Best way to resize an equation without affencting its tag and other values?

Question

Some time, in my typesetting work, I need to resize some equations like in the example (it's just a for explanation purposes):

\documentclass[11pt]{article}
\pagestyle{empty}

\usepackage{blindtext}

\renewcommand{\baselinestretch}{1.1}

\begin{document}
\flushbottom
\section{Section}
\blindtext\footnote{Equation:
\begin{equation}
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}\end{equation}}
\begin{equation}
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}
\blindtext
{\small\begin{equation}
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}}\relax


\end{document}

I'd like to know if there is a solution that:

1. Does non affect the resized equation's tag like in eq. (3) in the example. I need it in the default size.
2. Does not affect the footnotes equations tag. (This does not happen in the example but in some solutions I tried.)
3. Does not affect the baselinestretch of the last paragraph's line before the resized equation (like in the example)
4. Does prevent a pagebreak in between the resized equation and the corresponding paragraph.
5. Does work with multiline aligned ambients (align, alignat).

Edit. The solution I generally use is:

\documentclass[11pt]{article}
\pagestyle{empty}

\usepackage{blindtext}

\renewcommand{\baselinestretch}{1.1}

\usepackage{mathtools}
\newtagform{normal}[\normalsize]{\normalsize (}{)}
\newtagform{footnotesize}[\footnotesize]{\footnotesize (}{)}
\usetagform{normal}

\begin{document}
\flushbottom
\section{Section}
\blindtext\footnote{\usetagform{footnotesize}Equation:
\begin{equation}
\frac{2 x_{1} + 2 x_{2} +  2 x_{3} + 2 x_{4} +  2 x_{5} + 2 x_{6} +  2 x_{7} + 2 x_{8} +  2 x_{9} + 2 x_{10} +  2 x_{11} + 2 x_{12} + 2 x_{13} }{z}\end{equation}}
\begin{equation}
\frac{2 x_{1} + 2 x_{2} +  2 x_{3} + 2 x_{4} +  2 x_{5} + 2 x_{6} +  2 x_{7} + 2 x_{8} +  2 x_{9} + 2 x_{10} +  2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}
\blindtext
\par\vskip -\baselineskip
{\small\begin{equation}
\frac{2 x_{1} + 2 x_{2} +  2 x_{3} + 2 x_{4} +  2 x_{5} + 2 x_{6} +  2 x_{7} + 2 x_{8} +  2 x_{9} + 2 x_{10} +  2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}}\relax    

\end{document}

But it does not prevent page-break between the equation and the corresponding paragraph. Also I was searching for something simpler and quicker.

Note1. I know that I can reduce the math operators space (e.g. \!+\! in the simpler way) but I really need a generic solution to "resize" the whole content of the math-environment except for the tag.

Note2. Feel free to correct my english and the technical terms if they are wrong or not easy to understand.

Answer 1

if you're using amsmath, you can redefine \maketag@@@ to keep the "normal" size.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\def\newmaketag{%
  \def\maketag@@@##1{\hbox{\m@th\normalfont\normalsize##1}}%
  }
\makeatother

\begin{document}
Ordinary display:
\begin{equation}
a + b + c = d
\end{equation}

Small numbered display:
\begin{small}
\begin{equation}
a + b + c = d
\end{equation}
\end{small}

\newmaketag
Small numbered display with redefined tag:
\begin{small}
\begin{equation}
a + b + c = d
\end{equation}
\end{small}
\end{document}

this will work with any of the amsmath multiline display environments, providing full-size equation numbers on every line.

if the text above the "smallified" display has more than one line, the baselines will be affected; this requires some additional care, but i haven't time to address that right now; i'll try to come back to it.

Answer 2

As typeset er you have very tied hands ... Only two things besides use smaller fonts as you try in your MWE, what you can do, cross my mind: - enclose operators + into curly braces, i.e.: {+} (as exception for this equation) - spill-out equation to outer border

Both cases are shown in MWE below:

\documentclass[11pt]{article}
\usepackage[strict]{changepage}

\usepackage{blindtext}
\renewcommand{\baselinestretch}{1.1}

\begin{document}
\pagestyle{empty}
\flushbottom
\section{Section}
\blindtext\footnote{Equation:
\begin{equation}
\frac{2 x_{1}{+}2 x_{2}{+}2 x_{3}{+}2 x_{4}{+}2 x_{5}{+}2 x_{6}{+}2 x_{7}{+}2 x_{8}{+}2 x_{9}{+}2 x_{10}{+}2 x_{11}{+}2 x_{12}{+}2 x_{13} }{z}
\end{equation}}
    \begin{adjustwidth*}{}{-4em}
\begin{equation}
\frac{2 x_{1}{+}2 x_{2}{+}2 x_{3}{+}2 x_{4}{+}2 x_{5}{+}2 x_{6}{+}2 x_{7}{+}2 x_{8}{+}2 x_{9}{+}2 x_{10}{+}2 x_{11}{+}2 x_{12}{+}2 x_{13} }{z}
\end{equation}
    \end{adjustwidth*}
or with smaller font in equation
   {\small\begin{equation}
\frac{2 x_{1}{+}2 x_{2}{+}2 x_{3}{+}2 x_{4}{+}2 x_{5}{+}2 x_{6}{+}2 x_{7}{+}2 x_{8}{+}2 x_{9}{+}2 x_{10}{+}2 x_{11}{+}2 x_{12}{+}2 x_{13} }{z}
    \end{equation}}
or shortly (as pointed in comments below answer)%
    \footnote{Equation
\begin{equation}\medmuskip=0mu
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}
        }:
    \begin{adjustwidth*}{}{-4em}
\begin{equation}\medmuskip=0mu
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}
    \end{adjustwidth*}
or with smaller font in equation
{\small\begin{equation}\medmuskip=0mu
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
    \end{equation}}

\end{document}

I can't say, what is more appropriate. Probably you should ask author(s), that (s)he rewrote this equation and shown him result of this test :)

Edit: to MWE is added part which consider @campa comment below. From picture below follows, that results are the same (it had to be ...) but use \muskip make equation writing far more concise :).

Answer 3

The {\small\begin{equation}...} workaround is as wrong as it could be, sorry.

Here are some better solutions:

\documentclass[11pt]{article}
\usepackage{amsmath}% for text, recommended anyway
\usepackage{mathtools}% for \splitdfrac

\pagestyle{empty}
\renewcommand{\baselinestretch}{1.1}
\flushbottom

\begin{document}
\section{Section}
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
Some dummy text.\footnote{Equation:
\begin{equation}
\frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5}
      + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10}
      + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}
\end{equation}}
\begin{equation}
\text{\footnotesize$\displaystyle
  \frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5}
        + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10}
        + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}$%
}
\end{equation}
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
\begin{equation}
\frac{
  \splitdfrac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7}}
             {+ 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13}}
  }{z}
\end{equation}
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
Some dummy text. Some dummy text. Some dummy text. Some dummy text.
\begin{equation}
\begin{split}
  \frac{1}{z}\bigl(
    & 2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5} + 2 x_{6} + 2 x_{7}\\
    & + 2 x_{8} + 2 x_{9} + 2 x_{10} + 2 x_{11} + 2 x_{12} + 2 x_{13}
  \bigr)
\end{split}
\end{equation}

\end{document}

You might want to do the first as

\begin{equation}
\text{\footnotesize\medmuskip=0mu}$\displaystyle
  \frac{2 x_{1} + 2 x_{2} + 2 x_{3} + 2 x_{4} + 2 x_{5}
        + 2 x_{6} + 2 x_{7} + 2 x_{8} + 2 x_{9} + 2 x_{10}
        + 2 x_{11} + 2 x_{12} + 2 x_{13} }{z}$%
}
\end{equation}

and you'd get

An alternative is using nccmath and

\medmath{\frac{...}{...}}