How do you make such a beautiful generalized Cartesian product?

Question

In one of the books I came across such a beautiful designation of a generalized Cartesian product. I tried to repeat it for a long time and nothing happened.

Hello! For future questions please provide the code you already have, so others can work with it. — Roland, Dec 01 '20 at 23:52

score 7 · Accepted Answer · answered Dec 02 '20 at 00:47

\documentclass{article}
\usepackage{amsmath,graphicx}
\newcommand{\bigX}{\mathchoice
  {\raisebox{-.33\height}{\scalebox{2.07}{X}}}
  {\raisebox{-.25\height}{\scalebox{1.47}{X}}}
  {\raisebox{-.25\height}{\scalebox{1.03}{X}}}
  {\raisebox{-.25\height}{\scalebox{0.73}{X}}}
}
\DeclareMathOperator*{\X}{\bigX}
\begin{document}
[
  [a, b) \cap [c, d) = 
    \X_{k = 1}^n \bigl( \max {a_k, c_k}, \min {b_k, d_k} \bigr)
]
$
  \displaystyle      \prod \X
  \textstyle         \prod \X
  \scriptstyle       \prod \X
  \scriptscriptstyle \prod \X
$
\end{document}

The choice of scaling factors came from trial-and-error to match it up with \prod:

Roland · Answer 2 · 2020-12-02T08:08:41.487

4

\documentclass{article}

\usepackage{amsmath}
\DeclareMathOperator*{\X}{\text{\Large{X}}}

\begin{document}

    \[ [a,b) \cap [c,d) = \overset{n}{\X_{k=1}} \left (\max\{ a_{k},c_{k}\}, \min\{ b_{k},d_{k}\} \right) \]


\end{document}

edited Dec 02 '20 at 08:08

answered Dec 01 '20 at 23:48

Roland

6,655

3

...you could use \max and \min. How about resizing X to look different based on its use in a display, text or script environment? – Werner Dec 02 '20 at 00:00
Ah yes thanks! It should be the other way around \text{\Large{X}. I changed it. – Roland Dec 02 '20 at 08:10
\Large does not take an argument so \Large X would be more standard than \Large{X} (the {} are not an error but do nothing. \Large though is a fixed size and will not adapt to the surrounding math font size. – David Carlisle Dec 02 '20 at 08:13

score 3 · Answer 3 · answered Dec 02 '20 at 06:56

3

In plain TeX, we can write:

\font\bigrm=\fontname\textfont0 \space scaled2000
\def\X{\mathop{\vcenter{\hbox{\bigrm X}}}}
$$
  [a, b) \cap [c, d) = 
    \X_{k=1}^n \bigl( \max {a_k, c_k}, \min {b_k, d_k} \bigr)
$$
\bye

answered Dec 02 '20 at 06:56

wipet

74,238

score 2 · Answer 4 · answered Dec 02 '20 at 08:28

While it may "look nice", the output shown is fairly obviously an X which may be confusing. Unicode has a codepoint for n-ary product, ⨉ U+2A09 (N-ARY TIMES OPERATOR).

In unicode-math, stix2 and compatible packages this is denoted \bigtimes

Unlike answers using X, the font supplies the character at sizes suitable for inline and display without having to do any scaling at the TeX macro level.

\documentclass{article}
\usepackage{stix2}
\begin{document}
display
[
 [a, b) \cap [c, d) = 
    \bigtimes_{k=1}^n \bigl( \max {a_k, c_k}, \min {b_k, d_k} \bigr)
]
inline
$ [a, b) \cap [c, d) = 
    \bigtimes_{k=1}^n \bigl( \max {a_k, c_k}, \min {b_k, d_k} \bigr)$
large
\Large
[
 [a, b) \cap [c, d) = 
    \bigtimes_{k=1}^n \bigl( \max {a_k, c_k}, \min {b_k, d_k} \bigr)
]
\end{document}

How do you make such a beautiful generalized Cartesian product?

4 Answers4