In GAP Forum article 356 Lewis McCarthy writes
where ER(-3) supposedly returns E(3)-E(3)^2.
Either someone's got a fancy unreleased version of GAP, or they
cheated a bit with the examples ;)
Sorry, but this is neither a fancy unreleased version of GAP nor
cheated. All versions GAP 3.2, 3.3, 3.4 do produce this answer, as
you could easily have seen before writing. I am a little bit
embarrassed about this unjustified supposition of cheating, in fact we
do spend quite a bit of time with releases trying to make sure that
examples given in the manual are what the respective version of GAP
does produce. (It is such unnoticed work of several days that
sometimes adds to releases coming late).
All that is the case - as Frank has said - is that the manual first
restricts N to be positive , but that among the examples ER is applied
to an odd negative number, which according to the above restriction
should not be done. In fact ER produces correct results for *some*
negative N but not for all and this is not a desirable state of
affairs. Thomas Breuer, who is looking at this part of GAP is not at
Aachen at the moment, when he returns he will decide if the definition
domain of N will be extended to all integers (with correct answers) or
if the definition domain will be kept restricted to the positive
integers (or some other subset of the integers) and an error message
issued if the function is applied to illegal arguments, or some other
totally consistent regulation.
Perhaps we should have used the ATLAS formulation:
'Then for suitable integers N we define ...' , (ATLAS, p. xvii)!
This way we could never be blamed for cheating.