Using aligned and align without amsmath

Question

I am currently working on a proceedings paper, and have realised after finishing it that only specific packages are permitted - one of which is not amsmath. As a result, many of the nice equations that I have written can now no longer be built. To save me switching back to \begin{cases} \end{cases} and giving up, I thought I would try asking on here to see if anyone could provide me with a solution?

I cannot define add any new commands before \begin{document}, so everything must be done after that point. I thought about trying to grab the relevant components from the style file, but to be perfectly honest I am not a TeX-wizard and have no idea whether this would even work.Could anyone provide me with a work-around, so that I can still use align and aligned, but by doing so after \begin{document}?

If it helps, the packages I am permitted to use are:

\usepackage{mathptmx}       
\usepackage{helvet}         
\usepackage{courier}        
\usepackage{type1cm}        
\usepackage{graphicx}        
\usepackage[bottom]{footmisc}    
\usepackage{amssymb}    
\usepackage{amsfonts}   
\usepackage{amsbsy}   
\usepackage{amscd}   
\usepackage{amstext}   
\usepackage{dsfont}   
\usepackage[english]{babel}   
\usepackage{color}   
\usepackage{graphics}   
\usepackage{epsfig}   
\usepackage{subfigure}   
\usepackage{wrapfig}   
\usepackage{psfrag}   
\usepackage{color}   
\usepackage{url}   
\usepackage{verbatim}   
\usepackage{algorithm}   
\usepackage{algorithmic}   

Edit: An MWE is as follows:

\documentclass{svmult}   
\usepackage{mathptmx}       
\usepackage{helvet}         
\usepackage{courier}        
\usepackage{type1cm}        

\usepackage{graphicx}        

\usepackage[bottom]{footmisc}

\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amsbsy}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{dsfont}
\usepackage[english]{babel}
\usepackage{color}
\usepackage{graphics}
\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{wrapfig}
\usepackage{psfrag}
\usepackage{color}
\usepackage{url}
\usepackage{verbatim}
\usepackage{algorithm}
\usepackage{algorithmic}


\begin{document}

\begin{equation}
\label{InitSystemNL}
\left\{
\begin{aligned}
\mathcal{R} \colon= -\Delta u &= f  \quad & &\text{in} \,\, \Omega \\ u &= 0 \quad & &\text{on} \,\, \partial\Omega, \end{aligned} \right.
\end{equation}

\end{document}

Answer 1

To avoid needing to edit the existing doc you can defined a poor man's aligned as follows (but first try to get the rules changed)

\documentclass{article}   
\usepackage{mathptmx}       
\usepackage{helvet}         
\usepackage{courier}        
\usepackage{type1cm}        

\usepackage{graphicx}        

\usepackage[bottom]{footmisc}

\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amsbsy}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{dsfont}
\usepackage[english]{babel}
\usepackage{color}
\usepackage{graphics}
\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{wrapfig}
\usepackage{psfrag}
\usepackage{color}
\usepackage{url}
\usepackage{verbatim}
\usepackage{algorithm}
\usepackage{algorithmic}


\begin{document}
\def\aligned{\vcenter\bgroup\let\\\cr
\halign\bgroup&\hfil${}##{}$&${}##{}$\hfil\cr}
\def\endaligned{\crcr\egroup\egroup}

\begin{equation}
\label{InitSystemNL}
\left\{
\begin{aligned}
\mathcal{R} \colon= -\Delta u &= f  \quad & &\text{in} \,\, \Omega \\ u &= 0 \quad & &\text{on} \,\, \partial\Omega, 
\end{aligned} 
\right.
\end{equation}

\end{document}

Answer 2

Here is an example showing the output generated with and without amsmath:

\documentclass{svmult}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}

\noindent With \verb|amsmath|:
\begin{equation}
  \left\{\begin{aligned}
    \mathcal{R} \colon= -\Delta u &= f  \quad & &\text{in} \,\, \Omega \\ 
    u &= 0 \quad & &\text{on} \,\, \partial\Omega,
  \end{aligned}\right.
\end{equation}

\noindent Without \verb|amsmath|:
\begin{equation}
  \left\{\begin{array}{r@{}l@{\qquad}l}
    \mathcal{R}\colon=-\Delta u & {}=f & \textrm{in}\ \Omega \\[\jot]
    u & {}=0 & \textrm{on}\ \partial\Omega,
  \end{array}\right.
\end{equation}
\end{document}

The most important part to address is the choice of your column specification in order to adequately address the alignment matching with that of align or aligned. The use of \jot is to provide a similar line-spacing to array between rows.