How Do I Horizontally Center An Operator Relative To Aligned Equations Above and Below

Question

I want to achieve the following effect in a new enviornment I'm defining where the stuff inside what's supposed to be delimeters is a \begin{aligned} \end{aligned} block.

\begin{equation}

                  /    math math math math math \
(outside aligned)|               \lor            |
                 \     math math                 /
\end{equation}

This is all straightforward except I want to center the \lor inside the aligned equations, i.e., center it between the two delimiters. How do I do this in a macro (no hand setting alignment characters)?

Do I need to make the \lor a middle delimiter or something? Note sometimes the outside delimiters may need to be invisible if not absent entirely but \lor should still be centered inside the aligned environment.

Answer 1

I do not understand what exactly should be in the new environment.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
\text{(outside aligned)}
\left(\arraycolsep=1.35pt
        \begin{array}{@{}rl@{}}
        f(x) &= g(x)+h(x)\\
        \multicolumn{2}{c}{\lor}\\
        f(x) &= x
        \end{array}
\right)
\end{align}
\end{document}

Answer 2

I'm not totally positive, but are you looking for something like this?

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\makeatletter
\newcommand*\addlor[2][]{%
        \begingroup
        \ifx\relax#1\relax
                \mathpalette\addlor@aux{#2}%
        \else
                \addlor@aux#1{#2}%
        \fi
        \endgroup
}
\def\addlor@aux#1#2{
        \setbox0\hbox{$\m@th#1#2$}%
        \rlap{\hbox to\wd0{\hfill$\m@th#1\lor$\hfill}}%
        \box0
}
\makeatother
\begin{document}
\begin{equation}
\text{(outside aligned)}
\left<
\addlor{
        \begin{aligned}
        f(x)&=g(x)+h(x)\\
        &\\
        f(x)&=x
        \end{aligned}
}
\right>
\end{equation}
\makeatother
\end{document}

The \addlor macro takes an optional first argument that can be one of \displaystyle, \textstyle, \scriptstyle, or \scriptscriptstyle. Without the optional argument, it just uses the surrounding style.