Cartesian Product Notation

Questions
1

Just like we can enter summation notation into a text cell, how can we do so with a Cartesian Product expression?

In a text cell I type the Cartesian product of sets A,B,C as A x B x C.

But for sets A(1) thru A(n), I want to use the conventional “Big X” that designates a Cartesian product of indexed sets. The indexing parameters would go above and below the Big X.

But then I want to format it nicely, just as the Basic Palette’s summation button does (although I would modify the look by selecting the summation and indexing parameters and then punch OptionInspector / FormattingOptions / ExpressionFormatting / DisplayOptions and set ScriptLevel to 0).

When I replace the sigma by a capital X and increase the font size, the expression looks awkward – the terms aren’t centered on the X.

Any ideas? Tech Support says this may not be so easy to do, since there’s no Big X character available. I believe them but just in case, I’m checking here. I recall a long ago issue with the semidirect product symbol that at first started as a “can’t do” but Tech Support persisted to eventually find a simple solution, as they always do. Hopefully someone has already figured this out, given that it’s probably not so easy. Thanks.

2

Can you post the InputForm of a sample cell and/or a screenshot of how the terms “aren’t centered on the X?”

3

Underoverscript[X, k = 1, n]*
Subscript[A, k]

BigX.png

4

The standard form of the cross-type symbol for the Cartesian product of a family of sets should not look like a big letter X, with serifs. It should look like what you get if in LaTeX you first load package mathtools and then typeset:

$\bigtimes_{k=1}^n A_k$.

And the result should look like this:

bigtimes.png
bigtimes.png289×123 4.98 KB