From aa2d0083d3131d7dabc52c33296f7aa05e2e94eb Mon Sep 17 00:00:00 2001
From: kalmar <kalmar@amu.edu.pl>
Date: Tue, 1 Aug 2017 15:07:05 +0200
Subject: [PATCH] add -X flag for computations over SL(3,Z[X])

---
 SL_orbit.jl | 39 ++++++++++++++++++++++++---------------
 1 file changed, 24 insertions(+), 15 deletions(-)

diff --git a/SL_orbit.jl b/SL_orbit.jl
index 4d73a3c..b5f234f 100644
--- a/SL_orbit.jl
+++ b/SL_orbit.jl
@@ -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
     m = one(M)
-    m[i,j] = m[1,1]
+    m[i,j] = val
     return m
 end
 
@@ -53,24 +53,26 @@ function SLsize(n,p)
     return div(result, p-1)
 end
 
-function SL_generatingset(n::Int)
-    indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
-    G = MatrixSpace(ZZ, n, n)
-    S = [E(i,j,G) for (i,j) in indexing]
-    S = vcat(S, [transpose(x) for x in S])
-    S = vcat(S, [inv(x) for x in S])
-    return G, unique(S)
+function SL_generatingset(n::Int, X::Bool=false)
+   indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
+   G = MatrixSpace(ZZ, n, n)
+   if X
+      S = [E(i,j,G,v) for (i,j) in indexing for v in [1, 100]]
+   else
+      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
 
-function SL_generatingset(n::Int, p::Int)
-    p == 0 && return SL_generatingset(n)
+function SL_generatingset(n::Int, p::Int, X::Bool=false)
+    p == 0 && return SL_generatingset(n, X)
     (p > 1 && n > 1) || throw("Both n and p should be positive integers!")
     info("Size(SL($n,$p)) = $(SLsize(n,p))")
     F = ResidueRing(ZZ, p)
     G = MatrixSpace(F, n, n)
     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 = vcat(S, [transpose(x) for x in S])
+    S = [E(i, j, G, v) for (i,j) in indexing]
     S = vcat(S, [inv(x) for x in S])
     return G, unique(S)
 end
@@ -113,6 +115,9 @@ function parse_commandline()
             help = "Find the decomposition over B_r(e,S)"
             arg_type = Int
             default = 2
+        "-X"
+            help = "Matrices are over ZZ⟨X⟩"
+            action = :store_true
     end
 
     return parse_args(settings)
@@ -131,7 +136,11 @@ function main()
    p = parsed_args["p"]
 
    if p == 0
-      dirname = "oSL$(N)Z"
+      if parsed_args["X"]
+         dirname = "oSL$(N)Z⟨X⟩"
+      else
+         dirname = "oSL$(N)Z"
+      end
    else
       dirname = "oSL$(N)_$p"
    end
@@ -151,7 +160,7 @@ function main()
    info(logger, "Precision:   $tol")
    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, "Symmetric generating set of size $(length(S))")
    info(logger, S)