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Add is_left and is_right for SubgroupTransversal #4298

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Merged
fingolfin merged 2 commits into from
Nov 13, 2024
Merged

Add is_left and is_right for SubgroupTransversal #4298

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is_left and is_right for SubgroupTransversal
fingolfin Nov 11, 2024
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fingolfin Nov 12, 2024
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27 changes: 17 additions & 10 deletions src/Groups/cosets.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ function ==(C1::GroupCoset, C2::GroupCoset)
end

function Base.show(io::IO, ::MIME"text/plain", x::GroupCoset)
side = x.side === :left ? "Left" : "Right"
side = is_left(x) ? "Left" : "Right"
io = pretty(io)
println(io, "$side coset of ", Lowercase(), x.H)
print(io, Indent())
Expand All @@ -57,7 +57,7 @@ function Base.show(io::IO, ::MIME"text/plain", x::GroupCoset)
end

function Base.show(io::IO, x::GroupCoset)
side = x.side === :left ? "Left" : "Right"
side = is_left(x) ? "Left" : "Right"
if is_terse(io)
print(io, "$side coset of a group")
else
Expand Down Expand Up @@ -146,7 +146,7 @@ Base.:*(g::GAPGroupElem, H::GAPGroup) = left_coset(H,g)

function Base.:*(c::GroupCoset, y::GAPGroupElem)
@assert y in c.G "element not in the group"
if c.side == :right
if is_right(x)
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return right_coset(c.H, representative(c)*y)
else
return left_coset(c.H^y, representative(c)*y)
Expand All @@ -155,15 +155,15 @@ end

function Base.:*(y::GAPGroupElem, c::GroupCoset)
@assert y in c.G "element not in the group"
if c.side == :left
if is_left(x)
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return left_coset(c.H, y*representative(c))
else
return right_coset(c.H^(y^-1), y*representative(c))
end
end

function Base.:*(c::GroupCoset, d::GroupCoset)
@req (c.side == :right && d.side == :left) "Wrong input"
@req (is_right(c) && is_left(d)) "Wrong input"
return double_coset(c.H, representative(c)*representative(d), d.H)
end

Expand Down Expand Up @@ -325,11 +325,14 @@ end
SubgroupTransversal{T<: GAPGroup, S<: GAPGroup, E<: GAPGroupElem}

Type of left/right transversals of subgroups in groups.
The elements are encoded via a right transversal object in GAP.
(Note that GAP does not support left transversals.)

Objects of this type are created by [`right_transversal`](@ref) and
[`left_transversal`](@ref).

# Note for developers

The elements are encoded via a right transversal object in GAP.
(Note that GAP does not support left transversals.)
"""
struct SubgroupTransversal{T<: GAPGroup, S<: GAPGroup, E<: GAPGroupElem} <: AbstractVector{E}
G::T # big group containing the subgroup
Expand All @@ -341,7 +344,7 @@ end
GAP.@install GapObj(T::SubgroupTransversal) = T.X

function Base.show(io::IO, ::MIME"text/plain", x::SubgroupTransversal)
side = x.side === :left ? "Left" : "Right"
side = is_left(x) ? "Left" : "Right"
println(io, "$side transversal of length $(length(x)) of")
io = pretty(io)
print(io, Indent())
Expand All @@ -351,7 +354,7 @@ function Base.show(io::IO, ::MIME"text/plain", x::SubgroupTransversal)
end

function Base.show(io::IO, x::SubgroupTransversal)
side = x.side === :left ? "Left" : "Right"
side = is_left(x) ? "Left" : "Right"
if is_terse(io)
print(io, "$side transversal of groups")
else
Expand All @@ -361,13 +364,17 @@ function Base.show(io::IO, x::SubgroupTransversal)
end
end

is_left(x::SubgroupTransversal) = x.side == :left

is_right(x::SubgroupTransversal) = x.side == :right

Base.hash(x::SubgroupTransversal, h::UInt) = h # FIXME

Base.length(T::SubgroupTransversal) = index(Int, T.G, T.H)

function Base.getindex(T::SubgroupTransversal, i::Int)
res = group_element(T.G, GapObj(T)[i])
if T.side === :left
if is_left(T)
res = inv(res)
end
return res
Expand Down