add -X flag for computations over SL(3,Z[X])
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SL_orbit.jl
39
SL_orbit.jl
@ -38,10 +38,10 @@ end
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#
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###############################################################################
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function E(i::Int, j::Int, M::MatSpace)
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function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
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@assert i≠j
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m = one(M)
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m[i,j] = m[1,1]
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m[i,j] = val
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return m
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end
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@ -53,24 +53,26 @@ function SLsize(n,p)
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return div(result, p-1)
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end
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function SL_generatingset(n::Int)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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G = MatrixSpace(ZZ, n, n)
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S = [E(i,j,G) for (i,j) in indexing]
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S = vcat(S, [transpose(x) for x in S])
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S = vcat(S, [inv(x) for x in S])
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return G, unique(S)
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function SL_generatingset(n::Int, X::Bool=false)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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G = MatrixSpace(ZZ, n, n)
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if X
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S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
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else
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S = [E(i,j,G,v) for (i,j) in indexing for v in [1]]
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end
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S = vcat(S, [inv(x) for x in S])
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return G, unique(S)
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end
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function SL_generatingset(n::Int, p::Int)
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p == 0 && return SL_generatingset(n)
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function SL_generatingset(n::Int, p::Int, X::Bool=false)
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p == 0 && return SL_generatingset(n, X)
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(p > 1 && n > 1) || throw("Both n and p should be positive integers!")
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info("Size(SL($n,$p)) = $(SLsize(n,p))")
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F = ResidueRing(ZZ, p)
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G = MatrixSpace(F, n, n)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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S = [E(i, j, G) for (i,j) in indexing]
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S = vcat(S, [transpose(x) for x in S])
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S = [E(i, j, G, v) for (i,j) in indexing]
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S = vcat(S, [inv(x) for x in S])
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return G, unique(S)
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end
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@ -113,6 +115,9 @@ function parse_commandline()
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help = "Find the decomposition over B_r(e,S)"
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arg_type = Int
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default = 2
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"-X"
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help = "Matrices are over ZZ⟨X⟩"
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action = :store_true
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end
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return parse_args(settings)
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@ -131,7 +136,11 @@ function main()
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p = parsed_args["p"]
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if p == 0
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dirname = "oSL$(N)Z"
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if parsed_args["X"]
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dirname = "oSL$(N)Z⟨X⟩"
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else
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dirname = "oSL$(N)Z"
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end
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else
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dirname = "oSL$(N)_$p"
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end
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@ -151,7 +160,7 @@ function main()
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info(logger, "Precision: $tol")
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info(logger, "Upper bound: $upper_bound")
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G, S = SL_generatingset(N, p)
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G, S = SL_generatingset(N, p, parsed_args["X"])
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info(logger, G)
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info(logger, "Symmetric generating set of size $(length(S))")
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info(logger, S)
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