Vertical Alignment Every Other Line and Wide Expressions

Question

I'm sorry if this was asked elsewhere, but I couldn't find anything. I've had this question for a while now, and it really bothers me; I seem to run into these situations relatively often.

The generic problem is that I have a derivation I want to show in which I want to 1) align equals signs where appropriate but 2) the LHS at the start of the derivation is rather wide and 3) the intermediate results might spill across multiple lines, and I especially 4) need some of these intermediate results to print to the left of the alignment set up by the equals sign on the first line (because the LHS of the first line is wide and the intermediate lines are also wide).

What I'd really like is for the intermediate results to automatically justify similar to multline or, depending on the situation, for me to align them myself independently of the & from the enveloping align environment.

mathtools' multlined environment doesn't seem to work because all printing is to the right of the equals sign, which is itself to the right of a wide expression.

I've included some code below that shows my best attempt to tackle the problem, which required some fine tuning of a negative horizontal shift to try to align the right justification of the intermediate steps. I apologize that it's a bit hard to read.

\documentclass[]{article}

\usepackage{amsmath}

\setlength{\jot}{10pt}

\newcommand{\an}[1]{\langle #1 \rangle}

\begin{document}

\begin{align}
\begin{split}
A(1^-6^-5^+2^+4^+3^-) & = \frac{\an{13}^3\an{23}}{\an{12}\an{24}\an{43}\an{31}}\frac{\an{12}}{\an{16}\an{65}\an{52}}\biggl( \\
& \hspace{-0.8in} \frac{\langle2|6|1]}{\langle2|5+6|1]}\frac{\an{26}^2}{(p_2+k_5+k_6)^2}\frac{[12]}{\an{12}}%\frac{\an{56}}{[56]}
+ \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
\biggr)\end{split} \\
\begin{split} & = A(1^-2^+4^+3^-)\frac{\an{12}}{\an{16}\an{65}\an{52}}\biggl( \\
& \hspace{-0.5in} \frac{1}{\langle2|5+6|1]}\frac{\an{26}^3}{(p_2+k_5+k_6)^2}+ \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
\biggr)\end{split}
\end{align}

\end{document}

I've included a picture of the output from the above code from my machine below:

Thank you very much for your help!

Answer 1

I propose two layouts, both based on align:

\documentclass[]{article}

\usepackage{amsmath,mathtools}

\usepackage{showframe}

\DeclarePairedDelimiter{\an}{\langle}{\rangle}

\begin{document}

\begin{align}
A(1^-6^-5^+2^+4^+3^-)
& = 
    \frac{\an{13}^3\an{23}}{\an{12}\an{24}\an{43}\an{31}}\frac{\an{12}}{\an{16}\an{65}\an{52}} \notag\\
&   \quad\cdot\biggl(
        \frac{\langle2|6|1]}{\langle2|5+6|1]}\frac{\an{26}^2}{(p_2+k_5+k_6)^2}\frac{[12]}{\an{12}} \notag\\
&   \qquad + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr)
\\
& = 
    A(1^-2^+4^+3^-)\frac{\an{12}}{\an{16}\an{65}\an{52}} \notag\\
&   \quad\cdot\biggl(
      \frac{1}{\langle2|5+6|1]}\frac{\an{26}^3}{(p_2+k_5+k_6)^2} \notag\\
&     \qquad + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr)
\end{align}

\begin{align}
&\lefteqn{A(1^-6^-5^+2^+4^+3^-)=} \notag \\
& = 
    \frac{\an{13}^3\an{23}}{\an{12}\an{24}\an{43}\an{31}}\frac{\an{12}}{\an{16}\an{65}\an{52}} \notag\\
&   \quad\cdot\biggl(
        \frac{\langle2|6|1]}{\langle2|5+6|1]}\frac{\an{26}^2}{(p_2+k_5+k_6)^2}\frac{[12]}{\an{12}}
   + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr)
\\
& = 
    A(1^-2^+4^+3^-)\frac{\an{12}}{\an{16}\an{65}\an{52}} \notag\\
&   \quad\cdot\biggl(
      \frac{1}{\langle2|5+6|1]}\frac{\an{26}^3}{(p_2+k_5+k_6)^2} 
      + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr)
\end{align}

\end{document}

Note that showframe is used just to show the margins of the text block.

Answer 2

\documentclass[a4paper]{article}
\usepackage{mathtools}
\newcommand{\an}[1]{\langle #1 \rangle}
\begin{document}

\begin{multline}
A(1^-6^-5^+2^+4^+3^-) = 
    \frac{\an{13}^3\an{23}}{\an{12}\an{24}\an{43}\an{31}}\frac{\an{12}}{\an{16}\an{65}\an{52}}\cdot\\
    \biggl(\frac{\langle2|6|1]}{\langle2|5+6|1]}\frac{\an{26}^2}{(p_2+k_5+k_6)^2}\frac{[12]}{\an{12}}%\frac{\an{56}}{[56]}
            + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
            \biggr)
\end{multline}
\begin{multline}
\phantom{A(1^-6^-5^+2^+4^+3^-)} =
A(1^-2^+4^+3^-)\frac{\an{12}}{\an{16}\an{65}\an{52}}\cdot\\
   \biggl(\frac{1}{\langle2|5+6|1]}\frac{\an{26}^3}{(p_2+k_5+k_6)^2}+ 
    \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
\biggr)
\end{multline}

\end{document}

or with only one equation number:

\documentclass[a4paper]{article}
\usepackage{mathtools}
\newcommand{\an}[1]{\langle #1 \rangle}
\begin{document}

    \begin{multline}
    A(1^-6^-5^+2^+4^+3^-) = 
    \frac{\an{13}^3\an{23}}{\an{12}\an{24}\an{43}\an{31}}\frac{\an{12}}{\an{16}\an{65}\an{52}}\cdot\\
    \biggl(\frac{\langle2|6|1]}{\langle2|5+6|1]}\frac{\an{26}^2}{(p_2+k_5+k_6)^2}\frac{[12]}{\an{12}}%\frac{\an{56}}{[56]}
    + \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr) \\
\shoveleft{\phantom{A(1^-6^-5^+2^+4^+3^-)} =
    A(1^-2^+4^+3^-)\frac{\an{12}}{\an{16}\an{65}\an{52}}\cdot}\\
    \biggl(\frac{1}{\langle2|5+6|1]}\frac{\an{26}^3}{(p_2+k_5+k_6)^2}+ 
    \frac{\langle2|5|1]}{\langle2|5+6|1]}\frac{[15]^2}{(p_1+k_5+k_6)^2}\frac{\an{16}}{[16]} 
    \biggr)
\end{multline}

\end{document}