How to define switches for turning on and off the option `fleqn` of `amsmath`

Question

There are switches for amsmath options leqno and reqno.

Then, how to define switches for turning on and off the option fleqn after amsmath is loaded?

---

I looked into the source of amsmath.sty and define the switches as

\makeatletter
\newcommand*{\fleqnon}{\setboolean{@fleqn}{true}}
\newcommand*{\fleqnoff}{\setboolean{@fleqn}{false}}
\makeatother

These two switches work only when amsmath is loaded with the option fleqn.

MWE:

\documentclass[b6paper]{scrartcl}

%\usepackage[fleqn]{amsmath}  % works with the option `fleqn`
\usepackage{amsmath}          % fails without the option `fleqn`
\usepackage{ifthen}

\makeatletter
% https://tex.stackexchange.com/a/212099
\newcommand*{\leqnomode}{\tagsleft@true\let\veqno=\@@leqno}
\newcommand*{\reqnomode}{\tagsleft@false\let\veqno=\@@eqno}
% based on my guess on `amsmath.sty`
\newcommand*{\fleqnon}{\setboolean{@fleqn}{true}}
\newcommand*{\fleqnoff}{\setboolean{@fleqn}{false}}
\makeatother

\begin{document}

\fleqnon

\begin{align}
  f(x) &= ax^2 + bx + c \\
  g(x) &= dx^2 + ex + f
\end{align}

\fleqnoff

\begin{align}
  f(x) &= ax^2 + bx + c \\
  g(x) &= dx^2 + ex + f \tag{e}
\end{align}

\fleqnon
\leqnomode

\begin{align}
  f(x) &= ax^2 + bx + c \\
  g(x) &= dx^2 + ex + f \tag{a}
\end{align}

\fleqnoff
\begin{align}
  f(x) &= ax^2 + bx + c \\
  g(x) &= dx^2 + ex + f
\end{align}

\begin{equation}
  a^2+b^2=c^2.
\end{equation}

\reqnomode

\begin{equation}
  -\Delta\phi=4\pi k\rho.\tag{2}
\end{equation}

\end{document}

Answer 1

The comments in amsmath.dtx say:

%    The code for calculating the appropriate placement of equation
%    tags in the \env{align} environments is quite complicated and
%    varies wildly depending on the settings of the |tagsleft@| and
%    |@fleqn| switches.  To minimize memory and hash space usage, we
%    only define the variant appropriate for the current setting of
%    those switches.
%

this means that of the four possible combinations of fleqn and leqno options being used or not used, definitions are made for only one combination, chosen at package loading time. The other three possibilities are skipped over and the TeX definitions for that combination are not made.

So if you change either of these switches mid document without copying code from the package sources and implementing the appropriate definitions, then the layout will basically be arbitrary and typically wrong, as you show.