
      \tl_if_eq:enF { \tl_head:N \l_helen_dss_q_tl } { - } { + }
     }
    \tl_use:N \l_helen_dss_q_tl \diff z \diff x
    \bool_set_true:N \l__helen_dss_check_bool
   }
  \tl_if_blank:VF \l_helen_dss_r_tl
   {
    \bool_if:NT \l__helen_dss_check_bool
     {
      \tl_if_eq:enF { \tl_head:N \l_helen_dss_r_tl } { - } { + }
     }
    \tl_use:N \l_helen_dss_r_tl \diff x \diff y
   }
  \group_end:
 }

\ExplSyntaxOff

\begin{document}

\begin{gather}
\dss{P=(x+y+z),Q=xy,R=(x-y-z)}    % 1
\\
\dss{P=(x+y+z),Q=-xy,R=(x-y-z)}   % 2
\\
\dss{P=(x+y+z),R=(x-y-z)}         % 3
\\
\dss{Q=xy,R=(x-y-z)}              % 4
\\
\dss[D]{R=(x-y-z)}                % 5
\\
\dss{P=(x+y+z)}                   % 6
\\
\dss{Q=(x+y+z),R=-xy}             % 7
\end{gather}

\end{document}

Care has been taken not to add a spurious + sign when one of the trailing parts starts with a minus sign.

Sorry, but I can't stand the upright d for the differential. 😉 In case you prefer it, just choose the second definition of \diff. Use \diff whenever you have a differential in your document. This way you can switch to the alternative typesetting by just changing the definition.

Answer 2

As noted in the comments, consecutive optional arguments mean that if you want later, then you must have the earlier, and they're no longer really optional. So I'm going to make them mandatory. I'm also going to object to the syntax \dss{\Sigma,P,Q,R}, because the \Sigma is different than the other arguments. So we'll end up with a signature \dss[\Sigma]{P}{Q}{R}.

I'm going to use expl3 after all, because its seq (and clist) have an easy way to join several values with something between, which is what you're needing with the +.

\documentclass{article}
\usepackage{amsmath}
\newcommand{\dss}[4][\Sigma]{\iint_{#1}\plusJoinedDiffs{#2}{#3}{#4}}
\ExplSyntaxOn
\seq_new:N \l__helenburns_args_seq
\cs_new:Npn \plusJoinedDiffs #1#2#3 {
  \seq_clear:N \l__helenburns_args_seq
  \IfBlankF{#1}
    { \seq_put_right:Nn \l__helenburns_args_seq {#1\,\mathrm{d}y\mathrm{d}z} }
  \IfBlankF{#2}
    { \seq_put_right:Nn \l__helenburns_args_seq {#2\,\mathrm{d}z\mathrm{d}x} }
  \IfBlankF{#3}
    { \seq_put_right:Nn \l__helenburns_args_seq {#3\,\mathrm{d}x\mathrm{d}y} }
  \seq_use:Nn \l__helenburns_args_seq {+}
}
\ExplSyntaxOff

\begin{document}
\begin{gather*}
\dss[D]{(x+y+z)}{xy}{(x-y-z)}\\
\dss[D]{}{xy}{(x-y-z)}\\
\dss[D]{}{}{x-y-z}\\
\dss[D]{(x+y+z)}{}{}
\end{gather*}
\end{document}

(You could split the input in {P,Q,R}, but then you'd also need to have an input of {,,R}, which I don't like.)