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+ and - for SU3 elements produce M3x3 types

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Alberto Ramos 2025-09-01 10:10:54 +02:00
commit 40426f561a
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74
src/Groups/M3x3.jl
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@ -105,10 +105,84 @@ Base.:+(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11+b.u11, a
a.u21+b.u21, a.u22+b.u22, a.u23+b.u23, a.u21+b.u21, a.u22+b.u22, a.u23+b.u23,
a.u31+b.u31, a.u32+b.u32, a.u33+b.u33) a.u31+b.u31, a.u32+b.u32, a.u33+b.u33)
function Base.:+(a::SU3{T},b::M3x3{T}) where T <: AbstractFloat
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
return M3x3{T}(a.u11+b.u11, a.u12+b.u12, a.u13+b.u13,
a.u21+b.u21, a.u22+b.u22, a.u23+b.u23,
au31+b.u31, au32+b.u32, au33+b.u33)
end
function Base.:+(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
return M3x3{T}(a.u11+b.u11, a.u12+b.u12, a.u13+b.u13,
a.u21+b.u21, a.u22+b.u22, a.u23+b.u23,
a.u31+bu31, a.u32+bu32, a.u33+bu33)
end
function Base.:+(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
return M3x3{T}(a.u11+b.u11, a.u12+b.u12, a.u13+b.u13,
a.u21+b.u21, a.u22+b.u22, a.u23+b.u23,
au31+bu31, au32+bu32, au33+bu33)
end
Base.:-(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-b-u13, Base.:-(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-b-u13,
a.u21-b.u21, a.u22-b.u22, a.u23-b-u23, a.u21-b.u21, a.u22-b.u22, a.u23-b-u23,
a.u31-b.u31, a.u32-b.u32, a.u33-b-u33) a.u31-b.u31, a.u32-b.u32, a.u33-b-u33)
function Base.:-(a::SU3{T},b::M3x3{T}) where T <: AbstractFloat
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
return M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-b.u13,
a.u21-b.u21, a.u22-b.u22, a.u23-b.u23,
au31-b.u31, au32-b.u32, au33-b.u33)
end
function Base.:-(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
return M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-b.u13,
a.u21-b.u21, a.u22-b.u22, a.u23-b.u23,
a.u31-bu31, a.u32-bu32, a.u33-bu33)
end
function Base.:-(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
return M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-b.u13,
a.u21-b.u21, a.u22-b.u22, a.u23-b.u23,
au31-bu31, au32-bu32, au33-bu33)
end
Base.:-(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(-b.u11, -b.u12, -b.u13, Base.:-(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(-b.u11, -b.u12, -b.u13,
-b.u21, -b.u22, -b.u23, -b.u21, -b.u22, -b.u23,
-b.u31, -b.u32, -b.u33) -b.u31, -b.u32, -b.u33)