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Fix show for RelativeBrauerGroupElem #3373

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merged 3 commits into from
Feb 19, 2024
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Fix show for RelativeBrauerGroupElem #3373

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a1843b8
Fix show for RelativeBrauerGroupElem
fingolfin Feb 15, 2024
bfa0a89
Make show(RelativeBrauerGroupElem) output less random
fingolfin Feb 16, 2024
8d8131a
Update experimental/GModule/GaloisCohomology.jl
lgoettgens Feb 16, 2024
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38 changes: 30 additions & 8 deletions experimental/GModule/GaloisCohomology.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@ import Oscar.GrpCoh: CoChain, MultGrpElem, MultGrp, GModule, is_consistent,
Group
import Base: parent
import Oscar: direct_sum
import Oscar: pretty, Lowercase
import Oscar: pretty, Lowercase, Indent, Dedent

export is_coboundary, idel_class_gmodule, relative_brauer_group
export local_invariants, global_fundamental_class, shrink
Expand Down Expand Up @@ -1398,14 +1398,12 @@ end

function Base.show(io::IO, m::MIME"text/plain", a::RelativeBrauerGroupElem)
io = pretty(io)
print(io, "Element of relative Brauer group of $(parent(a).k)\n")
ioC = IOContext(io, :supercompact => true, :compact => true)
print(io, "Element of relative Brauer group of ", Lowercase(), parent(a).k)
io = IOContext(io, :supercompact => true, :compact => true)
print(io, Indent())
for (p,v) = a.data
show(ioC, p)
print(io, " -> ")
show(ioC, v)
print(io, "\n")
data = sort(collect(a.data); by =(x -> first(x) isa AbsSimpleNumFieldEmbedding ? Inf : minimum(first(x))))
for (p,v) in data
print(io, "\n", p, " -> ", v)
end
print(io, Dedent())
end
Expand Down Expand Up @@ -1514,6 +1512,30 @@ an infinite direct sum of the local Brauer groups.

The second return value is a map translating between the local data
and explicit 2-cochains.

```jldoctest
julia> G = SL(2,5)
SL(2,5)

julia> T = character_table(G);

julia> R = gmodule(T[9])
G-module for G acting on vector space of dimension 6 over abelian closure of Q

julia> S = gmodule(CyclotomicField, R)
G-module for G acting on vector space of dimension 6 over cyclotomic field of order 5

julia> B, mB = relative_brauer_group(base_ring(S), character_field(S));

julia> B
Relative Brauer group for cyclotomic field of order 5 over number field of degree 1 over QQ

julia> b = B(S)
Element of relative Brauer group of number field of degree 1 over QQ
<2, 2> -> 1//2 + Z
<5, 5> -> 0 + Z
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Seems the order in which these three lines are printed is not stable, hence some of the doctest CI jobs fail :/

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Is there a canonical way to sort them (for a consistent printing)? If not, you might use a doctest-filter

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I don't see a good way to sort the keys in general, they are ideals in a number field, or field embeddings. But we could make sure that the ideals come first. And perhaps the ideals could be sorted by minimum or norm. That won't give a unique sorting in all cases, but it is good enough for this example and it probably is nice for the user overall. Will do that for now.

@fieker I also wonder if we should print something nicer instead of "Complex embedding of number field"?

Complex embedding of number field -> 1//2 + Z
```
"""
function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimpleNumField} = QQ)
G, mG = automorphism_group(PermGroup, K)
Expand Down
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