Aligning across 'aligned' equation blocks

Question

I'd like to format two groups of equations such that all their equal signs line up and such that I can put a big brace to the right of each block to annotate that block. The last part is easily achieved using the aligned environment of amsmath:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
  \left.\begin{aligned}
    \alpha_X \times \alpha_Y &= \chi \\
    \alpha_X \times \beta_Y &= \xi \\
    \beta_X \times \beta_Y &= \zeta
  \end{aligned}\right\} \quad X<Y \\[2em]
  \left.\begin{aligned}
    \Upsilon_j &= 0 \\
    \Psi_j &= \sqrt{\sinh E - \tan^2\tfrac{F}{2}} \\
    \Gamma_j &= F
  \end{aligned}\right\} \quad j=1,\ldots,g
\end{align}
\end{document}

But that doesn't line up the equal signs. I guess I could achieve this with some manual horizontal white space, but I'd like something automatic. Something like the split environment which supports reusing the anchor points of the outside 'align' environment:

\begin{align}
  A &= 0 \\
  BB &= AVE + VEA + EAV \\
  \begin{split}
  CCC &= UVWXY + VWXYU + WXYUV \\
      &\quad {} + XYUVW + YUVWX
  \end{split}
\end{align}

Is there a way to make aligned reuse the anchor points of the outside align?

Also, is there an automatic way to additionally line up the big braces in the first example?

Answer 1

I have a solution as well. It is taken from the MathMode documentation on CTAN, page 112.

\documentclass{article}
\usepackage{amssymb}
\usepackage{amsmath}
\newcommand{\fakealign}{%
   \mbox{\hspace{5cm}} & \mbox{\hspace{5cm}} \nonumber\\%
}
\begin{document}
An equation;
\vspace{-1cm}
\begin{align}
   \fakealign
   D &= I\left(1+r\right)^t
\end{align}
Equation with a long left hand side;
\vspace{-1cm}
\begin{align}
   \fakealign
   \left(1+d\right)^{-T} &= U
\end{align}
Equation with a long right hand side
\vspace{-1cm}
\begin{align}
   \fakealign
   PV &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{align}
They all align with the = sign :)
\end{document}

I can't post an image because I am a new user and therefore don't have enough reputation. But build it and observe!

I think this simpler and more elegant than Stefan's solution, but hey. Horses for courses.

Enjoy!

Answer 2

Here's a solution using the widths of the widest expression on each side. You have to specify which expression it is:

\documentclass{article}
\usepackage{amsmath}
\newlength{\leftside}
\newlength{\rightside}
\newcommand*{\leftterm}{}
\newcommand*{\rightterm}{}
\newcommand*{\term}[1]{$\displaystyle#1$}
\begin{document}
\[
\renewcommand*{\leftterm}{\alpha_X \times \alpha_Y}
\renewcommand*{\rightterm}{\sqrt{\sinh E - \tan^2\tfrac{F}{2}}}
\settowidth{\leftside}{\term{\leftterm}}
\settowidth{\rightside}{\term{\rightterm}}
\begin{array}{l}
  \left.\begin{aligned}
    \leftterm &= \makebox[\rightside][l]{\term{\chi}} \\
    \alpha_X \times \beta_Y &= \xi \\
    \beta_X \times \beta_Y &= \zeta
  \end{aligned}\right\} \quad X<Y \\[2em]
  \left.\begin{aligned}
    \makebox[\leftside][r]{\term{\Upsilon_j}} &= 0 \\
    \Psi_j &= \rightterm \\
    \Gamma_j &= F
  \end{aligned}\right\} \quad j=1,\ldots,g
\end{array}
\]
\end{document}

Equal signs as well as the big braces line up:

Answer 3

You could adopt Andrew's or my answer to this question.