Update GAP.jl to 0.16, i.e. GAP to 4.15.1

[lgoettgens]

Resolves #5388, resolves #5387, closes #5283.

[lgoettgens]

The one remaining failures that running the testsuite on tutulla against GAP.jl master and https://github.com/lgoettgens/Hecke.jl#lg/GAP-0.16 reports is due to

Oscar.jl/test/book/specialized/decker-schmitt-invariant-theory/cox_ring.jlcon

Line 12 in 3b275ca

julia> chi = character_table(G)[6];

returning a different character and thus some changes in the following lines of output. What do we do here? Also use the sort from #5486? (ping @fingolfin @ThomasBreuer)

[lgoettgens]

This now waits for thofma/Hecke.jl#2054

[lgoettgens]

The one remaining failures that running the testsuite on tutulla against GAP.jl master and https://github.com/lgoettgens/Hecke.jl#lg/GAP-0.16 reports is due to

Oscar.jl/test/book/specialized/decker-schmitt-invariant-theory/cox_ring.jlcon

Line 12 in 3b275ca

julia> chi = character_table(G)[6];

returning a different character and thus some changes in the following lines of output. What do we do here? Also use the sort from #5486? (ping @fingolfin @ThomasBreuer)

We still need to resolve this issue

[ThomasBreuer]

We still need to resolve this issue

One possibility is what I had sketched yesterday in Slack:

tbl = character_table(G);
F, _ = abelian_closure(QQ);
p = x -> order(kernel(x)[1]) == 8 && x(G(g2)) == F(z_3);
chi = iterate(x for x in tbl if p(x))[1];

This way, we describe the character we are interested in, the condition is encoded via p.
The code is ugly, but since we want a character with irrational values, we have to use information about the group.
Shall I make a pull request for that, or do you have a better idea?

[lgoettgens]

I have an idea how to slightly simplify your code a bit. I'll update this PR in a bit