\left and \right with array

Question

The following definition, from How to continue a piece of text so it is aligned with the last line of an inline multiline box?, allows splitting a math set-builder expression across two lines:

\newcommand\setst[2]{\{#1 : 
   \begin{array}[t]{@{}l@{}}#2 \}\end{array}}

I want:

1. to change \{ and \} to \left\{ and \right\}, respectively. The following attempt generates an error of a missing `\right. ; and

2. not to have symbols that would normally be tall in display math, such as integral signs, get squashed down by the array environment.

   What's wrong with my syntax?

   \newcommand\Setst2{\left{#1 : \right. % \begin{array}[t]{@{}l@{}}\left.#2 \right}\end{array}}

And how fix the issue of squashed normally-tall symbols retain their noraml display-math height? (See 2nd source file below.)

Example source (modified from above-cited link):

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand\setst[2]{\{#1 : 
  \begin{array}[t]{@{}l@{}}#2 \}\end{array}}

% my attempted mod
\newcommand\Setst[2]{\left\{#1 : \right. %
  \begin{array}[t]{@{}l@{}}\left.#2 \right\}\end{array}}

\begin{document}

Braces OK:
\[
\setst{x}{ x \in S_1 \land {} \\
          (x \in S_2 \lor x \in S_3) }
\]

Error:
\[
\Setst{x}{ x \in S_1 \land {} \\
          (x \in S_2 \lor x \in S_3) }
\]

\end{document}

Here's the printed output from just the "OK" version, using the original command \setst:

The aim is to replace the { and the } in the output with the coresponding large versions — assuming, of course, that the math expression within causes those braces to expand. But each brace should not expand so as to encompass both lines of the printed output!

Here's a more realistic example, where larger braces are really needed:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand\setst[2]{\{#1 : 
  \begin{array}[t]{@{}l@{}}#2 \}\end{array}}

% my attempted mod
\newcommand\Setst[2]{\left\{#1 : \right. %
  \begin{array}[t]{@{}l@{}}\left.#2 \right\}\end{array}}

\begin{document}

Works, but integral sign and absolute value get squashed down smaller than they ought to appear in display math:
\[
\setst{f}{f(t) > 0 \text{ for all $t$ with } 0 < t < 1\\
    \text{and }\left|\int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t) dt\right| \leq 1 }
\]

\end{document}

And the output from that, with the two braces indicated:

Answer 1

I suggest pursuing a less-than-fully-automatic approach to sizing the outer curly braces. In the code below the default size of the outer curly braces is \big, but this may be changed by specifying an optional sizing-related parameter, which may take on values Bigg, bigg, Big (and, of course, big). I favor a minimum size of big (rather than normalsize) as IMNSHO, the curly braces simply need to "look" a bit more prominent.

In the following screenshot, the curly braces in the first example are of size \big (the default); they are of size \bigg in the second, where \displaystyle is in effect for the second row.

\documentclass{article}
\usepackage{mathtools} % for '\DeclarePairedDelimiter' macro
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} % "absolute value" macro

\newcommand\Setst[3][big]{\csname #1l\endcsname\{ #2 : 
  \begin{array}[t]{@{}l@{}}#3\csname #1r\endcsname \}\end{array}}

\begin{document}
\[
\Setst{f}{\text{$f(t)>0$ for all $t$ with $0<t<1$}\\
          \text{and }\abs[\big]{\int_0^1 e^{-\frac{1}{2}t^2}\!f(t)\,dt}\leq1}
\]

\[ % use \displaystyle directive in second row; hence, use "bigg" curly braces
\Setst[bigg]{f}{\text{$f(t)>0$ for all $t$ with $0<t<1$}\\
  \displaystyle \text{and }\abs[\bigg]{\int_0^1 e^{-\frac{1}{2}t^2}\!f(t)\,dt}\leq1}
\] 
\end{document}

Answer 2

I'd set the components slightly differently to allow for \left-\right to be used to span the entire construction:

\documentclass{article}

\usepackage{amsmath,amssymb}

\newcommand\setst[2]{\{#1 : 
  \begin{array}[t]{@{}l@{}}#2 \}\end{array}}

% my attempted mod
\newcommand\Setst[2]{%
  \expandafter\setsttopandbottom#2\relax
  \begin{array}{@{}l @{\ } l@{}}
    \left\{#1 :\vphantom{\setsttop}\vphantom{\setstbottom}\right.\kern-\nulldelimiterspace & 
    \begin{array}[t]{@{}l@{}}
      \setsttop \\ \kern-\nulldelimiterspace\left.\setstbottom\vphantom{\setsttop}\right\}
    \end{array}
  \end{array}
  }

\def\setsttopandbottom#1\\#2\relax{\def\setsttop{#1}\def\setstbottom{#2}}

\begin{document}

OK:
\[
  \setst{f}{f(t) > 0 \text{ for all $t$ with } 0 < t < 1 \\
      \text{and }\left|\int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t) dt\right| \leq 1 }
\]

Modified:
\[
  \Setst{f}{f(t) > 0 \text{ for all $t$ with } 0 < t < 1\\
      \text{and }\left|\int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t) dt\right| \leq 1 }
\]

\end{document}

In particular, the top and bottom part of the construction in the second argument is extracted and used in measurements for the first row (for the opening \{) as well as the last row (for the closing \}).

The above solution assumes that you will always use a \\ inside your construction and therefore have two lines. A separate macro would have to be constructed for a single-line application.

---

Using

\usepackage{array}

\newcommand\Setst[2]{%
  \expandafter\setsttopandbottom#2\relax
  \begin{array}{@{}>{\displaystyle}l @{\ } l@{}}
    \left\{#1 :\vphantom{\setsttop}\vphantom{\setstbottom}\right.\kern-\nulldelimiterspace & 
    \begin{array}[t]{@{}>{\displaystyle}l@{}}
      \setsttop \\ \kern-\nulldelimiterspace\left.\setstbottom\vphantom{\setsttop}\right\}
    \end{array}
  \end{array}
  }

you can always ensure that the cells within the array construction will be set using \displaystyle.

Answer 3

This answer is just a draft intended to explain what I had in mind when I posted my comment.

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{amsmath}

\makeatletter

\newcommand*{\SetSt}[2]{%
    \setbox\z@ \hbox{%
        % Inside this box, the "\\" command is `turned off'. 
        % BEWARE: WE ASSUME THAT "&" IS **NOT** USED INSIDE #2!
        \let\\\relax
        $#2$%
    }%
    \dimen@   \ht\z@
    \dimen@ii \dp\z@
    % Now typesetting begins:
    \left\{\,#1%
    % select one of the two following alternatives:
    % {}:{}% colon as separator
    \,\middle|\,% vertical bar as separator
    \vrule \@height\dimen@ \@depth\dimen@ii \@width\z@
    \right.\kern-\nulldelimiterspace
    \begin{array}[t]{@{}l@{}}%
        #2%
        \left.\kern-\nulldelimiterspace
        \vrule \@height\dimen@ \@depth\dimen@ii \@width\z@
        \right\}%
    \end{array}%
}

\makeatother



\begin{document}

With tall symbols:
\[
    \SetSt{f}{f(t) > 0 \text{ for all $t$ with } 0 < t < 1\\
        \text{and }\left|\int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t) dt\right| \leq 1 }
\]

WIthout tall symbols:
\[ \SetSt{x}{x\in A \land x\in B\\x\in C \land x\in D\\x\in E \land x\in F} \]
As you can see, no restriction is imposed on the number of lines.  Even a 
single line is OK\@:
\[ \SetSt{x}{\int_{0}^{x} f(t)\,dt > 0} \]

Another example with two lines:
\[
    \SetSt{x}{\int_{0}^{x} f(t)\,dt > 0\\\int_{0}^{x} g(t)\,dt > 0}
\]

\end{document}

It can be refined in at least two respects:

• the \\ command shouldn’t be simply redefined as \relax, it should gobble a star and an optional argument, if present;

• the \SetSt command should take the current math style into account; this is easily achived with a routine application of \mathpalette.

I’m sorry, but now I’m too tired to make these refinements…

Edit

I’m now able to post an amended version of the code:

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{amsmath}
\usepackage{array}

\makeatletter

\newcommand*\SetSt[2]{\mathpalette{\@SetSt{#1}}{#2}}
\newcommand*\@SetSt[3]{%
    % #1 := 1st argument of "\SetSt"
    % #2 := style selector (e.g., "\displaystyle")
    % #3 := 2nd argument of "\SetSt"
    \setbox\z@ \hbox{%
        % Inside this box, the "\\" command is `turned off'. 
        % BEWARE: WE ASSUME THAT "&" IS **NOT** USED INSIDE #3!
        \let\\\@Murray@NoopCR
        $#2#3$%
    }%
    \dimen@   \ht\z@
    \dimen@ii \dp\z@
    % Now typesetting begins:
    \left\{\@nonscript@thinspace #2% style selector
    % The following group protects the value of "\dimen@" and "\dimen@ii":
    \begingroup #1\endgroup
    % select one of the two following alternatives:
    % {}:{}% colon as separator
    \@nonscript@thinspace\middle|\@nonscript@thinspace % vertical bar as separator
    \@Murray@mathstrut
    \right.\kern-\nulldelimiterspace
    % The group around the cells allows this macro to be nested;
    % it is important only for the last row, but we cannot avoid specifying it 
    % for every entry.
    \begin{array}[t]{@{}>{#2\begingroup}l<{\endgroup}@{}}%
        #3\endgroup % end the group to restore the values of "\dimen@" and 
                    % "dimen@ii"
        \left.\kern-\nulldelimiterspace
        \@Murray@mathstrut
        \right\}%
        \begingroup % to balance the "\endgroup" at the end of the entry
    \end{array}%
}
\newcommand*\@Murray@NoopCR{\@ifstar\x@Murray@NoopCR\x@Murray@NoopCR}
\newcommand*\x@Murray@NoopCR{\@ifnextchar[\y@Murray@NoopCR {}}
\@ifdefinable\y@Murray@NoopCR{\def\y@Murray@NoopCR[#1]{}}
\newcommand*\@nonscript@thinspace{\nonscript\mskip\thinmuskip}
\newcommand*\@Murray@mathstrut{%
    \vrule \@height\dimen@ \@depth\dimen@ii \@width\z@
}

\makeatother



\begin{document}

With tall symbols:
\[
    \SetSt{f}{f(t) > 0 \text{ for all $t$ with } 0 < t < 1\\[\medskipamount]
        \text{and }\left|\int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t) dt\right| \leq 1 }
\]

WIthout tall symbols:
\[ \SetSt{x}{x\in A \land x\in B\\x\in C \land x\in D\\x\in E \land x\in F} \]
As you can see, no restriction is imposed on the number of lines.  Even a 
single line is OK\@:
\[ \SetSt{x}{\int_{0}^{x} f(t)\,dt > 0} \]

Another example with two lines:
\[
    \SetSt{x}{\int_{0}^{x} f(t)\,dt > 0
    \\*[\bigskipamount]% the star serves no purpose, we just want to check that 
                       % it is handled correctly
    \int_{0}^{x} g(t)\,dt > 0}
\]

An example of nesting:
\[
    \SetSt{x}{x\in A\\x\in B\\x\in\SetSt{y}{y<-1\\y>1}}
\]
This last example clearly shows the limits of the algorithm.

\end{document}

And here is the output it produces:

Answer 4

I propose another layout for this set builder notation, with a simple solution based on delarray and stackengine. In addition, I defined an \abs command with \DeclarePairedDelimiterX from mathtools, and a diffrential symbol with a correct spacing in integrals:

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb, delarray}
\usepackage[usestackEOL]{stackengine}

\DeclarePairedDelimiterX{\abs}[1]{\lvert}{\rvert}{\ifblank{#1}{\:\cdot\:}{#1}}%%

\newcommand\mySetst[2]{ \begin{array}\{{@{}>{\everymath{\displaystyle}}c@{\::\:}>{\everymath{\displaystyle}}l@{}}\}
#1 & \stackMath\Shortunderstack[l]{#2}
 \end{array}}

\newcommand\dd[1]{\,\mathrm{d}\mkern 1mu#1} %% differential symbol for integrals

\begin{document}

 \[ \mySetst{f}{f(t)>0 \text{ for all $t$ with } 0<t<1\\\text{and }\abs*{int_{0}^{1}e^{-\frac{1}{2} t^{2}}f(t)\dd t} \leq 1} \]%
\
\end{document}