include sqadjop.jl from 1812.03456.jl file

src/1812.03456.jl

@@ -0,0 +1,26 @@
+indexing(n) = [(i,j) for i in 1:n for j in 1:n if i≠j]
+
+function generating_set(G::AutGroup{N}, n=N) where N
+
+    rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing(n)]
+    lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing(n)]
+    gen_set = G.([rmuls; lmuls])
+
+    return [gen_set; inv.(gen_set)]
+end
+
+function EltaryMat(M::MatAlgebra, i::Integer, j::Integer, val=1)
+    @assert i ≠ j
+    @assert 1 ≤ i ≤ nrows(M)
+    @assert 1 ≤ j ≤ ncols(M)
+    m = one(M)
+    m[i,j] = val
+    return m
+end
+
+function generating_set(M::MatAlgebra, n=nrows(M))
+    elts = [EltaryMat(M, i,j) for (i,j) in indexing(n)]
+    return elem_type(M)[elts; inv.(elts)]
+end
+
+include("sqadjop.jl")

src/PropertyT.jl

@@ -22,9 +22,8 @@ include("RGprojections.jl")
 include("orbitdata.jl")
 include("sos_sdps.jl")
 include("checksolution.jl")
-include("sqadjop.jl")
 
 include("1712.07167.jl")
-
+include("1812.03456.jl")
 
 end # module Property(T)

src/sqadjop.jl

@@ -1,29 +1,3 @@
-indexing(n) = [(i,j) for i in 1:n for j in 1:n if i≠j]
-
-function generating_set(G::AutGroup{N}, n=N) where N
-
-    rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing(n)]
-    lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing(n)]
-    gen_set = G.([rmuls; lmuls])
-
-    return [gen_set; inv.(gen_set)]
-end
-
-function E(M::MatAlgebra, i::Integer, j::Integer, val=1)
-    @assert i ≠ j
-    @assert 1 ≤ i ≤ nrows(M)
-    @assert 1 ≤ j ≤ ncols(M)
-    m = one(M)
-    m[i,j] = val
-    return m
-end
-
-function generating_set(M::MatAlgebra, n=M.n)
-
-    elts = [E(M, i,j) for (i,j) in indexing(n)]
-    return elem_type(M)[elts; inv.(elts)]
-end
-
 isopposite(σ::perm, τ::perm, i=1, j=2) =
     σ[i] ≠ τ[i] && σ[i] ≠ τ[j] &&
     σ[j] ≠ τ[i] && σ[j] ≠ τ[j]
@@ -91,9 +65,6 @@ function Op(RG::GroupRing, N::Integer)
     return op÷factorial(N-2)^2
 end
 
-AbstractAlgebra.nrows(M::MatAlgebra) = M.n
-AbstractAlgebra.ncols(M::MatAlgebra) = M.n
-
 for Elt in [:Sq, :Adj, :Op]
     @eval begin
         $Elt(RG::GroupRing{AutGroup{N}}) where N = $Elt(RG, N)

test/1812.03456.jl

@@ -9,8 +9,8 @@
         for N in [3,4]
             M = MatrixAlgebra(zz, N)
 
-            @test PropertyT.E(M, 1, 2) isa MatAlgElem
-            e12 = PropertyT.E(M, 1, 2)
+            @test PropertyT.EltaryMat(M, 1, 2) isa MatAlgElem
+            e12 = PropertyT.EltaryMat(M, 1, 2)
             @test e12[1,2] == 1
             @test inv(e12)[1,2] == -1
 
@@ -65,9 +65,9 @@
         @test op == PropertyT.Op(RG)
 
         e = one(M)
-        g = PropertyT.E(M, 1,2)
-        h = PropertyT.E(M, 1,3)
-        k = PropertyT.E(M, 3,4)
+        g = PropertyT.EltaryMat(M, 1,2)
+        h = PropertyT.EltaryMat(M, 1,3)
+        k = PropertyT.EltaryMat(M, 3,4)
 
         edges = N*(N-1)÷2
         @test sq[e] == 20*edges
@@ -93,7 +93,7 @@ end
 
 @testset "1812.03456 examples" begin
 
-        function SOS_residual(x::GroupRingElem, Q::Matrix)
+    function SOS_residual(x::GroupRingElem, Q::Matrix)
         RG = parent(x)
         @time sos = PropertyT.compute_SOS(RG, Q);
         return x - sos