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Hello!

When I read the very good introductory chapter "About GAP" of the GAP manual,

some minor comments/questions came to my mind.

1) The contrary of "Intersection" is in many Categories not the "Union",

but the smallest object (domain), containing the given ones.

Such a function, maybe called "Compositum", would make more sense

than "Union".

2) Why are there no Iterators, generating all elements of a domain

exactly once, but without putting them all into a list.

This is easy to achieve for e.g. permutation groups,

and useful in various places. There could also be a

construct like "for a in D do" where D is a domain, and an

iterator is used to generate the a.

(Similar to "for i in [1..6] do")

3) It seems to me that the definition of "<" in the ResidueClass

example in 1.28 leads to problems if you want to define two

new types of group elements independently and to compare

two of those. The problems arise if you want to put them

into a sorted list (a set).

I must admit that I could implement the proposals 1) and 2) (partially) for

myself, if I really needed them. Maybe the designers of GAP have

thought about these things and have their reasons for not doing them.

But if this is not case they are certainly better in doing a proper

implementation and defining a good standard for these things.

Greetings

Ralf Dentzer

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