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Move user facing functions to separate file
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@lgoettgens
lgoettgens committed Oct 24, 2023
1 parent 1cfdc19 commit df15207
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1 change: 1 addition & 0 deletions experimental/BasisLieHighestWeight/src/BasisLieHighestWeight.jl
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Expand Up @@ -49,6 +49,7 @@ include("RootConversion.jl")
include("WeylPolytope.jl")
include("WordCalculations.jl")
include("MainAlgorithm.jl")
include("UserFunctions.jl")

end

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278 changes: 0 additions & 278 deletions experimental/BasisLieHighestWeight/src/MainAlgorithm.jl
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Expand Up @@ -94,284 +94,6 @@ function basis_lie_highest_weight_compute(
)
end

@doc """
basis_lie_highest_weight(
type::Symbol,
rank::Int,
highest_weight::Vector{Int};
reduced_expression::Union{String, Vector{Union{Int, Vector{Int}}}} = "regular",
monomial_ordering::Union{Symbol, Function} = :degrevlex,
)
Computes a monomial basis for the highest weight module with highest weight
``highest_weight`` (in terms of the fundamental weights), for a simple Lie algebra of type
``type`` and rank ``rank``.
# Parameters
- `type`: type of liealgebra we want to investigate, one of :A, :B, :C, :D, :E, :F, :G
- `rank`: rank of liealgebra
- `highest_weight`: highest-weight
- `reduced_expression`: list of operators, either "regular" or integer array. The functionality of choosing a random longest word
is currently not implemented, because we used https://github.com/jmichel7/Gapjm.jl to work with coxeter
groups need a method to obtain all non left descending elements to extend a word
- `monomial_ordering`: monomial order in which our basis gets defined with regards to our operators
# Examples
```jldoctest
julia> base = BasisLieHighestWeight.basis_lie_highest_weight(:A, 2, [1, 1])
Monomial basis of a highest weight module
of highest weight [1, 1]
of dimension 8
with monomial ordering degrevlex
over lie-Algebra of type A and rank 2
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[1, 0]
[0, 1]
[1, 1]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0]
[0, 1]
julia> base = BasisLieHighestWeight.basis_lie_highest_weight(:A, 3, [2, 2, 3]; monomial_ordering = :lex)
Monomial basis of a highest weight module
of highest weight [2, 2, 3]
of dimension 1260
with monomial ordering lex
over lie-Algebra of type A and rank 3
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[1, 1, 0]
[0, 1, 1]
[1, 1, 1]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
julia> base = BasisLieHighestWeight.basis_lie_highest_weight(:A, 2, [1, 0]; reduced_expression = [1,2,1])
Monomial basis of a highest weight module
of highest weight [1, 0]
of dimension 3
with monomial ordering degrevlex
over lie-Algebra of type A and rank 2
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[1, 0]
[0, 1]
[1, 0]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0]
julia> base = BasisLieHighestWeight.basis_lie_highest_weight(:C, 3, [1, 1, 1]; monomial_ordering = :lex)
Monomial basis of a highest weight module
of highest weight [1, 1, 1]
of dimension 512
with monomial ordering lex
over lie-Algebra of type C and rank 3
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[1, 1, 0]
[0, 1, 1]
[1, 1, 1]
[0, 2, 1]
[1, 2, 1]
[2, 2, 1]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[0, 1, 1]
[1, 1, 1]
```
"""
function basis_lie_highest_weight(
type::Symbol,
rank::Int,
highest_weight::Vector{Int};
reduced_expression::Union{String,Vector{Int},Vector{GAP.GapObj},Any}="regular",
monomial_ordering::Union{Symbol,Function}=:degrevlex,
)
"""
Standard function with all options
"""
lie_algebra, chevalley_basis = lie_algebra_with_basis(type, rank)
operators = get_operators_normal(lie_algebra, chevalley_basis, reduced_expression)
return basis_lie_highest_weight_compute(
lie_algebra, chevalley_basis, highest_weight, operators, monomial_ordering
)
end

@doc """
# Examples
```jldoctest
julia> base = BasisLieHighestWeight.basis_lie_highest_weight_lustzig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
Monomial basis of a highest weight module
of highest weight [1, 1, 1, 1]
of dimension 4096
with monomial ordering oplex
over lie-Algebra of type D and rank 4
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 1, 1, 1]
[0, 1, 1, 0]
[0, 1, 0, 1]
[0, 1, 0, 0]
[1, 2, 1, 1]
[1, 1, 1, 1]
[1, 1, 0, 1]
[1, 1, 1, 0]
[1, 1, 0, 0]
[1, 0, 0, 0]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0, 0]
[0, 1, 0, 0]
[0, 0, 1, 0]
[0, 0, 0, 1]
[0, 0, 1, 1]
```
"""
function basis_lie_highest_weight_lustzig(
type::Symbol,
rank::Int,
highest_weight::Vector{Int},
reduced_expression::Vector{Int};
monomial_ordering::Union{Symbol,Function}=:oplex,
)
"""
Lustzig polytope
BasisLieHighestWeight.basis_lie_highest_weight_lustzig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
"""
# operators = some sequence of the String / Littelmann-Berenstein-Zelevinsky polytope
lie_algebra, chevalley_basis = lie_algebra_with_basis(type, rank)
operators = get_operators_lustzig(lie_algebra, chevalley_basis, reduced_expression)
return basis_lie_highest_weight_compute(
lie_algebra, chevalley_basis, highest_weight, operators, monomial_ordering
)
end

@doc """
# Examples
```jldoctest
julia> BasisLieHighestWeight.basis_lie_highest_weight_string(:B, 3, [1,1,1], [3,2,3,2,1,2,3,2,1])
Monomial basis of a highest weight module
of highest weight [1, 1, 1]
of dimension 512
with monomial ordering oplex
over lie-Algebra of type B and rank 3
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[0, 0, 1]
[0, 1, 0]
[0, 0, 1]
[0, 1, 0]
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[0, 1, 0]
[1, 0, 0]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
```
"""
function basis_lie_highest_weight_string(
type::Symbol, rank::Int, highest_weight::Vector{Int}, reduced_expression::Vector{Int};
)
"""
String / Littelmann-Berenstein-Zelevinsky polytope
BasisLieHighestWeight.basis_lie_highest_weight_string(:B, 3, [1,1,1], [3,2,3,2,1,2,3,2,1])
BasisLieHighestWeight.basis_lie_highest_weight_string(:B, 4, [1,1,1,1], [4,3,4,3,2,3,4,3,2,1,2,3,4,3,2,1])
BasisLieHighestWeight.basis_lie_highest_weight_string(:A, 4, [1,1,1,1], [4,3,2,1,2,3,4,3,2,3])
"""
# reduced_expression = some sequence of the String / Littelmann-Berenstein-Zelevinsky polytope
monomial_ordering = :oplex
lie_algebra, chevalley_basis = lie_algebra_with_basis(type, rank)
operators = get_operators_normal(lie_algebra, chevalley_basis, reduced_expression)
return basis_lie_highest_weight_compute(
lie_algebra, chevalley_basis, highest_weight, operators, monomial_ordering
)
end

@doc """
# Examples
```jldoctest
julia> BasisLieHighestWeight.basis_lie_highest_weight_fflv(:A, 3, [1,1,1])
Monomial basis of a highest weight module
of highest weight [1, 1, 1]
of dimension 64
with monomial ordering oplex
over lie-Algebra of type A and rank 3
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[1, 1, 1]
[0, 1, 1]
[1, 1, 0]
[0, 0, 1]
[0, 1, 0]
[1, 0, 0]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
```
"""
function basis_lie_highest_weight_fflv(type::Symbol, rank::Int, highest_weight::Vector{Int})
"""
Feigin-Fourier-Littelmann-Vinberg polytope
BasisLieHighestWeight.basis_lie_highest_weight_fflv(:A, 3, [1,1,1])
"""
monomial_ordering = :oplex
lie_algebra, chevalley_basis = lie_algebra_with_basis(type, rank)
operators = reverse(get_operators_normal(lie_algebra, chevalley_basis, "regular"))
return basis_lie_highest_weight_compute(
lie_algebra, chevalley_basis, highest_weight, operators, monomial_ordering
)
end

@doc """
# Examples
```jldoctest
julia> BasisLieHighestWeight.basis_lie_highest_weight_nz(:C, 3, [1,1,1], [3,2,3,2,1,2,3,2,1])
Monomial basis of a highest weight module
of highest weight [1, 1, 1]
of dimension 512
with monomial ordering lex
over lie-Algebra of type C and rank 3
where the birational sequence used consists of operators to the following weights (given as coefficients w.r.t. alpha_i):
[0, 0, 1]
[0, 1, 0]
[0, 0, 1]
[0, 1, 0]
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
[0, 1, 0]
[1, 0, 0]
and the basis was generated by Minkowski sums of the bases of the following highest weight modules:
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
```
"""
function basis_lie_highest_weight_nz(
type::Symbol, rank::Int, highest_weight::Vector{Int}, reduced_expression::Vector{Int};
)
"""
Nakashima-Zelevinsky polytope
BasisLieHighestWeight.basis_lie_highest_weight_nz(:C, 3, [1,1,1], [3,2,3,2,1,2,3,2,1])
BasisLieHighestWeight.basis_lie_highest_weight_nz(:A, 4, [1,1,1,1], [4,3,2,1,2,3,4,3,2,3])
"""
monomial_ordering = :lex
lie_algebra, chevalley_basis = lie_algebra_with_basis(type, rank)
operators = get_operators_normal(lie_algebra, chevalley_basis, reduced_expression)
return basis_lie_highest_weight_compute(
lie_algebra, chevalley_basis, highest_weight, operators, monomial_ordering
)
end

function compute_monomials(
lie_algebra::LieAlgebraStructure,
birational_sequence::BirationalSequence,
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