Custom QED Alignment with thmtools

Question

I am trying to create a custom theorem format using the thmtools package. However, I am running into problems with the alignment of the QED symbol. When I end the theorem with normal text, it placed the QED symbol at the end of the line, and when I end with an equation and use \qedhere, it places the QED symbol right next to the equation. However, I would like the opposite: for the QED to be at the end of the line with an equation, and right next to the period of regular text.

You can see my MWE below:

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage{ifthen}
\usepackage{calc}

\declaretheoremstyle[
    spaceabove=10pt,
    headpunct={},
    headformat=\ifthenelse{ \equal{\NOTE}{} }%
    {% yes
    $\underset{%
        \raisebox{2pt}[0pt][0pt]{%
        \rule{\widthof{\text{\NAME\ \NUMBER}}+6ex}{.1ex}}%
        }{%
        \text{\NAME\ \NUMBER}\hfill%
        }$%
    }{% no
    $\underset{%
        \raisebox{5.5pt}[0pt][0pt]{%
        \rule{\widthof{\text{\NAME\ \NUMBER\hspace{1ex}$|$\hspace{1ex}\NOTE}}+6ex}{.1ex}}%
        }{%
        \text{\NAME\ \NUMBER\hspace{1ex}$\bm{|}$\hspace{1ex}\NOTE}\hfill%
        }$%
    }\newline,
    spacebelow=10pt,
    qed=\qedsymbol
]{thmdefault}

\declaretheorem[style=thmdefault]{Theorem}

\begin{document}

Here is some text.

\begin{Theorem}[Important Theorem]
    This is a theorem. Notice that this QED symbol is right next to my equation. I would like it at the end of that line. $$a^2 + b^2 = c^2\qedhere$$
\end{Theorem}

Here is some more text.

\begin{Theorem}[Another Theorem]
    This is another theorem. Notice that the QED symbol is placed at the end of the line. I would like it right next to this period.
\end{Theorem}

And here is a little more text.

\end{document}

(I included the large headformat option because the QED does not behave the same if it is not there.)

This seems like it should be a very simple problem with an easy solution (I am only beginning to learn LaTeX), but after a few days of searching, I cannot seem to find a solution.

Answer 1

You need to use \[...\] for your display math which sets \qedhere at the location you want. For the text-related adjustment, we redefine \qed to not include the \hfill:

\documentclass{article}
\usepackage{amsmath,amsthm,bm,thmtools}
\usepackage{ifthen}
\usepackage{calc}

\declaretheoremstyle[
  spaceabove=10pt,
  headpunct={},
  headformat=\ifthenelse{ \equal{\NOTE}{} }%
  {% yes
  $\underset{%
    \raisebox{2pt}[0pt][0pt]{%
    \rule{\widthof{\text{\NAME\ \NUMBER}}+6ex}{.1ex}}%
    }{%
    \text{\NAME\ \NUMBER}\hfill%
    }$%
  }{% no
  $\underset{%
    \raisebox{5.5pt}[0pt][0pt]{%
    \rule{\widthof{\text{\NAME\ \NUMBER\hspace{1ex}$|$\hspace{1ex}\NOTE}}+6ex}{.1ex}}%
    }{%
    \text{\NAME\ \NUMBER\hspace{1ex}$\bm{|}$\hspace{1ex}\NOTE}\hfill%
    }$%
  }\newline,
  spacebelow=10pt,
  qed=\qedsymbol
]{thmdefault}

\declaretheorem[style=thmdefault]{Theorem}

% Update \qed to remove \hfill
\DeclareRobustCommand{\qed}{%
  \ifmmode
    \mathqed
  \else
    \leavevmode\unskip
    \penalty 9999
    \hbox{}\nobreak\quad\hbox{\qedsymbol}
  \fi
}
\begin{document}

Here is some text.

\begin{Theorem}[Important Theorem]
This is a theorem. Notice that this QED symbol is right next to my equation.
I would like it at the end of that line.
\[
  a^2 + b^2 = c^2\qedhere
\]
\end{Theorem}

Here is some more text.

\begin{Theorem}[Another Theorem]
This is another theorem. Notice that the QED symbol is placed at the end of the line. 
I would like it right next to this period.
\end{Theorem}

And here is a little more text.

\end{document}