Krdytkyu

Is there an environment (or standard framework) to typeset a (single line) displayed equation with a "short" quantification that gives the following result?

That is, the "main" part of the equation is centered (as if nothing else were there), and the quantifier part is aligned to the left with some indentation. I don't think this is supposed to work for longer strings, and I am not looking for a solution that does.

I have found similar questions here (e.g. equation center, quantifier push right), but solutions like

begin{flalign}

 forall x in X  &&&  P(x)  &&

end{flalign}

are not what I'm looking for since $P(x)$ is not centred within the page, and $forall xin X$ is not indented. Adding

begin{flalign}

qquad forall x in X  &&&  P(x)  &&

end{flalign}

does seem to get the desired indentation, but $P(x)$ is now even less centred.

Here's a proposal that does the centering when feasible, resorting to standard centering otherwise. (Thanks to Mico for the coding.)

documentclass{book}

usepackage{amsmath,amssymb,amsthm}

usepackage{environ}



theoremstyle{definition}

newtheorem{defn}{Definition}[section]



newcommandbff{mathbf{f}}

newcommandbfg{mathbf{g}}



makeatletter

NewEnviron{quantifiedequation}[1]{% #1 is the quantifiers

  begin{equation}

  expandaftermake@quantifiedequationexpandafter{BODY}{#1}

  end{equation}

}

NewEnviron{quantifiedequation*}[1]{% #1 is the quantifiers

  begin{equation*}

  expandaftermake@quantifiedequationexpandafter{BODY}{#1}

  end{equation*}

}

newcommand{make@quantifiedequation}[2]{%

  m@th % remove mathsurround

  sboxz@{$displaystyle#2$}% measure the quantifiers

  sboxtw@{letlabel@gobble$displaystyle#1$}

  ifdimdimexpr 1em+wdz@+0.5wdtw@+2em>0.5displaywidth

    % centering is not possible

    #2qquad#1

  else

    makebox[0pt][r]{%

      makebox[dimexpr0.5displaywidth-0.5wdtw@][l]{quadboxz@}%

    }#1

  fi

}

makeatother



begin{document}

setcounter{chapter}{1}

setcounter{section}{1}

setcounter{defn}{12}



begin{defn}

Let $M$ be a manifold. A emph{derivation} at a point $pin M$ 

is an $mathbb{R}$-linear map $Xcolon C^infty(p)tomathbb{R}$ 

which satisfies the emph{Leibniz rule}

begin{quantifiedequation*}{forall,bff,bfgin C^infty(p)}

    X(bffbfg)=bff(p)X(bfg)+bfg(p)X(bff)

end{quantifiedequation*}

end{defn}



begin{defn}

Let $M$ be a manifold. A emph{derivation} at a point $pin M$ 

is an $mathbb{R}$-linear map $Xcolon C^infty(p)tomathbb{R}$ 

which satisfies the emph{Leibniz rule}

begin{quantifiedequation}{forall,bff,bfgin C^infty(p)}

    X(bffbfg)=bff(p)X(bfg)+bfg(p)X(bff)

    label{qeq}

end{quantifiedequation}

end{defn}



Here's the reference eqref{qeq}.



begin{defn}

Let $M$ be a manifold. A emph{derivation} at a point $pin M$ 

is an $mathbb{R}$-linear map $Xcolon C^infty(p)tomathbb{R}$ 

which satisfies the emph{Leibniz rule}

begin{quantifiedequation*}{forall,bff,bfgin C^infty(p)}

    X(bffbfg)=bff(p)X(bfg)+bfg(p)X(bff)

    +bff(p)X(bfg)+bfg(p)X(bff)

end{quantifiedequation*}

end{defn}

end{document}

I'm not aware of a ready-made environment or "standard framework" that does exactly what you're looking to achieve. However, it's not too much work to create a custom macro that gets the job done.

Note that the macro quant -- you're obviously free to choose a different name for this macro -- takes 2 arguments: the quantifier (which is indented by quad from the left-hand edge of the text block; feel free to change the indentation amount) and the actual equation. Do note that because the equation is centered exactly on the line, the whitespace to its left and right won't be of equal length (since the whitespace on the left is reduced by the presence of the quantier).

Observe that equation numbering isn't an option, but then I got the impression that automatic equation numbering isn't a requirement. Do advise if it is.

Observe also that if quantifier and/or the equation are quite long, they will likely overlap in a very unsightly way. I gather, though, that this is not likely to be an issue.

documentclass{report}

usepackage[T1]{fontenc}

usepackage{amsmath,amssymb,amsthm}

theoremstyle{definition}

newtheorem{defn}{Definition}

counterwithin{defn}{section}



%% Set up a macro called "quant":

newcommand{quant}[2]{par%

   vspace{abovedisplayskip}%

   noindent%

   parbox{0pt}{mbox{quad$displaystyle #1$}}

   hfil $displaystyle #2$ hfillpar

   vspace{belowdisplayskip}}



newcommandbff{mathbf{f}}

newcommandbfg{mathbf{g}}



begin{document}

setcounter{chapter}{1}

setcounter{section}{1}

setcounter{defn}{12}



begin{defn}

Let $M$ be a manifold. A emph{derivation} at a point $pin M$ 

is an $mathbb{R}$-linear map $Xcolon C^infty(p)tomathbb{R}$ 

which satisfies the emph{Leibniz rule}

quant{forall,bff,bfgin C^infty(p)}{%

    X(bffbfg)=bff(p)X(bfg)+bfg(p)X(bff)}

end{defn}

end{document}

How about this?

documentclass{article}

usepackage{showframe}

renewcommand{ShowFrameLinethickness}{0.3pt}

 usepackage{mathtools}



begin{document}



begin{flalign}

quad mathrlap{forall x in X} &&& P(x) &&

end{flalign}



end{document}