Why \allowbreak is not working?

Question

So, here's the code I have:

\usepackage{amsthm}

\begin{theorem}
...could be now considered as an algebraic structure $DB_E =
\left\langle \mathbb{S},\allowbreak \mathbb{E},\allowbreak
f,\allowbreak \mathbb{V},\allowbreak \mathbb{R},\allowbreak
\mathbb{C},\allowbreak Op_a,\allowbreak Op_c,\allowbreak
Op_m \right\rangle$.
\end{theorem}

and here is the result (grey area denotes the edge of the page):

Obviously, \allowbreak does not do anything. Why is it?

Answer 1

This is another case for which \left and \right are not appropriate:

1. there is no delimiter to increase the size of;

2. the spaces after commas cannot participate to stretching or shrinking together with the other spaces in the same line;

3. the formula is not breakable across lines under any circumstance.

So the first step to do is to remove \left and \right (and to disable any automatic feature in the editor). Then a carefully placed \linebreak[0] will help in the pagination.

\documentclass[a4paper]{article}
\usepackage{amsfonts,amsthm}
\newtheorem{theorem}{Theorem}


\begin{document}

\noindent\parbox{4cm}{
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},f,
  \mathbb{V},\mathbb{R},\mathbb{C},\linebreak[0]
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}
}

\noindent\parbox{6.5cm}{
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},f,\linebreak[0]
  \mathbb{V},\mathbb{R},\mathbb{C},
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}
}

\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},\linebreak[0]
  f,\mathbb{V},\mathbb{R},\mathbb{C},
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}

\end{document}

Answer 2

You could try the following middlebreak macro:

[not using at all \left and \right was better in your posted case, as pointed out in comments; but then look at the second proposal below for more general usage]

\documentclass{article}
\usepackage{amsfonts,amsthm}
\newtheorem{theorem}{Theorem}

% to be used within a \left \right pair
\def\middlebreak {\nulldelimiterspace0pt
\right.\allowbreak\mskip 0mu plus .5mu \nulldelimiterspace0pt\left.}%

\begin{document}

{%
\hsize 3cm
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \left\langle
  \mathbb{S},\middlebreak \mathbb{E},\middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},\middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m \right\rangle$.
\end{theorem}
}%

{%
\hsize 7cm
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \left\langle
  \mathbb{S},\middlebreak \mathbb{E},\middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},\middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m \right\rangle$.
\end{theorem}
}%

\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \left\langle
  \mathbb{S},\middlebreak \mathbb{E},\middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},\middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m \right\rangle$.
\end{theorem}

\end{document}

\documentclass{article}
\usepackage{amsfonts,amsthm}
\newtheorem{theorem}{Theorem}


\newlength{\IrresponsibleFantasy}

\newcommand*{\ReserveVerticalSpace}[1]
   {\setlength{\IrresponsibleFantasy}{#1}\global\IrresponsibleFantasy=\IrresponsibleFantasy
    \parbox{0pt}{\rule{0pt}{\IrresponsibleFantasy}}}

\newcommand*{\middlebreak}{\nulldelimiterspace0pt
\right.\allowbreak\mskip 0mu plus .5mu \nulldelimiterspace0pt
\left.\parbox{0pt}{\rule{0pt}{\IrresponsibleFantasy}}}%

\begin{document}

{%
\hsize 3cm
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = 
\left\langle\ReserveVerticalSpace{1cm}
  \mathbb{S},\middlebreak \mathbb{E},
  \middlebreak {X^X}^X, \middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},
  \middlebreak {q_q}_q, \middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m 
\right\rangle$.
\end{theorem}
}%

{%
\hsize 7cm
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = 
\left\langle\ReserveVerticalSpace{1cm}
  \mathbb{S},\middlebreak \mathbb{E},
  \middlebreak {X^X}^X, \middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},
  \middlebreak {q_q}_q, \middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m 
\right\rangle$.
\end{theorem}
}%

\begin{theorem}
...could be now considered as an algebraic structure $DB_E = 
\left\langle\ReserveVerticalSpace{1cm}
  \mathbb{S},\middlebreak \mathbb{E},
  \middlebreak {X^X}^X, \middlebreak f,\middlebreak
  \mathbb{V},\middlebreak \mathbb{R},\middlebreak \mathbb{C},
  \middlebreak {q_q}_q, \middlebreak
  Op_a,\middlebreak Op_c,\middlebreak Op_m 
\right\rangle$.
\end{theorem}


\end{document}

Answer 3

You could rewrite the token stream associated with your algebraic structure to automatically append \allowbreak after each comma and wrap its elements with an auto-sizing pair of angle brackets (excluding \left...\right):

\documentclass[preview]{standalone}
\usepackage{amsmath,amsfonts,amsthm}
\usepackage{expl3,xparse}

\newtheorem{theorem}{Theorem}

\ExplSyntaxOn
\NewDocumentCommand{\mstruct}{m}{%
  \group_begin:
  \tl_set:Nn \l_tmpa_tl {#1}
  \hbox_set:Nn \l_tmpa_box {\ensuremath{\l_tmpa_tl}}
  \dim_set:Nn \l_tmpa_dim {\box_ht:N \l_tmpa_box}
  \dim_add:Nn \l_tmpa_dim {\box_dp:N \l_tmpa_box}
  \dim_add:Nn \l_tmpa_dim {0.3em}
  \dim_set:Nn \l_tmpb_dim {1.2\l_tmpa_dim}
  \tl_replace_all:Nnn \l_tmpa_tl {,} {,\allowbreak}
  \ifmmode%
    \text{\fontsize{\l_tmpa_dim}{\l_tmpb_dim}\selectfont$\langle$}
  \else%
    {\fontsize{\l_tmpa_dim}{\l_tmpb_dim}\selectfont$\langle$}
  \fi
  \ensuremath{\l_tmpa_tl}
  \ifmmode%
    \text{\fontsize{\l_tmpa_dim}{\l_tmpb_dim}\selectfont$\rangle$}
  \else%
    {\fontsize{\l_tmpa_dim}{\l_tmpb_dim}\selectfont$\rangle$}
  \fi
  \group_end:
}
\ExplSyntaxOff

\begin{document}

\mstruct{\text{my}^{\text{very}^{\text{very}^{\text{very}^{\text{big}^\text{object}}}}}}

\mstruct{this,is,a,very,very,very,very,very,very,very,very,very,very,very,very,very,long,sentence,because,I'm,testing,mstruct,against,very,long,text,with,\text{my}^{\text{very}^{\text{very}^{\text{very}^{\text{big}^\text{object}}}}}}

\begin{theorem}
$\mstruct{\text{my}^{\text{very}^{\text{big}^\text{object}}}}_a^b$
\end{theorem}

\begin{theorem}
...could be now considered as an algebraic structure $DB_E =
\mstruct{\mathbb{S}, \mathbb{E}, f, \mathbb{V}, \mathbb{R}, \mathbb{C}, Op_a,
Op_c, Op_m}$.
\end{theorem}

\end{document}