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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.

Joachim Neubueser

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