How can I change a math symbol's size globally?

Question

I'm writing a document with many numbers in scientific notation, with LuaTeX.
I don't like \cdot because it leaves too much white space on both sides of the number.
I don't like {\cdot} because it leaves too little space. Using \times creates a x too large.

I would like to redefine \times at the beginning of the document to change the behavior of all subsequent occurrences of that command, I would like to get a smaller "x" every time I type \times, and keep it at mid height.

How can I redefine the size of \times?
How can I also control the space on both sides of the "x" and the thickness of the symbol?

I know I could also use siunitx, but now it would be more difficult to modify all my tables without getting unexpected errors.

I don't have the knowledge to figure out myself any solution but I have tried two things I've found googleing:

\usepackage{scalerel}
\newcommand\Times{\scaleobj{0.6}{\times}}


\usepackage{relsize}
\newcommand{\Times}{\mbox{\smaller$\times$}}

But they leave the "x" on the bottom and very thin.

Answer 1

I'd not do it. In any case I'd not redefine \times, but use a different name for the specific purpose.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}
\usepackage{siunitx}

\makeatletter
\let\skan@times\times
\DeclareRobustCommand{\rtimes}{% you may want to redefine \times, but don't
  \mathbin{%
    \nonscript\mspace{-0.75\medmuskip}%
    \mspace{1mu}\mathpalette\rtimes@\relax\mspace{1mu}%
    \nonscript\mspace{-0.75\medmuskip}%
  }%
}
\newcommand{\rtimes@}[2]{%
  \vcenter{\hbox{%
    \begingroup
    \settoheight{\unitlength}{$#1\skan@times$}%
    \setlength{\unitlength}{0.5\unitlength}%
    \begin{picture}(1,1)
    \roundcap
    \linethickness{1\getfontdimen{8}{#1}{3}}
    \Line(0,0)(1,1)\Line(1,0)(0,1)
    \end{picture}%
    \endgroup
  }}%
}
\newcommand{\getfontdimen}[3]{%
  \fontdimen#1
  \ifx#2\displaystyle\textfont\else
  \ifx#2\textstyle\textfont\else
  \ifx#2\scriptstyle\scriptfont\else
  \scriptscriptfont\fi\fi\fi #3%
}
\makeatother

\begin{document}

$5.12\times 10^{-49}$

$5.12\rtimes 10^{-49}$ $\scriptstyle5.12\rtimes 10^{-49}$

\num{5.12e-49}

\sisetup{exponent-product=\rtimes}

\num{5.12e-49}

\end{document}

This exploits that \times in Computer Modern is a very simple geometric shape with rounded caps. With other fonts it would be different.

You should consider typing in such numbers with siunitx that allows for a very simple syntax and doesn't require to explicitly mention the symbol for the operation, so you can change your mind anytime.

The control of the thickness is done by using the default thickness of the fraction line, which is stored in \fontdimen8 of the font in math group 3.

Note that \rtimes won't behave properly in every context (next to a parenthesis, for instance), but for your purpose it will.

Answer 2

This keeps the same line thickness, but shrinks it down to .6 scale. If you need this in smaller math styles, let me know.

\documentclass{article}
\usepackage{scalerel,stackengine}
\newcommand\shortminus{\ensuremath{\hstretch{0.6}{-}}}
\newcommand\Times{\mathbin{\!\rotatebox[origin=c]{45}{\stackinset{c}{}{c}{}{%
  \rotatebox[origin=c]{90}{\shortminus}}{\shortminus}}\!}}
\begin{document}
$5.12\times10^{-49}$

$5.12\Times10^{-49}$
\end{document}

Answer 3

You can play with scale, margin and raise to form a desired output.

\documentclass{article}
\usepackage{fontspec}
\usepackage{unicode-math}
\usepackage{amsmath}
\usepackage{adjustbox}


\setmainfont{TeX Gyre Termes}
\setmathfont[FakeBold=4.0, version=bold]{TeX Gyre Termes Math}
\setmathfont[version=default]{TeX Gyre Termes Math}


\begin{document}
% use default math font
\mathversion{default}

\let\oldtimes\times
\renewcommand{\times}{%
\adjustbox{scale=0.6, margin=-0.2pt, raise=0.4pt}{$\mathversion{bold}\boldsymbol{\oldtimes}$}%
}

$a \oldtimes b$

$a \times b$

\end{document}