Is there any way I can create a custom function in a math environment?

I'm writing a lot of formulas that basically have the same style for variables:
\underset{\sim}{I}
\underset{\sim}{P_1}

What I would like is to type (within LyX math environment):
\fuzzy

And that it shows an underset with wiggly line on the bottom.

So? Can I?

\newcommand{\fuzzy}[1]{\underset{\sim}{#1}}

Select it and press Ctrl-m

You get a math macro (also documented in the documentation). You can then use \fuzzy in your formulas.

Schimmi

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