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Adapt to Lie algebra module changes
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@lgoettgens
lgoettgens committed Feb 22, 2024
1 parent 0040c91 commit 1ec650d
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Showing 10 changed files with 266 additions and 266 deletions.
170 changes: 80 additions & 90 deletions src/DeformationBases/ArcDiagDeformBasis.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -32,22 +32,24 @@ struct ArcDiagDeformBasis{C <: RingElem} <: DeformBasis{C}
V = base_module(sp)

V_nice, h = isomorphic_module_with_simple_structure(V)
if !is_direct_sum(V_nice)
fl, V_nice_summands = is_direct_sum_with_data(V_nice)
if !fl
temp = direct_sum(V_nice)
h = compose(h, hom(V_nice, temp, identity_matrix(coefficient_ring(temp), dim(temp))))
V_nice_summands = [V_nice]
V_nice = temp
end

extra_data = Dict{DeformationMap{C}, Set{ArcDiagram}}()
normalize = no_normalize ? identity : normalize_default

n_cases = div(length(base_modules(V_nice)) * (length(base_modules(V_nice)) + 1), 2)
n_cases = div(length(V_nice_summands) * (length(V_nice_summands) + 1), 2)
lens = []
iters = []
for d in degs
case = 0
for (i_l, V_nice_summand_i_l) in enumerate(base_modules(V_nice)),
(i_r, V_nice_summand_i_r) in enumerate(base_modules(V_nice))
for (i_l, V_nice_summand_i_l) in enumerate(V_nice_summands),
(i_r, V_nice_summand_i_r) in enumerate(V_nice_summands)

if i_l > i_r
continue
Expand All @@ -59,7 +61,7 @@ struct ArcDiagDeformBasis{C <: RingElem} <: DeformBasis{C}
proj_to_summand_r = compose(h, canonical_projection(V_nice, i_r))

W = if i_l == i_r
exterior_power(V_nice_summand_i_l, 2)
exterior_power_obj(V_nice_summand_i_l, 2)
else
tensor_product(V_nice_summand_i_l, V_nice_summand_i_r)
end
Expand Down Expand Up @@ -136,17 +138,21 @@ function is_tensor_generator(::SO, V::LieAlgebraModule)
end

function is_tensor_generator(::GL, V::LieAlgebraModule)
return is_standard_module(V) || (is_dual(V) && is_standard_module(base_module(V)))
if is_standard_module(V)
return true
end
fl, base = is_dual_with_data(V)
return fl && is_standard_module(base)
end


function arc_diagram_upper_points(T::SO, V::LieAlgebraModule)
if is_standard_module(V)
return 1
elseif is_tensor_product(V)
return sum(arc_diagram_upper_points(T, W) for W in base_modules(V))
elseif is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V)
return arc_diagram_upper_points(T, base_module(V)) * get_attribute(V, :power)
elseif ((fl, Ws) = is_tensor_product_with_data(V); fl)
return sum(arc_diagram_upper_points(T, W) for W in Ws)
elseif ((fl, W, k) = is_power_with_data(V); fl)
return arc_diagram_upper_points(T, W) * k
else
error("Not implemented.")
end
Expand All @@ -155,12 +161,12 @@ end
function arc_diagram_upper_points(T::GL, V::LieAlgebraModule)
if is_standard_module(V)
return 1
elseif is_dual(V) && is_standard_module(base_module(V))
elseif ((fl, W) = is_dual_with_data(V); fl) && is_standard_module(W)
return 0
elseif is_tensor_product(V)
return reduce(vcat, arc_diagram_upper_points(T, W) for W in base_modules(V))
elseif is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V)
return reduce(vcat, [arc_diagram_upper_points(T, base_module(V)) for _ in 1:get_attribute(V, :power)])
elseif ((fl, Ws) = is_tensor_product_with_data(V); fl)
return reduce(vcat, arc_diagram_upper_points(T, W) for W in Ws)
elseif ((fl, W, k) = is_power_with_data(V); fl)
return reduce(vcat, [arc_diagram_upper_points(T, W) for _ in 1:k])
else
error("Not implemented.")
end
Expand All @@ -178,20 +184,17 @@ end
function arc_diagram_upper_iss(T::Union{SO, GL}, V::LieAlgebraModule)
if is_tensor_generator(T, V)
return Vector{Int}[]
elseif is_tensor_product(V)
inner_mods = base_modules(V)
elseif ((fl, inner_mods) = is_tensor_product_with_data(V); fl)
offset = 0
iss = Vector{Int}[]
for mod in inner_mods
append!(iss, [is .+ offset for is in arc_diagram_upper_iss(T, mod)])
offset += arc_diagram_num_upper_points(T, mod)
end
return iss
elseif is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_power_with_data(V); fl)
if is_tensor_generator(T, inner_mod)
if is_exterior_power(V)
if is_exterior_power_with_data(V)[1]
return [collect(1:power)]
else
return Vector{Int}[]
Expand Down Expand Up @@ -267,29 +270,22 @@ end
function arc_diagram_label_iterator(T::Union{SO, GL}, V::LieAlgebraModule, base_labels::AbstractVector{Int})
if is_tensor_generator(T, V)
return [[l] for l in base_labels]
elseif is_tensor_product(V)
inner_mods = base_modules(V)
elseif ((fl, inner_mods) = is_tensor_product_with_data(V); fl)
return ProductIterator([
arc_diagram_label_iterator(T, inner_mod, base_labels) for inner_mod in reverse(inner_mods)
]) .|>
reverse .|>
Iterators.flatten .|>
collect
elseif is_exterior_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_exterior_power_with_data(V); fl)
return combinations(collect(arc_diagram_label_iterator(T, inner_mod, base_labels)), power) .|>
Iterators.flatten .|>
collect
elseif is_symmetric_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_symmetric_power_with_data(V); fl)
return multicombinations(collect(arc_diagram_label_iterator(T, inner_mod, base_labels)), power) .|>
Iterators.flatten .|>
collect
elseif is_tensor_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_tensor_power_with_data(V); fl)
return ProductIterator(arc_diagram_label_iterator(T, inner_mod, base_labels), power) .|>
reverse .|>
Iterators.flatten .|>
Expand All @@ -301,20 +297,13 @@ end


function basis_index_mapping(V::LieAlgebraModule)
if is_tensor_product(V)
inner_mods = base_modules(V)
if ((fl, inner_mods) = is_tensor_product_with_data(V); fl)
return ProductIterator([1:dim(inner_mod) for inner_mod in reverse(inner_mods)]) .|> reverse .|> collect
elseif is_exterior_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_exterior_power_with_data(V); fl)
return combinations(dim(inner_mod), power) .|> collect
elseif is_symmetric_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_symmetric_power_with_data(V); fl)
return multicombinations(dim(inner_mod), power) .|> collect
elseif is_tensor_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_tensor_power_with_data(V); fl)
return ProductIterator(1:dim(inner_mod), power) .|> reverse .|> collect
else
error("Not implemented.")
Expand All @@ -326,8 +315,7 @@ function arc_diagram_label_permutations(T::Union{SO, GL}, V::LieAlgebraModule, l
if is_tensor_generator(T, V)
@req length(label) == 1 "Number of labels mismatch."
return [(label, 1)]
elseif is_tensor_product(V)
inner_mods = base_modules(V)
elseif ((fl, inner_mods) = is_tensor_product_with_data(V); fl)
@req length(label) == sum(mod -> arc_diagram_num_upper_points(T, mod), inner_mods) "Number of labels mismatch."
return [
begin
Expand All @@ -346,45 +334,43 @@ function arc_diagram_label_permutations(T::Union{SO, GL}, V::LieAlgebraModule, l
) for (i, inner_mod) in enumerate(inner_mods)
])
]
elseif is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V)
inner_mod = base_module(V)
power = get_attribute(V, :power)
elseif ((fl, inner_mod, power) = is_exterior_power_with_data(V); fl)
m = arc_diagram_num_upper_points(T, inner_mod)
@req length(label) == m * power "Number of labels mismatch."
if is_exterior_power(V)
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign * outer_sign)
end for (outer_perm, outer_sign) in permutations_with_sign(1:power) for inner_iter in ProductIterator([
arc_diagram_label_permutations(T, inner_mod, label[(outer_perm[i]-1)*m+1:outer_perm[i]*m]) for
i in 1:power
])
]
elseif is_symmetric_power(V)
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign)
end for outer_perm in permutations(1:power) for inner_iter in ProductIterator([
arc_diagram_label_permutations(T, inner_mod, label[(outer_perm[i]-1)*m+1:outer_perm[i]*m]) for
i in 1:power
])
]
elseif is_tensor_power(V)
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign)
end for inner_iter in
ProductIterator([arc_diagram_label_permutations(T, inner_mod, label[(i-1)*m+1:i*m]) for i in 1:power])
]
else
error("Unreachable.")
end
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign * outer_sign)
end for (outer_perm, outer_sign) in permutations_with_sign(1:power) for inner_iter in ProductIterator([
arc_diagram_label_permutations(T, inner_mod, label[(outer_perm[i]-1)*m+1:outer_perm[i]*m]) for
i in 1:power
])
]
elseif ((fl, inner_mod, power) = is_symmetric_power_with_data(V); fl)
m = arc_diagram_num_upper_points(T, inner_mod)
@req length(label) == m * power "Number of labels mismatch."
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign)
end for outer_perm in permutations(1:power) for inner_iter in ProductIterator([
arc_diagram_label_permutations(T, inner_mod, label[(outer_perm[i]-1)*m+1:outer_perm[i]*m]) for
i in 1:power
])
]
elseif ((fl, inner_mod, power) = is_tensor_power_with_data(V); fl)
m = arc_diagram_num_upper_points(T, inner_mod)
@req length(label) == m * power "Number of labels mismatch."
return [
begin
inner_label = reduce(vcat, first.(inner_iter))
inner_sign = prod(last.(inner_iter))
(inner_label, inner_sign)
end for inner_iter in
ProductIterator([arc_diagram_label_permutations(T, inner_mod, label[(i-1)*m+1:i*m]) for i in 1:power])
]
else
error("Not implemented.")
end
Expand All @@ -404,7 +390,7 @@ function arcdiag_to_deformationmap(
T::GL,
diag::ArcDiagramDirected,
sp::SmashProductLie{C},
W::LieAlgebraModule=exterior_power(base_module(sp), 2),
W::LieAlgebraModule=exterior_power_obj(base_module(sp), 2),
) where {C <: RingElem}
return arcdiag_to_deformationmap(T, arc_diagram(Undirected, diag), sp, W)
end
Expand All @@ -413,20 +399,24 @@ function arcdiag_to_deformationmap(
T::Union{SO, GL},
diag::ArcDiagramUndirected,
sp::SmashProductLie{C},
W::LieAlgebraModule=exterior_power(base_module(sp), 2),
W::LieAlgebraModule=exterior_power_obj(base_module(sp), 2),
) where {C <: RingElem}
@req !is_direct_sum(W) "Not permitted for direct sums."
@req !is_direct_sum_with_data(W)[1] "Not permitted for direct sums."
ind_map = basis_index_mapping(W)

dim_stdmod_V = base_lie_algebra(sp).n

iso_pair_to_L = arc_diagram_lower_pair_to_L(T, dim_stdmod_V)

case = :unknown

if is_exterior_power(W)
nrows_kappa = ncols_kappa = dim(base_module(W))
elseif is_tensor_product(W)
nrows_kappa, ncols_kappa = dim.(base_modules(W))
if ((fl, Wbase, k) = is_exterior_power_with_data(W); fl)
@assert k == 2
nrows_kappa = ncols_kappa = dim(Wbase)
case = :exterior_power
elseif ((fl, W_factors) = is_tensor_product_with_data(W); fl)
nrows_kappa, ncols_kappa = dim.(W_factors)
case = :tensor_product
end

kappa = zero_matrix(underlying_algebra(sp), nrows_kappa, ncols_kappa)
Expand All @@ -447,7 +437,7 @@ function arcdiag_to_deformationmap(
entry = _normal_form(entry, sp.rels)

kappa[i, j] += entry
if is_exterior_power(W)
if case == :exterior_power
kappa[j, i] -= entry
end
end
Expand Down
5 changes: 2 additions & 3 deletions src/DeformationBases/PseudographDeformBasis.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -27,9 +27,8 @@ struct PseudographDeformBasis{C <: RingElem} <: DeformBasis{C}
degs::AbstractVector{Int};
no_normalize::Bool=false,
) where {C <: RingElem}
@req is_exterior_power(base_module(sp)) && is_standard_module(base_module(base_module(sp))) "Only works for exterior powers of the standard module."

e = get_attribute(base_module(sp), :power)
fl, Vbase, e = is_exterior_power_with_data(base_module(sp))
@req fl && is_standard_module(Vbase) "Only works for exterior powers of the standard module."

extra_data = Dict{DeformationMap{C}, Set{Tuple{PseudographLabelled{Int}, Partition{Int}}}}()
normalize = no_normalize ? identity : normalize_default
Expand Down
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