77 lines
2.2 KiB
Julia
77 lines
2.2 KiB
Julia
struct ElementarySymplectic{N,T} <: Groups.GSymbol
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symbol::Symbol
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i::Int
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j::Int
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val::T
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function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where {N}
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@assert s ∈ (:A, :B)
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@assert iseven(N)
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n = N ÷ 2
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if s === :A
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@assert 1 ≤ i ≤ n && 1 ≤ j ≤ n && i ≠ j
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elseif s === :B
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@assert xor(1 ≤ i ≤ n, 1 ≤ j ≤ n) && xor(n < i ≤ N, n < j ≤ N)
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end
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return new{N,typeof(val)}(s, i, j, val)
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end
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end
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function Base.show(io::IO, s::ElementarySymplectic)
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i, j = Groups.subscriptify(s.i), Groups.subscriptify(s.j)
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print(io, s.symbol, i, j)
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!isone(s.val) && print(io, "^$(s.val)")
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end
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_ind(s::ElementarySymplectic{N}) where {N} = (s.i, s.j)
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_local_ind(N_half::Integer, i::Integer) = ifelse(i <= N_half, i, i - N_half)
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function _dual_ind(s::ElementarySymplectic{N}) where {N}
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if s.symbol === :A && return _ind(s)
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else#if s.symbol === :B
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return _dual_ind(N ÷ 2, s.i, s.j)
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end
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end
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function _dual_ind(N_half, i, j)
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@assert i <= N_half < j || j <= N_half < i
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if i <= N_half # && j > N_half
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i, j = j - N_half, i + N_half
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else
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i, j = j + N_half, i - N_half
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end
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return i, j
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end
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function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N,M}
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N == M || return false
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s.symbol == t.symbol || return false
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s.val == t.val || return false
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return _ind(t) == _ind(s) || _ind(t) == _dual_ind(s)
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end
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Base.hash(s::ElementarySymplectic, h::UInt) =
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hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
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LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N} =
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ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
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Base.inv(s::ElementarySymplectic{N}) where {N} =
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ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
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function matrix(s::ElementarySymplectic{N,T}) where {N,T}
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@assert iseven(N)
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n = div(N, 2)
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m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
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i, j = _ind(s)
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m[i, j] = s.val
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if s.symbol === :A
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m[n+j, n+i] = -s.val
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else#if s.symbol === :B
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if i > n
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m[j+n, i-n] = s.val
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else
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m[j-n, i+n] = s.val
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end
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end
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return StaticArrays.SMatrix{N,N}(m)
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end
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