[GAP Forum] pseudo-random elements of a free group

[Laurent Bartholdi]

hi,
i'm playing around with the "PseudoRandom" command, as applied
to free groups. I know that there's no preferred choice of a random
element in an infinite (worse, non-amenable) object; however:

* PseudoRandom(FreeGroup(2)); always returns positive words, i.e.
  words that contain no inverses of generators

* The returned words are usually extremely long; in the sense that,
  for example, they are too complicated to be fed into the
  ReducedForm() command of KBMAG.

Would it make some sense to have a
"ReasonablyShortPseudoRandom()" command?

Best, Laurent

--
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD   \    Téléphone: +41 21-6930380
CH-1015 Lausanne, Switzerland \      Fax: +41 21-6930385