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75 lines
2.9 KiB
Julia
75 lines
2.9 KiB
Julia
###
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### "THE BEER-WARE LICENSE":
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### Alberto Ramos wrote this file. As long as you retain this
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### notice you can do whatever you want with this stuff. If we meet some
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### day, and you think this stuff is worth it, you can buy me a beer in
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### return. <alberto.ramos@cern.ch>
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###
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### file: GroupSU3.jl
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### created: Sun Jul 11 17:23:02 2021
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###
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inverse(a::SU3{T}) where T <: AbstractFloat = SU3{T}(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22), conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
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dag(a::SU3{T}) where T <: AbstractFloat = inverse(a)
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tr(a::SU3{T}) where T <: AbstractFloat = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
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function Base.:*(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
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a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
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a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
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a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
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a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
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a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33)
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end
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function Base.:/(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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bu31 = (b.u12*b.u23 - b.u13*b.u22)
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bu32 = (b.u13*b.u21 - b.u11*b.u23)
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bu33 = (b.u11*b.u22 - b.u12*b.u21)
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return SU3{T}(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
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a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
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a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
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a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
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a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
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a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33))
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end
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function Base.:\(a::SU3{T},b::SU3{T}) where T <: AbstractFloat
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au31 = (a.u12*a.u23 - a.u13*a.u22)
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au32 = (a.u13*a.u21 - a.u11*a.u23)
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bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
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bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
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bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
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return SU3{T}(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + (au31)*bu31,
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conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + (au31)*bu32,
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conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + (au31)*bu33,
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conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + (au32)*bu31,
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conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + (au32)*bu32,
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conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + (au32)*bu33)
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end
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function isgroup(a::SU3{T}) where T <: AbstractFloat
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tol = 1.0E-10
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g = a/a
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if ( (abs(g.u11 - 1.0) < tol) &&
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(abs(g.u12) < tol) &&
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(abs(g.u13) < tol) &&
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(abs(g.u21) < tol) &&
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(abs(g.u22 - 1.0) < tol) &&
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(abs(g.u23) < tol) )
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return true
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else
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return false
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end
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end
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