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:
- Arranging the multi-line equation one equation per line.
- Making sure none of the equations oversteps the margins.
- 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: