Hello Ignacio García,
on 1/31/2008 you wrote:

> In my system, LyX 1.5.3, Ubuntu gutsy, Spanish keyboard with dead
> keys, to print isolated accents, caret, accute..., in the text I can
> press twice the accent key.
> In math mode, exponents are obtained pressing caret and space, "^space",
> but I get exponents using twice the caret key: "^^", it's a little
> faster for me.

I'm running Windows XP SP2. I'm German using both German and English
keyboard layouts. Here is how it works for me:

Using German keyboard layout:
  Outside math mode:
    Pressing caret once: nothing happens.
    Pressing caret plus combinable key: caret plus letter combined
      appear e.g., "â".
    Pressing caret plus any other key: one caret plus the other key
      appear e.g., "^p".
    Pressing caret twice: two cares "^^" appear (special case of the
      above case).
  Inside math mode:
    Pressing caret once: nothing happens.
    Pressing caret plus combinable key: caret plus letter combined
      appear e.g., "â".
    Pressing caret plus any other key: an exponent placeholder is
      created and the second pressed key is put into the exponent of the
      preceding symbol (no caret appears, very quick for x^2).
    Pressing caret twice: an empty exponent placeholder is created.

Using English keyboard layout:
There is one keyboard layout (or shape) called United States -
International. This one also knows accents and such. It behaves just
as the German layout.
The "regular" United-States layout outputs any accents, carets, and
such immediately and also its effects in math mode. This means:
  Outside math mode:
    Pressing caret once: one caret appears "^" and the sequence is
      over.
  Inside math mode:
    Pressing caret once: an empty exponent placeholder is created and
      the sequence is over (same effect as pressing the caret twice in
      German layout).

Wou, that got a bit lengthy. Well, I hope it's the more helpful.

Greetings
Martin
      


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