[GAP Forum] re: some simple and obvious and MISSING items for the FAQ

[shane miller]

Hi,

I installed gap without problem using gapsync. GAP is
an impressive algebra system. However, some really 
obvious things are missing. Perhaps this needs mere
FAQ documentation:

1. Almost every tutorial or other documentation tells
    how one can compute 43 million things (like subgroups
    or cosets) on a given group but fails to:
    a. tell how to perform a binary operation on the
        darned elements of the group. Now, for Sn groups
        this appears documented via constructions like
        (1 2 3)(4 2 1) etc. But,
        1. what do you if 4 or 5 Sn groups have been
            constructed. Then the command (1 2 3)(4 2 1)
            applies to which Sn group? How does GAP match
            the binary operation request with a group
            structure esp. if more than one has been defined?
            Please make this general: Q8 or Z4 do not 
            (typically) use permutation notation.
        2. how to add, say, 5+13 in some Z/Z15 (i.e.
            15>5, 15>13) or Z/Z3 group? 
        3. How does GAP know Z/Z3 is using + (add) or
            '*'? This must be implied by the groups's
            generator?
2. Many classic groups like D4, Q8 can be constructed
    via simple commands. But there are no elements; they're
    only generators! How in the heck do you get GAP to
    tell you what the actual elements are for Q8? i.e.
           q8:=SmallGroup(8,4);
           Elements(q8) = [f1,f2,f3] <-- not elements
    In any basic algebra book Q8 is a group on 8 distinct
    symbols {i,j,k,1,-1,-i,-j,-k}. How do you make GAP use
    these elements? How can you get GAP to do this:
           Elements(q8)={i,j,k,1,-1,-i,-j,-k}
    Of course the i,j,k etc. are not special; but how can
    one specify this set? And finally how would one then
    ask GAP to compute, say, "-1*j" in q8?
3. Presumably, once (2) is solved, then commands like
           NormalSubgroups(q8)
    will print all the normal subgroups using (user
    specified) elements and not darned generator expressions.
    Ditto computing cosets, normalizers etc.
4. Another super feature is the GraphicSubgroupLattice.
    But again, the numbered subgroups in the diagram are
    not that useful. Suppose you diagram D16 and pick,
    at random, subgroup #3. How in the heck do you ask
    GAP to tell you the generating elements (not generator
    expressions) for that subgroup (#3 here)?
5. And finally, given (4), how do you tell GAP to generate
    the number #3 subgroup of D16 using the generation
    information from (4)?

Shane


-- 
Sure it's a technical problem of fine pedigree ... But all such problems
are wrapped inside a management problem. And there's the rub.