Dear Joachim, my version of the manual (3.3) has on p 392:
IsLaurentPolynomialRing. I couldn't find any reference to the
Euclidean algorithm. Yet now that you mention it I find it the
on line manual. Can I get a more up to date manual?
Yours Chris Charnes

The reference 'EuclideanRemainder' *is* further down the page! There
is no manual entry 'Euclidean algorithm' since the function names in
general try to reflect what the function returns, not by which
algorithm the result is obtained. By the way, I think that the general
usage of the term 'Euclidean algorithm' means the algorithm for the
computation of the gcd by repeated use of division with remainder, not
just the division with remainder. There is also a function Gcd for the
computation of the gcd.For polynomials it is descibed on p. 393 (in
the middle of it!). Please note that the index gives p. 392 for it.
This is because page numbers in the index mostly refer to the
beginning of the section in which the function is described, which in
this case is section 18.16 'Ring Functions for Polynomial Rings'. I
think it is not too difficult to glance through such a section.

But really please let us now stop now to bother other members of the
GAP-forum with this discussion. If you want to continue discussion
how to find a reference please write directly to me.

As to versions of the manual, we are obviously both using the manual
for GAP 3.3, which today is still the latest, however will be replaced
by a new, extended one with the release of version 3.4., which will be
available with the program via ftp as before.

Joachim Neubueser