Make big plus and big times symbols

Question

I want to create from suitable symbols ‐ and not using TikZ or other drawing method — large sum (\bigsum) and large times (\mybigtimes) math symbols, for cartesian sum and cartesian product, respectively, that:

• are the same vertical size as \bigcup and \bigcap;
• have strokes with the same thickness as the curves in \bigcup and \bigcap;
• in the case of \mybigtimes, is scaled down horizontally only;
• will scale properly for in-line math, display math, etc. (presumably, by using \mathchoice; and
• will work with both pdfLaTeX and `XeLaTeX.

How can this be done?

Here is what I have so far. The output shown is produced only when the part after This does \emph{not} work is commented out.

\documentclass[12pt,fleqn]{article}
\usepackage{amsmath}
\usepackage{iftex}

\ifTUTeX
  \usepackage{fontspec}
  \usepackage{unicode-math}
  \defaultfontfeatures{ Scale=MatchLowercase, Ligatures=TeX }
  \setmainfont{TeX Gyre Termes}[Scale=1.0]
  \setmathfont{TeX Gyre Termes Math}
  \mathchardef\timessymbol=\numexpr\times-"2000\relax % WHAT IS THE NAME-NUMBER?
\else
  \RequirePackage[scaled=0.93]{newtxtext}
  \RequirePackage{newtxmath}%
  \mathchardef\timessymbol=\numexpr\times-"2000\relax % WHAT IS THE NAME-NUMBER?
\fi

\usepackage{graphicx}
\usepackage{scalerel}
\DeclareMathOperator*{\bigplus}{\scalerel*{+}{\sum}}
\DeclareMathOperator*{\Bigplus}{\scalerel*{+}{\textstyle\sum}}

% Attempt to shrink a big times horizontally:
\DeclareMathOperator*{\mybigtimes}{\scalebox{0.7}[1]{\timessymbol}}

\begin{document}
\ifTUTeX With Xe\LaTeX\else With pdf\LaTeX\fi

\bigskip
These work, but geometry is wrong:

\bigskip

$\bigtimes_{n=0}^{\infty} X_{i} = \bigcup_{k=0}^{\infty}U_{k}$ 
\quad to shrink \verb!\bigtimes! horizontally (but not vertically)

\bigskip
$\bigplus_{n=0}^{\infty} X_{i} = \bigcap_{k=0}^{\infty}U_{k}$ \quad \verb!\bigsum! too thick 
%
\begin{gather*}
\bigtimes_{n=0}^{\infty} X_{i}= \bigcup_{k=0}^{\infty}U_{k}
\quad \text{to shrink bigtimes symbol horizontally (but not vertically)}
\\
\bigplus_{n=0}^{\infty} X_{i} = \bigcap_{k=0}^{\infty}U_{k} 
\quad \text{bigplus symbol too thick}
\end{gather*}

This does \emph{not} work:

$\mybigtimes_{n=0}^{\infty} X_{i}$
\[
\mybigtimes_{n=0}^{\infty} X_{i}
\]
\end{document} 

Related:

https://tex.stackexchange.com/a/394912/13492

Big cartesian product & cartesian sum symbols with Lucida Math fonts?

Continuation: See Make non-square bigtimes.

Answer 1

You can use \pdfliteral directly in pdfTeX:

\def\mybigtimes{\mathop{\mathchoice{%display:
   \vcenter{\hbox to10bp{\vrule height15bp width0pt \pdfliteral{
   q 1 J .8 w 0 1 m 10 14 l S 0 14 m 10 1 l S Q
}\hss}}}{%text:
   \vcenter{\hbox to10bp{\kern1bp\vrule height10bp width0pt \pdfliteral{
   q 1 J .65 w 0 0 m 8 10 l S 0 10 m 8 0 l S Q
}\hss}}}{\times}{\times}%script, scriptscript not defined
}}

\def\mybigplus{\mathop{\mathchoice{%display:
   \vcenter{\hbox to12bp{\vrule height15bp width0pt \pdfliteral{
   q 1 J .8 w 0 7.5 m 12 7.5 l S 6 1 m 6 14 l S Q
}\hss}}}{%text:
   \vcenter{\hbox to12bp{\kern1bp\vrule height10bp width0pt \pdfliteral{
   q 1 J .65 w 0 5 m 10 5 l S 5 0 m 5 10 l S Q
}\hss}}}{+}{+}%script, scriptscript not defined
}}

You can define \def\pdfliteral#1{\special{pdf:literal #1}} in XeTeX and then you can use the same macros.

Answer 2

This is the image with pdflatex:

This is the image with xelatex:

For mysterious reasons, the developers of TeX Gyre Termes Math decided not to give all big operators the same dimensions. It's up to you to decide whether to use \bigcup as a model or \sum as in the code below.

\documentclass{article}
\usepackage{amsmath,pict2e}
\usepackage{iftex}

\ifTUTeX
  \usepackage{unicode-math}
  \setmainfont{TeX Gyre Termes}[Scale=1.0]
  \setmathfont{TeX Gyre Termes Math}
\else
  \usepackage{newtxtext,newtxmath}
\fi

\makeatletter
\newcommand{\murray@big}[1]{%
  \mathop{\vphantom{\sum}\mathpalette\murray@makebig{#1}}\slimits@
}
\AtBeginDocument{%
  \DeclareRobustCommand{\bigplus}{\DOTSB\murray@big\murray@plus}%
  \DeclareRobustCommand{\bigtimes}{\DOTSB\murray@big\murray@times}%
}

\newcommand{\murray@makebig}[2]{%
  \vcenter{%
    \sbox\z@{$\m@th#1\sum$}%
    \setlength{\unitlength}{0.9\dimexpr\ht\z@+\dp\z@}%
    \hbox{\kern0.1\wd\z@\murray@draw{#1}{#2}\kern0.1\wd\z@}%
  }%
}

\newcommand{\murray@draw}[2]{%
  \begin{picture}(1,1)
    \linethickness{%
      \ifx#1\displaystyle 1.2\fontdimen8\textfont3\else
      \ifx#1\textstyle 1.1\fontdimen8\textfont3\else
      \ifx#1\scriptstyle1\fontdimen8\scriptfont3\else
      1\fontdimen8\scriptscriptfont3\fi\fi\fi
    }%
    #2
  \end{picture}%
}


\newcommand{\murray@plus}{%
  \roundcap
  \Line(0.5,0)(0.5,1)
  \Line(0,0.5)(1,0.5)
}
\newcommand{\murray@times}{%
  \roundcap
  \Line(0.14645,0.14645)(0.85355,0.85355)
  \Line(0.14646,0.85355)(0.85355,0.14645)
}
\makeatother

\begin{document}

$\displaystyle\bigplus_{k=0}^\infty \bigcup_{k=0}^\infty \bigtimes_{k=0}^\infty$

\medskip

$\textstyle\bigplus_{k=0}^\infty \bigcup_{k=0}^\infty \bigtimes_{k=0}^\infty$

\medskip

$\scriptstyle\bigplus_{k=0}^\infty \bigcup_{k=0}^\infty \bigtimes_{k=0}^\infty$

\medskip

$\scriptscriptstyle\bigplus_{k=0}^\infty \bigcup_{k=0}^\infty \bigtimes_{k=0}^\infty$

\end{document}