69

In my own custom theorem environment, I'm using the \qed command to create a white box. This works wonderfully when the theorem ends with a regular paragraph -- the box is pushed to the right where it should be.

Note that I just type out the \qed manually whenever I need it. It works fine. I don't need it automated.

However, if I use this command when the theorem ends with displayed mathmode, the box is just put there right beside the formula -- it is not pushed to the right. How can I accomplish that?

Svend Tveskæg
  • 31,033
MayGodBlessKnuth
  • 2,843

8 Answers8

53

If the QED symbol (or tombstone) is needed only rarely, I suggest to use the \qedhere feature provided by amsthm.

\documentclass{article}
\usepackage{amsthm}

\newtheorem{thm}{Theorem}
\begin{document}

\begin{thm}
Some text some text some text some text some text some text some text some text some text
some text some text some text some text some text some text\qed
\end{thm}

\begin{thm}
Some text some text some text some text some text some text some text some text some text
some text some text some text some text some text some text
\[
\pushQED{\qed} 
a=b\qedhere
\popQED
\]     
\end{thm}     

\end{document}

enter image description here

egreg
  • 1,121,712
26

For the qed symbol to appear flushed right in the last line of aligned equations, I use:

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}


\renewcommand{\j}{\ensuremath{\text{j}}}
\newcommand{\qed}{\tag*{$\blacksquare$}}


\begin{document}
    \begin{align}
        \left(z_1\cdot z_2\right)^
            &=\left(\left(a_1+\j b_1\right)\cdot \left(a_2+\j b_2\right)\right)^* \
            &=\left(\left(a_1a_2-b_1b_2\right)+\j\left(a_1b_2+a_2b_1\right)\right)^* \
            &=\left(a_1a_2-b_1b_2\right)-\j\left(a_1b_2+a_2b_1\right) \
            &=a_1a_2-b_1b_2-\j a_1b_2-\j a_2b_1 \
            &=a_1a_2-a_1\j b_2-a_2\j b_1+\left(-\j\right)^2b_1b_2 \
            &=\left(a_1-\j b_1\right)\cdot\left(a_2-\j b_2\right) \
            &=\left(a_1+\j b_1\right)^\cdot\left(a_2+\j b_2\right)^ \
            &=z_1^\cdot z_2^
            \qed
    \end{align*}

\end{document}

enter image description here

Douba
  • 626
  • 5
  • 13
  • 1
    Thanks! I've been reading quite often, but this is the first time I felt I could actually contribute. – Douba Nov 14 '13 at 14:46
  • Amazing. That did for me. – Ory Band Mar 14 '14 at 13:21
  • 2
    @Douba Maybe it is better to use \mathrm{j} instead of \text{j}. – L. F. Mar 22 '19 at 12:07
  • 2
    @L.F. You may be right, thank you for the suggestion. I do not usually use \mathrm, because it explicitly requests a roman font. I prefer being able to switch the looks of a document in a centralized way and only mark up semantics elsewhere. However, I see that \text falls back to the surrounding font, which may not be what I expect either. – Douba Jan 31 '20 at 09:49
  • 1
    Used with the proof environment, this method places \qed symbol twice. To avoid this, I add the command \renewcommand{\qedsymbol}{} and \vspace{-\baselineskip} right before \end{proof}. – mathreader Oct 23 '20 at 03:42
  • 1
    @mathreader Or just change \qed in the example to \qedhere – Louis Deaett Apr 19 '23 at 14:57
13

Not sure with LaTeX, haven't worked with it for a long time, but in Plain, I would use \eqno.

$$\sum_{n=1}^\infty {1 \over n^2} = {\pi^2 \over 6} \eqno\qed$$
Svend Tveskæg
  • 31,033
Palec
  • 325
8

You should consider using the ntheorem package which does this kind of thing from the start. But if you really need to use your custom theorem environments, you can take inspiration from what amsthm does. By stripping the code of everything which is not necessary, you would get:

result of the code

\documentclass{article}

\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\providecommand{\openbox}{\leavevmode
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
\makeatletter
\DeclareRobustCommand{\qed}{%
  \ifmmode
    \eqno \def\@badmath{$$}%$$
    \let\eqno\relax \let\leqno\relax \let\veqno\relax
    \hbox{\openbox}%
  \else
    \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
    \quad\hbox{\openbox}%
  \fi
}
\makeatother

\begin{document}

\begin{theorem}
\lipsum*[1] \qed
\end{theorem}

\begin{theorem}
\lipsum*[1]
\[
  f(x)=ax^2+bx+c \qed
\]
\end{theorem}

\end{document}

Of course, in some situations, you might have problems, so for a more robust way of doing it, you should copy/paste the amsthm way of doing it:

\documentclass{article}

\usepackage{etoolbox}
\usepackage{lipsum}

\makeatletter
\let\@xp\expandafter
\DeclareRobustCommand{\qed}{%
  \ifmmode \mathqed
  \else
    \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
    \quad\hbox{\qedsymbol}%
  \fi
}
\let\QED@stack\@empty
\let\qed@elt\relax
\newcommand{\pushQED}[1]{%
  \toks@{\qed@elt{#1}}\@temptokena\expandafter{\QED@stack}%
  \xdef\QED@stack{\the\toks@\the\@temptokena}%
}
\newcommand{\popQED}{%
  \begingroup\let\qed@elt\popQED@elt \QED@stack\relax\relax\endgroup
}
\def\popQED@elt#1#2\relax{#1\gdef\QED@stack{#2}}
\newcommand{\qedhere}{%
  \begingroup \let\mathqed\math@qedhere
    \let\qed@elt\setQED@elt \QED@stack\relax\relax \endgroup
}
\newif\ifmeasuring@
\newif\iffirstchoice@ \firstchoice@true
\def\setQED@elt#1#2\relax{%
  \ifmeasuring@
  \else \iffirstchoice@ \gdef\QED@stack{\qed@elt{}#2}\fi
  \fi
  #1%
}
\def\qed@warning{%
  \PackageWarning{amsthm}{The \@nx\qedhere command may not work
    correctly here}%
}
\newcommand{\mathqed}{\quad\hbox{\qedsymbol}}
\def\linebox@qed{\hfil\hbox{\qedsymbol}\hfilneg}
\@ifpackageloaded{amsmath}{%
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning\quad\hbox{\qedsymbol}%
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\linebox@qed
      \else
        \eqno
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
  \@xp\let\csname equation*@qed\endcsname\displaymath@qed
  \def\equation@qed{%
    \iftagsleft@
      \hbox{\phantom{\quad\qedsymbol}}%
      \gdef\alt@tag{%
        \rlap{\hbox to\displaywidth{\hfil\qedsymbol}}%
        \global\let\alt@tag\@empty
      }%
    \else
      \gdef\alt@tag{%
        \global\let\alt@tag\@empty
        \vtop{\ialign{\hfil####\cr
                \tagform@\theequation\cr
                \qedsymbol\cr}}%
        \setbox\z@
      }%
    \fi
  }
  \def\qed@tag{%
    \global\tag@true \nonumber
    &\omit\setboxz@h {\strut@ \qedsymbol}\tagsleft@false
    \place@tag@gather
    \kern-\tabskip
    \ifst@rred \else \global\@eqnswtrue \fi \global\advance\row@\@ne \cr
  }
  \def\split@qed{%
    \def\endsplit{\crcr\egroup \egroup \ctagsplit@false \rendsplit@
      \aftergroup\align@qed
    }%
  }
  \def\align@qed{%
    \ifmeasuring@ \tag*{\qedsymbol}%
    \else \let\math@cr@@@\qed@tag
    \fi
  }
  \@xp\let\csname align*@qed\endcsname\align@qed
  \@xp\let\csname gather*@qed\endcsname\align@qed
%% Needs some patching up for amsmath 1.2
}{% end of amsmath branch, start plain LaTeX branch
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning \aftergroup\displaymath@qed
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\aftergroup\aftergroup\linebox@qed
      \else
        \eqno \def\@badmath{$$}%
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
  \@ifundefined{ver@leqno.clo}{%
    \def\equation@qed{\displaymath@qed \quad}%
  }{%
    \def\equation@qed{\displaymath@qed}%
  }
  \def\@tempa#1$#2#3\@nil{%
    \def\[{#1$#2\def\@currenvir{displaymath}#3}%
  }%
  \expandafter\@tempa\[\@nil
}
\@ifpackageloaded{amstex}{%
  \def\@tempa{TT}%
}{%
  \@ifpackageloaded{amsmath}{%
    \def\@tempb#1 v#2.#3\@nil{#2}%
    \ifnum\@xp\@xp\@xp\@tempb\csname ver@amsmath.sty\endcsname v0.0\@nil
       <\tw@
      \def\@tempa{TT}%
    \else
      \def\@tempa{TF}%
    \fi
  }{%
    \def\@tempa{TF}
  }%
}
\if\@tempa
  \renewcommand{\math@qedhere}{\quad\hbox{\qedsymbol}}%
\fi
\newcommand{\openbox}{\leavevmode
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
\DeclareRobustCommand{\textsquare}{%
  \begingroup \usefont{U}{msa}{m}{n}\thr@@\endgroup
}
\providecommand{\qedsymbol}{\openbox}
\makeatother

\newtheorem{theorem}{Theorem}
\preto{\theorem}{\pushQED{\qed}}
\preto{\endtheorem}{\popQED}

\begin{document}

\begin{theorem}
\lipsum*[1] \qedhere
\end{theorem}

\begin{theorem}
\lipsum*[1]
\[
  f(x)=ax^2+bx+c \qedhere
\]
\end{theorem}

\end{document}

A few comments on the code: the big chunk is just a copy/paste of the file amsthm.sty. If you decide to use this package, you won't need it anymore. The important point is to modify the {theorem} environment by adding \pushQED{\qed} before it starts and \popQED before it ends. For this, I've used the \preto command from the etoolbox package.

Philippe Goutet
  • 28,978
7

You can insert the display equation in text mode with a forced \displaystyle:

enter image description here

\documentclass{article}
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\newcommand{\qed}{\hfill\rule{1ex}{1ex}}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
\lipsum*[1] \qed
\end{theorem}
\begin{theorem}
\lipsum*[1]
\[
  f(x)=ax^2+bx+c \qed
\]
\end{theorem}
\begin{theorem}
\lipsum*[1]\par
\vspace{\abovedisplayshortskip}
\hfill $\displaystyle f(x)=ax^2+bx+c$ \qed
\end{theorem}
\end{document}

Since the last line of the preceding paragraph and "short", I've inserted a skip of \abovedisplayshortskip. A "long" paragraph ending should use \abovedisplayskip.

Werner
  • 603,163
  • This works. However, there is a problem with "abovedisplayshortskip" because it only works with your particular example, in which the last line of the previous paragraph is short enough. However, the skip should be larger if this line is a bit longer. Can you adjust this so that it works for all situations? – MayGodBlessKnuth Aug 07 '12 at 04:29
  • @MayGodBlessKnuth: As I mentioned at the end of my post, you should use \abovedisplayskip for a longer paragraph. I'll see what can be done to automate this requirement. – Werner Aug 07 '12 at 04:30
  • Oh, sorry. I must have missed that. But is there no way to combine both into one solution to make it automatic? – MayGodBlessKnuth Aug 07 '12 at 04:30
6

You can use \displaymath@qed from the amsthm package. Due to the @ in the name you'll need a wrapper macro. In the code below I "overload" \qed in such a way that it acts as \displaymath@qed in math mode and as the standard \qed in text mode.

output

\documentclass{article}
\usepackage{amsthm}
\makeatletter
\let\saveqed\qed
\renewcommand\qed{%
   \ifmmode\displaymath@qed
   \else\saveqed
   \fi}
\begin{document}
text
\[
  a=b\makeatletter\displaymath@qed
\]
more text \qed
\end{document}
Hendrik Vogt
  • 37,935
0

I think I found a much easier work around. Hopefully this helps anyone else who stumbles across this question:

\begin{align}
&E^2 + \frac{1}{4}(-2E^2 +2B^2)\\
 &= 1/2 (E^2 +B^2)\\
 &= \mathlarger{\boldsymbol{\varepsilon}}
\end{align}

\begin{flushright}
\qedsymbol
\end{flushright}
Max D
  • 9
  • The question is how to insert the QED symbol within a formula (and not afterwards). In case of an unfavorable page break formula and QED could be separated here. – dexteritas Sep 28 '20 at 12:08
  • 2
    Hey, thank you for your response. What I read was "..if I use this command when the theorem ends with displayed mathmode, the box is just put there right beside the formula -- it is not pushed to the right. How can I accomplish that?" I feel as though I did help answer that, though I suppose you feel there are better and more nuanced replies. That's fair. – Max D Sep 29 '20 at 05:48
0

A hack I can use even in mathjax when I take notes in typora is to set the equation number to the qed symbol. Example:

\begin{align}
k_m(x,y) =& \sum_{\substack{h, h'}} k((x,h), (y, h'))p(h|x)p(h'|y)\\
=&  \sum_{\substack{h, h'}} k((y,h), (x,h')) p(h'|x)p(h|y) \\
=& k_m(y, x) \tag*{$\blacksquare$} \\
\end{align}

enter image description here

Caveat:
If you ever reference this equation, you will have that symbol instead of an equation number. But you can of course just reference the line before that instead.

lucidbrot
  • 305