LaTeX \mathcal{w} has strange printout

Question

The follwing LaTex lines don't print out what I hope to see:

calculate $\rho_i^{t} = \| \mathcal{w}_{i}^{t} - \mathcal{w}_{i}^{t-1} \|_2$

what I get instead of the two w is that:

Can anyone help me please?

Thank you!

Answer 1

That's because the font does not have lowercase characters. This is also documented in the TeXbook (in plain TeX you get the effect of \mathcal using \cal).

For example, ‘$\cal A$’ produces ‘𝒜‘ and ‘$\cal Z$‘ produces ‘𝒵’. But beware: This works only with the letters A to Z; you'll get weird results if you apply \cal to lowercase or Greek letters.

As you can see from the symbols table below, there are other characters encoded in the slots where lowercase usually is (w maps to slot 119).

---

That being said, some Unicode math fonts have a lowercase script alphabet, e.g. XITS Math. The Unicode version of Latin Modern unfortunately does not have a lowercase script alphabet.

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\begin{document}
$\rho_i^{t} = \| \mathscr{w}_{i}^{t} - \mathscr{w}_{i}^{t-1} \|_2$
\end{document}