How to typeset ordered pairs?

Question

I'd like to typeset ordered pairs with comma-separated components while \langle and \rangle as their delimiters. I want line breaks at commas for an ordered pair in inline math mode.

So I came up with the following piece of code, however, there is an annoying bug in it.

\documentclass{article}
%\usepackage{amsmath,physics}
\def\opair#1{%
    \mathopen\langle
    \kern 2pt
    \begingroup
        \edef@tempa{#1,}%
        \expandafter
    \endgroup
    \expandafter\opairImpl@tempa\relax
    \kern 2pt
    \mathclose\rangle
}
\def\opairImpl#1,#2\relax{%
    {#1}%
    \begingroup
        \ifx\relax#2\relax
            \def\next{ \endgroup }%
        \else
            \def\next{
                \endgroup
                ,,\allowbreak
                \opairImpl#2\relax
            }
        \fi
    \next
}
\begin{document}
( \opair{x    ,     y,   z} )
( \opair{ \cos\alpha, \cos\beta, \cos\gamma } )
( \opair{x_1,x_2,\cdots{},x_n} )
(\opair{a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,z})
\end{document}

When \usepackage{amsmath,physics} is disabled, \( \opair{x_1,x_2,\cdots{},x_n} \) yields terrible output, where the comma behind x_2 went missing, as is shown in the screenshot below.

When \usepackage{amsmath,physics} is enabled, an even more annoying bug emerged. The log file is shown below.

This is XeTeX, Version 3.14159265-2.6-0.999992 (TeX Live 2020/W32TeX) (preloaded format=xelatex 2021.3.15)  11 APR 2021 22:34
entering extended mode
 restricted \write18 enabled.
 %&-line parsing enabled.
**tmp.tex
(./tmp.tex
LaTeX2e <2020-02-02> patch level 5
L3 programming layer <2020-03-06>
(~/texlive/2020/texmf-dist/tex/latex/base/article.cls
Document Class: article 2019/12/20 v1.4l Standard LaTeX document class
(~/texlive/2020/texmf-dist/tex/latex/base/size10.clo
File: size10.clo 2019/12/20 v1.4l Standard LaTeX file (size option)
)
\c@part=\count163
\c@section=\count164
\c@subsection=\count165
\c@subsubsection=\count166
\c@paragraph=\count167
\c@subparagraph=\count168
\c@figure=\count169
\c@table=\count170
\abovecaptionskip=\skip47
\belowcaptionskip=\skip48
\bibindent=\dimen134
)
(~/texlive/2020/texmf-dist/tex/latex/amsmath/amsmath.sty
Package: amsmath 2020/01/20 v2.17e AMS math features
\@mathmargin=\skip49
For additional information on amsmath, use the `?' option.
(~/texlive/2020/texmf-dist/tex/latex/amsmath/amstext.sty
Package: amstext 2000/06/29 v2.01 AMS text
(~/texlive/2020/texmf-dist/tex/latex/amsmath/amsgen.sty
File: amsgen.sty 1999/11/30 v2.0 generic functions
@emptytoks=\toks15
\ex@=\dimen135
))
(~/texlive/2020/texmf-dist/tex/latex/amsmath/amsbsy.sty
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
\pmbraise@=\dimen136
)
(~/texlive/2020/texmf-dist/tex/latex/amsmath/amsopn.sty
Package: amsopn 2016/03/08 v2.02 operator names
)
\inf@bad=\count171
LaTeX Info: Redefining \frac on input line 227.
\uproot@=\count172
\leftroot@=\count173
LaTeX Info: Redefining \overline on input line 389.
\classnum@=\count174
\DOTSCASE@=\count175
LaTeX Info: Redefining \ldots on input line 486.
LaTeX Info: Redefining \dots on input line 489.
LaTeX Info: Redefining \cdots on input line 610.
\Mathstrutbox@=\box45
\strutbox@=\box46
\big@size=\dimen137
LaTeX Font Info:    Redeclaring font encoding OML on input line 733.
LaTeX Font Info:    Redeclaring font encoding OMS on input line 734.
\macc@depth=\count176
\c@MaxMatrixCols=\count177
\dotsspace@=\muskip16
\c@parentequation=\count178
\dspbrk@lvl=\count179
\tag@help=\toks16
\row@=\count180
\column@=\count181
\maxfields@=\count182
\andhelp@=\toks17
\eqnshift@=\dimen138
\alignsep@=\dimen139
\tagshift@=\dimen140
\tagwidth@=\dimen141
\totwidth@=\dimen142
\lineht@=\dimen143
@envbody=\toks18
\multlinegap=\skip50
\multlinetaggap=\skip51
\mathdisplay@stack=\toks19
LaTeX Info: Redefining [ on input line 2859.
LaTeX Info: Redefining ] on input line 2860.
)
(~/texlive/2020/texmf-dist/tex/latex/physics/physics.sty
Package: physics
(~/texlive/2020/texmf-dist/tex/latex/l3packages/xparse/xparse.sty
(~/texlive/2020/texmf-dist/tex/latex/l3kernel/expl3.sty
Package: expl3 2020-03-06 L3 programming layer (loader)
(~/texlive/2020/texmf-dist/tex/latex/l3backend/l3backend-xdvipdfmx.def
File: l3backend-xdvipdfmx.def 2020-03-12 L3 backend support: xdvipdfmx
\g__graphics_track_int=\count183
\l__pdf_internal_box=\box47
\g__pdf_backend_object_int=\count184
\g__pdf_backend_annotation_int=\count185
))
Package: xparse 2020-03-06 L3 Experimental document command parser
\l__xparse_current_arg_int=\count186
\g__xparse_grabber_int=\count187
\l__xparse_m_args_int=\count188
\l__xparse_v_nesting_int=\count189
))
No file tmp.aux.
\openout1 = `tmp.aux'.
LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 31.
LaTeX Font Info:    Trying to load font information for TS1+cmr on input line 3



(~/texlive/2020/texmf-dist/tex/latex/base/ts1cmr.fd
File: ts1cmr.fd 2019/12/16 v2.5j Standard LaTeX font definitions
)
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for TU/lmr/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 31.
LaTeX Font Info:    ... okay on input line 31.
! Undefined control sequence.
\DN@ ->\def \next@
l.32 ( \opair{x_1,x_2,\cdots{},x_n}
                                     ) 
Here is how much of TeX's memory you used:
 1999 strings out of 479418
 31789 string characters out of 5884585
 281504 words of memory out of 5000000
 19574 multiletter control sequences out of 15000+600000
 532800 words of font info for 27 fonts, out of 8000000 for 9000
 1348 hyphenation exceptions out of 8191
 44i,3n,40p,309b,52s stack positions out of 5000i,500n,10000p,200000b,80000s
No pages of output.

I noticed that \( \opair{x_1,x_2, \cdots{},x_n} \) ensures the comma before \cdots{} show up correctly, in contrast to \( \opair{x_1,x_2,\cdots{},x_n} \); but I don't know why so.

What should I do then? Plz help and thx in advance.

EDIT:

Expected output:

Expected behavior:

Bug-free when using together with packages like amsmath and physics.

EDIT 1:

After taking @egrep 's approach, the following snipet yields Undefined control sequence error:

\begin{align*}
\mat{T}
&=\opair{
\eval{\jacobi{F,G}{y,z}}_M,
\eval{\jacobi{F,G}{z,x}}_M,
\eval{\jacobi{F,G}{x,y}}_M
} \\
&=\opair{
\begin{vmatrix}
F_y & F_z \\
G_y & G_z \\
\end{vmatrix}_{M},
\begin{vmatrix}
F_z & F_x \\
G_z & G_x \\
\end{vmatrix}_{M},
\begin{vmatrix}
F_x & F_y \\
G_x & G_y \\
\end{vmatrix}_{M}
}.
\end{align*}

Log file:

! Argument of \__clist_use:nwwwwnwn has an extra }.
<inserted text> 
                \par 
l.42 \end{align*}
?

BTW I defined \let\mat\boldsymbol and \newcommand{\jacobi}[2]{ \pdv{ (#1) }{ (#2) } }%

Expected output:

I think it is the fault of \jacobi, but I don't know what to do.

@Bernard I just edited and showcased the expected output and behavior. — KaiserKatze, Apr 11 '21 at 15:04

egreg · Accepted Answer · 2021-04-11T15:54:01.503

The error is in \edef\@tempa{#1,} because \cdots (in the amsmath version) doesn't survive it.

There is no need for \edef and \def suffices.

Here's an alternative implementation that doesn't substantially differs from yours, except that I use mu units for the leading and trailing space and I add some small flexibility in the glue after commas to allow for justification.

Instead of reinventing the wheel to process the comma list, I use a predefined method in expl3. If you're running a version of LaTeX prior to 2020-10-01, you need \usepackage{xparse}.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\opair}{m}
 {
  \langle\mspace{4mu}
  \clist_set:Nn \l_tmpa_clist { #1 }
  \clist_use:Nn \l_tmpa_clist {,\mspace{3mu plus 1mu minus 1mu}\allowbreak}
  \mspace{4mu}\rangle
}
\ExplSyntaxOff
\begin{document}
( \opair{x    ,     y,   z} )
( \opair{ \cos\alpha, \cos\beta, \cos\gamma } )
( \opair{x_1,x_2,\cdots,x_n} )
(\opair{a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,
z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,z})
\end{document}

Don't use {} to terminate commands in math mode, because it adds possibly unwanted empty atoms.

A different implementation that only allows line breaks after the second item but only up to the penultimate one: you don't want that an ordered pair is broken across lines, but possibly want it for longer tuples.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\opair}{m}
 {
  \langle\mspace{4mu}
  \kaiserkatze_opair:n { #1 }
  \mspace{4mu}\rangle
 }
\seq_new:N \l__kaiserkatze_opair_items_seq
\tl_new:N \l__kaiserkatze_opair_first_tl
\cs_new_protected:Nn \kaiserkatze_opair:n
 {
  \seq_set_from_clist:Nn \l__kaiserkatze_opair_items_seq { #1 }
  % set off the first item and insert it
  \seq_pop_left:NN \l__kaiserkatze_opair_items_seq \l__kaiserkatze_opair_first_tl
  \tl_use:N \l__kaiserkatze_opair_first_tl
  % now insert commas and allowed breaks
  \seq_map_indexed_inline:Nn \l__kaiserkatze_opair_items_seq
   {
    % comma and thin space
    ,\mspace{3mu plus 1mu minus 1mu}
    % but \allowbreak only after the second item and before the penultimate
    \int_compare:nT { 1 < ##1 < \seq_count:N \l__kaiserkatze_opair_items_seq }
     { \allowbreak }
    % the item
    ##2
   }
 }
\ExplSyntaxOff
\begin{document}
( \opair{x    ,     y,   z} )
( \opair{ \cos\alpha, \cos\beta, \cos\gamma } )
( \opair{x_1,x_2,\cdots{},x_n} )
(\opair{a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,
z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,p,q,r,s,t,u,v,w,x,y,z})
\parbox[t]{0pt}{
(\opair{a,b,c,d,e,f,g,h})
}
\end{document}

The \parbox is just to show where breaks are allowed.

Wow, I think your approach is quite modern so I decided to take it. :D — KaiserKatze, Apr 11 '21 at 15:37
Oh I forgot another case. Could you plz take a look at the latest edit of my post? — KaiserKatze, Apr 11 '21 at 15:43
@KaiserKatze Sorry, I don't endorse using physics with its funny syntax and implementation. But the error is about \mat being undefined: is it defined in physics? — egreg, Apr 11 '21 at 15:56

How to typeset ordered pairs?

1 Answers1

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