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add -X flag for computations over SL(3,Z[X])

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kalmar 2017-08-01 15:07:05 +02:00
parent 85841c9399
commit aa2d0083d3
1 changed files with 24 additions and 15 deletions
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39
SL_orbit.jl
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@ -38,10 +38,10 @@ end
# #
############################################################################### ###############################################################################
function E(i::Int, j::Int, M::MatSpace) function E(i::Int, j::Int, M::MatSpace, val=one(M.base_ring))
@assert i≠j @assert i≠j
m = one(M) m = one(M)
m[i,j] = m[1,1] m[i,j] = val
return m return m
end end
@ -53,24 +53,26 @@ function SLsize(n,p)
return div(result, p-1) return div(result, p-1)
end end
function SL_generatingset(n::Int) function SL_generatingset(n::Int, X::Bool=false)
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j] indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
G = MatrixSpace(ZZ, n, n) G = MatrixSpace(ZZ, n, n)
S = [E(i,j,G) for (i,j) in indexing] if X
S = vcat(S, [transpose(x) for x in S]) S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
S = vcat(S, [inv(x) for x in S]) else
return G, unique(S) S = [E(i,j,G,v) for (i,j) in indexing for v in [1]]
end
S = vcat(S, [inv(x) for x in S])
return G, unique(S)
end end
function SL_generatingset(n::Int, p::Int) function SL_generatingset(n::Int, p::Int, X::Bool=false)
p == 0 && return SL_generatingset(n) p == 0 && return SL_generatingset(n, X)
(p > 1 && n > 1) || throw("Both n and p should be positive integers!") (p > 1 && n > 1) || throw("Both n and p should be positive integers!")
info("Size(SL($n,$p)) = $(SLsize(n,p))") info("Size(SL($n,$p)) = $(SLsize(n,p))")
F = ResidueRing(ZZ, p) F = ResidueRing(ZZ, p)
G = MatrixSpace(F, n, n) G = MatrixSpace(F, n, n)
indexing = [(i,j) for i in 1:n for j in 1:n if i≠j] indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
S = [E(i, j, G) for (i,j) in indexing] S = [E(i, j, G, v) for (i,j) in indexing]
S = vcat(S, [transpose(x) for x in S])
S = vcat(S, [inv(x) for x in S]) S = vcat(S, [inv(x) for x in S])
return G, unique(S) return G, unique(S)
end end
@ -113,6 +115,9 @@ function parse_commandline()
help = "Find the decomposition over B_r(e,S)" help = "Find the decomposition over B_r(e,S)"
arg_type = Int arg_type = Int
default = 2 default = 2
"-X"
help = "Matrices are over ZZ⟨X⟩"
action = :store_true
end end
return parse_args(settings) return parse_args(settings)
@ -131,7 +136,11 @@ function main()
p = parsed_args["p"] p = parsed_args["p"]
if p == 0 if p == 0
dirname = "oSL$(N)Z" if parsed_args["X"]
dirname = "oSL$(N)Z⟨X⟩"
else
dirname = "oSL$(N)Z"
end
else else
dirname = "oSL$(N)_$p" dirname = "oSL$(N)_$p"
end end
@ -151,7 +160,7 @@ function main()
info(logger, "Precision: $tol") info(logger, "Precision: $tol")
info(logger, "Upper bound: $upper_bound") info(logger, "Upper bound: $upper_bound")
G, S = SL_generatingset(N, p) G, S = SL_generatingset(N, p, parsed_args["X"])
info(logger, G) info(logger, G)
info(logger, "Symmetric generating set of size $(length(S))") info(logger, "Symmetric generating set of size $(length(S))")
info(logger, S) info(logger, S)