[Tex/LaTex] How to label a multi-line equation

equationsformattinglabelsline-breakingmultline

I have a a multi-line equation, e_1 = e_2 = ... = e_n. Each of the expressions e_i is quite long. So long, in fact, that using the align environment results in some of the equations intruding into the right-hand margin, and even beyond the page. Using the multline environment solves these issues, however this causes another problem. With the align environment I am able to label each of the equations, and reference them further down the document; however, with the multline environment, the following error message is issued:

Package amsmath Error: Multiple \label's: label '...' will be lost.

How can I label the lines of a multline environment? Alternatively, is there another way to achieve the following goals simultaneously:

  1. Arranging the multi-line equation one equation per line.
  2. Making sure none of the equations oversteps the margins.
  3. Labeling each of the equations (or, more precisely, a selection of the equations), so they can be referenced.

Here's an example document that can be used for experimentation purposes.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\sup_{\mathbf{N}}V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(m+_{\mathbf{M}}n)\rangle &\geq_{\mathbf{N}}\sup_{\mathbf{N}}V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(m) +_{\mathbf{R}^{(S)}_{\mathbf{N}, \varphi}} S_{\mathbf{M}, S, \mathbf{N}, \varphi}(n) \rangle\label{eq:1}\\
&= \sup_{\mathbf{N}}\left(V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(m)\rangle +_{\mathbf{R}^{(S)}_{\mathbf{N}, \varphi}} V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(n) \rangle\right)\label{eq:2}\\
&\geq_{\mathbf{N}} \sup_{\mathbf{N}}\left(V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(m)\rangle\right) +_{\mathbf{N}} \sup_{\mathbf{N}}\left(V_{\mathbf{N}, S, \varphi}\langle S_{\mathbf{M}, S, \mathbf{N}, \varphi}(n) \rangle\right),\label{eq:3}
\end{align}

Referencing eq.~\ref{eq:1}.
\end{document}

Best Answer

I see no other sensible way than as follows:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\bvar}[1]{\mathbf{#1}}
\newcommand{\bM}{\bvar{M}}
\newcommand{\bN}{\bvar{N}}
\newcommand{\bR}{\bvar{R}}

\begin{document}

\begin{align}
&\sup_{\bN}V_{\bN, S, \varphi}\langle S_{\bM, S, \bN, \varphi}(m+_{\bM}n)\rangle
\notag \\
&\qquad\geq_{\bN}\sup_{\bN}
  V_{\bN, S, \varphi}\langle S_{\bM, S, \bN, \varphi}(m)
  +_{\bR^{(S)}_{\bN, \varphi}} S_{\bM, S, \bN, \varphi}(n) \rangle
\label{eq:1}\\
&\qquad= \sup_{\bN}
  \bigl(V_{\bN, S, \varphi}\langle S_{\bM, S, \bN, \varphi}(m)\rangle
  +_{\bR^{(S)}_{\bN, \varphi}} V_{\bN, S, \varphi}
    \langle S_{\bM, S, \bN, \varphi}(n) \rangle
  \bigr)
\label{eq:2}\\
&\qquad\geq_{\bN} \sup_{\bN}
  \bigl(V_{\bN, S, \varphi}\langle S_{\bM, S, \bN, \varphi}(m)\rangle)
  +_{\bN} \sup_{\bN}(V_{\bN, S, \varphi}\langle S_{\bM, S, \bN, \varphi}(n) \rangle
  \bigr),
\label{eq:3}
\end{align}
Referencing eq.~\ref{eq:1}.

\end{document}

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