Multiple split equations

Question

I find myself again and again using a combination of the gather and aligned environments. So it would be nice to not have to write so much. In particular, it is often only clear after writing the formula, whether it needs splitting. So the new environment should act like gather, only that when lines are separated by a special symbol/macro (\n for example) they should be put together into an aligned-environment. I tried the following

\documentclass{article}
\usepackage[fleqn]{amsmath}

\newenvironment{multeq}{%
    \let\n{\\}
    \let\\{\end{aligned}\\\begin{aligned}}
    \begin{aligned}
}{%
    \end{aligned}
    \let\\{\n}
}

\begin{document}

    \begin{gather}
        \begin{aligned}
            S(A) &= (I_{n-k, k}AI_{n-k,k})_{i,j} = (I_{n-k,k})_{i,i}A_{i,j}(I_{n-k,k})_{j,j}\\
            &= \begin{cases}A_{i,j}&\begin{aligned}&(i\leq n-k\wedge j\leq n-k)\\\vee&(i>n-k\wedge j>n-k)\end{aligned}\\-A_{i,j}&\text{otherwise}\end{cases}
        \end{aligned}\\
        \Rightarrow H = S(U(n-k)\times U(k))
    \end{gather}

    \begin{multeq}
        S(A) &= (I_{n-k, k}AI_{n-k,k})_{i,j} = (I_{n-k,k})_{i,i}A_{i,j}(I_{n-k,k})_{j,j}\n
        &= \begin{cases}A_{i,j}&\begin{aligned}&(i\leq n-k\wedge j\leq n-k)\n\vee&(i>n-k\wedge j>n-k)\end{aligned}\n-A_{i,j}&\text{otherwise}\end{cases}\\
    \Rightarrow H = S(U(n-k)\times U(k))
    \end{multeq}

\end{document}

where the output should be 2×

but it gives the error:

! LaTeX Error: There's no line here to end.
l.24    \begin{multeq}

How does this error come about and what is a good way to create such an environment?

---

So using David’s corrections, and adding gather:

\newenvironment{multeq}{\begin{gather}%
    \def\n{\\}%
    \def\\{\end{aligned}\\\begin{aligned}}%
    \begin{aligned}%
}{%
    \end{aligned}%
    \end{gather}}

I got

! Paragraph ended before \gather was complete.

So I tried using \Collect@Body from environ:

\def\savebody#1{\def\BODY{#1}}
\usepackage{environ}
\makeatletter

\newenvironment{multeq}{
    \def\n{\\}%
    \def\\{\end{aligned}\\\begin{aligned}}%
    \Collect@Body\savebody
}{\begin{gather}%
    \begin{aligned}%
            \BODY%
    \end{aligned}%
    \end{gather}}

\makeatother

But now the redefinition of \\ is ignored. What else could I do?

Answer 1

You need \def not \let \nd you need to get into math mode:

\documentclass{article}
\usepackage[fleqn]{amsmath}

\newenvironment{multeq}{\[%
    \def\n{\\}%
    \def\\{\end{aligned}\\\begin{aligned}}%
    \begin{aligned}%
}{%
    \end{aligned}%
    \]}

\begin{document}

    \begin{gather}
        \begin{aligned}
            S(A) &= (I_{n-k, k}AI_{n-k,k})_{i,j} = (I_{n-k,k})_{i,i}A_{i,j}(I_{n-k,k})_{j,j}\\
            &= \begin{cases}A_{i,j}&\begin{aligned}&(i\leq n-k\wedge j\leq n-k)\\\vee&(i>n-k\wedge j>n-k)\end{aligned}\\-A_{i,j}&\text{otherwise}\end{cases}
        \end{aligned}\\
        \Rightarrow H = S(U(n-k)\times U(k))
    \end{gather}

    \begin{multeq}
        S(A) &= (I_{n-k, k}AI_{n-k,k})_{i,j} = (I_{n-k,k})_{i,i}A_{i,j}(I_{n-k,k})_{j,j}\n
        &= \begin{cases}A_{i,j}&\begin{aligned}&(i\leq n-k\wedge j\leq n-k)\n\vee&(i>n-k\wedge j>n-k)\end{aligned}\n-A_{i,j}&\text{otherwise}\end{cases}\\
    \Rightarrow H = S(U(n-k)\times U(k))
    \end{multeq}

\end{document}

You may need some other changes, depending quite wh\t input markup you want, the above produces

Answer 2

After looking at some macro expansions, I found the actual problem. amsmath defines \let\\\math@cr when it expands gather. So whatever I do to \\ beforehand, will not matter. Thus I changed \math@cr et voilá, it works. At least if I collect the body with NewEnviron.

\documentclass{article}
\usepackage[fleqn]{amsmath}
\usepackage{environ}

\makeatletter
\NewEnviron{multeq}{%
    \begingroup
        \let\n\math@cr
        \begin{gather}
            \def\math@cr{\end{aligned}\n\begin{aligned}}
            \begin{aligned}
                \BODY
            \end{aligned}
        \end{gather}
    \endgroup
}
\makeatother

is the needed definition. It also works with align instead of gather or split instead of aligned. And for a simpler usage example:

\begin{document}
\begin{multeq}
    0 + 0 = 0\n
    0 * 0 = 0\\
    1 + 1 = 2\n
    1 * 1 = 1
\end{multeq}
\end{document}

will be printed as