Skip to content

Commit

Permalink
Make it work with new Oscar
Browse files Browse the repository at this point in the history
  • Loading branch information
@lgoettgens
lgoettgens committed Oct 13, 2023
1 parent 0643cc3 commit 81e8477
Showing 1 changed file with 86 additions and 50 deletions.
136 changes: 86 additions & 50 deletions src/ModuleSimpleStructure.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -23,11 +23,13 @@ function isomorphic_module_with_simple_structure(V::LieAlgebraModule; check::Boo
elseif is_symmetric_power(B)
C = base_module(B)
k = get_attribute(B, :power)
ind_map = get_attribute(B, :ind_map)
inv_pure = get_attribute(B, :symmetric_pure_preimage_function)
U = symmetric_power(dual(base_module(B)), k)
mat = zero_matrix(coefficient_ring(V), dim(V), dim(V))
for i in 1:dim(B)
mat[i, i] = div(factorial(k), prod(factorial(count(==(j), ind_map[i])) for j in 1:dim(C)))
pure_factors = inv_pure(basis(B, i))
mat[i, i] =
div(factorial(k), prod(factorial(count(==(xj), pure_factors)) for xj in unique(pure_factors)))
end
V_to_U = hom(V, U, mat; check)
elseif is_tensor_power(B)
Expand Down Expand Up @@ -91,17 +93,31 @@ function isomorphic_module_with_simple_structure(V::LieAlgebraModule; check::Boo
else
Es = [is_direct_sum(D) ? D : direct_sum(D) for D in Ds]
Fs = []
direct_summand_mappings = [_direct_summand_mapping(E) for E in Es]
ind_map = get_attribute(U, :ind_map)
inv_pure = get_attribute(U, :tensor_pure_preimage_function)
mat = zero_matrix(coefficient_ring(U), dim(U), dim(U))
dim_accum = 0
for summ_comb in reverse.(ProductIterator(reverse([1:length(base_modules(E)) for E in Es])))
F = tensor_product([base_modules(E)[i] for (E, i) in zip(Es, summ_comb)]...)
for i in 1:dim(U)
inds = ind_map[i]
if [direct_summand_mappings[j][ind][1] for (j, ind) in enumerate(inds)] == summ_comb
dsmap = [direct_summand_mappings[j][ind] for (j, ind) in enumerate(inds)]
img = F([basis(base_modules(E)[summ_comb[j]], dsmap[j][2]) for (j, E) in enumerate(Es)])
for (i, bi) in enumerate(basis(U))
pure_factors = inv_pure(bi)
dsmap = [
begin
local j, pr_f
projs = canonical_projections(Es[i])
if parent(f) !== Es[i]
f = Es[i]([f])
end
for outer j in 1:length(projs)
pr_f = projs[j](f)
if !iszero(pr_f)
break
end
end
(j, pr_f)
end for (i, f) in enumerate(pure_factors)
]
if [dsmap[l][1] for l in 1:length(Es)] == summ_comb
img = F([dsmap[j][2] for (j, E) in enumerate(Es)])
mat[i, dim_accum+1:dim_accum+dim(F)] = Oscar.LieAlgebras._matrix(img)
end
end
Expand All @@ -126,25 +142,35 @@ function isomorphic_module_with_simple_structure(V::LieAlgebraModule; check::Boo
U = exterior_power(C, k)
V_to_U = hom(V, U, elem_type(U)[U(B_to_C.(_basis_repres(V, i))) for i in 1:dim(V)]; check)
if is_direct_sum(C)
direct_summand_mapping = _direct_summand_mapping(C)
ind_map = get_attribute(U, :ind_map)
Ds = base_modules(C)
m = length(Ds)
Es = []
inv_pure = get_attribute(U, :exterior_pure_preimage_function)
projs = canonical_projections(C)
mat = zero_matrix(coefficient_ring(U), dim(U), dim(U))
dim_accum = 0
for summ_comb in multicombinations(m, k)
lambda = [count(==(i), summ_comb) for i in 1:m]
factors = [lambda[i] != 0 ? exterior_power(Ds[i], lambda[i]) : nothing for i in 1:m]
factors_cleaned = filter(!isnothing, factors)
E = tensor_product(factors_cleaned...)
for i in 1:dim(U)
inds = ind_map[i]
if [direct_summand_mapping[ind][1] for ind in inds] == summ_comb
dsmap = [direct_summand_mapping[ind] for ind in inds]
for (i, bi) in enumerate(basis(U))
pure_factors = inv_pure(bi)
dsmap = [
begin
local j, pr_f
for outer j in 1:length(projs)
pr_f = projs[j](f)
if !iszero(pr_f)
break
end
end
(j, pr_f)
end for f in pure_factors
]
if [dsmap[l][1] for l in 1:k] == summ_comb
img = E([
factors[j]([basis(Ds[j], dsmap[l][2]) for l in 1:k if dsmap[l][1] == j]) for
j in 1:m if lambda[j] != 0
factors[j]([dsmap[l][2] for l in 1:k if dsmap[l][1] == j]) for j in 1:m if lambda[j] != 0
])
mat[i, dim_accum+1:dim_accum+dim(E)] = Oscar.LieAlgebras._matrix(img)
end
Expand Down Expand Up @@ -176,25 +202,35 @@ function isomorphic_module_with_simple_structure(V::LieAlgebraModule; check::Boo
U = symmetric_power(C, k)
V_to_U = hom(V, U, elem_type(U)[U(B_to_C.(_basis_repres(V, i))) for i in 1:dim(V)]; check)
if is_direct_sum(C)
direct_summand_mapping = _direct_summand_mapping(C)
ind_map = get_attribute(U, :ind_map)
Ds = base_modules(C)
m = length(Ds)
Es = []
inv_pure = get_attribute(U, :symmetric_pure_preimage_function)
projs = canonical_projections(C)
mat = zero_matrix(coefficient_ring(U), dim(U), dim(U))
dim_accum = 0
for summ_comb in multicombinations(m, k)
lambda = [count(==(i), summ_comb) for i in 1:m]
factors = [lambda[i] != 0 ? symmetric_power(Ds[i], lambda[i]) : nothing for i in 1:m]
factors_cleaned = filter(!isnothing, factors)
E = tensor_product(factors_cleaned...)
for i in 1:dim(U)
inds = ind_map[i]
if [direct_summand_mapping[ind][1] for ind in inds] == summ_comb
dsmap = [direct_summand_mapping[ind] for ind in inds]
for (i, bi) in enumerate(basis(U))
pure_factors = inv_pure(bi)
dsmap = [
begin
local j, pr_f
for outer j in 1:length(projs)
pr_f = projs[j](f)
if !iszero(pr_f)
break
end
end
(j, pr_f)
end for f in pure_factors
]
if [dsmap[l][1] for l in 1:k] == summ_comb
img = E([
factors[j]([basis(Ds[j], dsmap[l][2]) for l in 1:k if dsmap[l][1] == j]) for
j in 1:m if lambda[j] != 0
factors[j]([dsmap[l][2] for l in 1:k if dsmap[l][1] == j]) for j in 1:m if lambda[j] != 0
])
mat[i, dim_accum+1:dim_accum+dim(E)] = Oscar.LieAlgebras._matrix(img)
end
Expand Down Expand Up @@ -226,25 +262,35 @@ function isomorphic_module_with_simple_structure(V::LieAlgebraModule; check::Boo
U = tensor_power(C, k)
V_to_U = hom(V, U, elem_type(U)[U(B_to_C.(_basis_repres(V, i))) for i in 1:dim(V)]; check)
if is_direct_sum(C)
direct_summand_mapping = _direct_summand_mapping(C)
ind_map = get_attribute(U, :ind_map)
Ds = base_modules(C)
m = length(Ds)
Es = []
inv_pure = get_attribute(U, :tensor_pure_preimage_function)
projs = canonical_projections(C)
mat = zero_matrix(coefficient_ring(U), dim(U), dim(U))
dim_accum = 0
for summ_comb in AbstractAlgebra.ProductIterator(1:m, k)
lambda = [count(==(i), summ_comb) for i in 1:m]
factors = [lambda[i] != 0 ? tensor_power(Ds[i], lambda[i]) : nothing for i in 1:m]
factors_cleaned = filter(!isnothing, factors)
E = tensor_product(factors_cleaned...)
for i in 1:dim(U)
inds = ind_map[i]
if [direct_summand_mapping[ind][1] for ind in inds] == summ_comb
dsmap = [direct_summand_mapping[ind] for ind in inds]
for (i, bi) in enumerate(basis(U))
pure_factors = inv_pure(bi)
dsmap = [
begin
local j, pr_f
for outer j in 1:length(projs)
pr_f = projs[j](f)
if !iszero(pr_f)
break
end
end
(j, pr_f)
end for f in pure_factors
]
if [dsmap[l][1] for l in 1:k] == summ_comb
img = E([
factors[j]([basis(Ds[j], dsmap[l][2]) for l in 1:k if dsmap[l][1] == j]) for
j in 1:m if lambda[j] != 0
factors[j]([dsmap[l][2] for l in 1:k if dsmap[l][1] == j]) for j in 1:m if lambda[j] != 0
])
mat[i, dim_accum+1:dim_accum+dim(E)] = Oscar.LieAlgebras._matrix(img)
end
Expand All @@ -270,22 +316,12 @@ end

function _basis_repres(V::LieAlgebraModule, i::Int)
@req is_exterior_power(V) || is_symmetric_power(V) || is_tensor_power(V) "Not a power module."
B = base_module(V)
ind_map = get_attribute(V, :ind_map)::Vector{Vector{Int}}
js = ind_map[i]
return map(j -> basis(B, j), js)
end

function _direct_summand_mapping(V::LieAlgebraModule)
@req is_direct_sum(V) "Not a direct sum"
map = [(0, 0) for _ in 1:dim(V)]
Bs = base_modules(V)
i = 1
for (j, Bj) in enumerate(Bs)
for k in 1:dim(Bj)
map[i+k-1] = (j, k)
end
i += dim(Bj)
inv_pure = if is_exterior_power(V)
get_attribute(V, :exterior_pure_preimage_function)
elseif is_symmetric_power(V)
get_attribute(V, :symmetric_pure_preimage_function)
elseif is_tensor_power(V)
get_attribute(V, :tensor_pure_preimage_function)
end
return map
return inv_pure(basis(V, i))
end

0 comments on commit 81e8477

Please sign in to comment.