Some misunderstood or unknown tricks (VIII) and Turing-completeness (LaTeX)

We will begin by exposing new tricks, i.e. how to
1. write ‘closed’ square roots,
2. insert blank pages,
3. ask the reader to turn the page,
4. write bold words in an index,
5. divide a cell by a diagonal,
6. draw ‘product integrals,’
7. understand what happens when \mathcal has a lower-case letter argument.
We will then consider an uncommon example of what one can do with LaTeX, in link with its Turing completeness.