[Tex/LaTex] Erratic position of QED symbol at the end of proof environment using SIAM template

Question

I already had issues (described here: amsmath package error using SIAM LaTeX template files) with the newest version of SIAM LaTeX template from http://www.siam.org/journals/auth-info.php

For now, I would like to clarify why the position of QED symbol in the proof environment depends on the equation environment type. Using example from manual with \begin{displaymath}\end{displaymath}:

\begin{corollary}
  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
  has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
  Let $a$ and $b$ be two distinct roots of $f$.
  By \cref{thm:mvt}, there exists a number $c$ such that
  \begin{displaymath}
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
  \end{displaymath}
\end{proof}

puts QED symbol at the right position (end of the equation).

However, using $$ $$ QED symbol is completely absent from the proof environment:

\begin{corollary}
    Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
    has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
    Let $a$ and $b$ be two distinct roots of $f$.
    By \cref{thm:mvt}, there exists a number $c$ such that
    $$
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
    $$
\end{proof}

Finally, using \begin{equation*}\end{equation*} puts QED symbol in a wrong position, i.e., above the equation.

\begin{corollary}
  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
  has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
  Let $a$ and $b$ be two distinct roots of $f$.
  By \cref{thm:mvt}, there exists a number $c$ such that
  \begin{equation*}
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
  \end{equation*}
\end{proof}

My questions are following:

1. Is this behavior typical for any proof environment containing math equations and adding the QED symbol at the end of it; or this another 'bug' in SIAM template file?

2. What is the correct way to type in proof environment math equations?
   Previously I have used most often \begin{equation*}\end{equation*}, but here it produces the wrong behavior.

Answer 1

First of all, never ever use $$...$$ in LaTeX: you have discovered another reason why, but please have a look at Why is \[ ... \] preferable to $$ ... $$?

Second, it's another feature of ntheorem with the thmmarks option, that modifies some environments but not all in order to provide automatic placement of the tombstone.

In particular equation* doesn't get redefined, so it's not in line with the automatic placement. You can make it compatible by redefining it.

\documentclass[
  %review
]{siamart0516}
\usepackage{amsmath}

\usepackage{etoolbox}
% fix for https://tex.stackexchange.com/questions/328946
\patchcmd{\SetTagPlusEndMark}{$}{}{}{}
\patchcmd{\SetTagPlusEndMark}{$}{}{}{}

% fix for the QED in equation*    
\renewenvironment{equation*}{\[}{\]\ignorespacesafterend}

\begin{document}
\begin{equation}
\bar{x} = x + y
\tag{$\bar{x}$}
\label{eq:x}
\end{equation}

\begin{corollary}
  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
  has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
  Let $a$ and $b$ be two distinct roots of $f$.
  By \cref{thm:mvt}, there exists a number $c$ such that
  \begin{displaymath}
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
  \end{displaymath}
\end{proof}

\begin{corollary}
  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
  has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
  Let $a$ and $b$ be two distinct roots of $f$.
  By \cref{thm:mvt}, there exists a number $c$ such that
  \begin{equation*}
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
  \end{equation*}
\end{proof}

\begin{corollary}
  Let $f(x)$ be continuous and differentiable everywhere. If $f(x)$
  has at least two roots, then $f’(x)$ must have at least one root.
\end{corollary}
\begin{proof}
  Let $a$ and $b$ be two distinct roots of $f$.
  By \cref{thm:mvt}, there exists a number $c$ such that
  \begin{equation}
    f’(c) = \frac{f(b)-f(a)}{b-a} = \frac{0-0}{b-a} = 0.
  \end{equation}
\end{proof}

\end{document}

However, equation will not push the QED in the same position as equation* (I deem wrong the placement in equation*, but apparently this pleases the author of ntheorem).