Merge branch 'Dev'

Project.toml

@@ -1,7 +1,7 @@
 name = "TensorCategories"
 uuid = "258c694e-7338-4d4d-b524-4851272a75cf"
 authors = ["Fabian Mäurer"]
-version = "0.2.2"
+version = "0.2.3"
 
 [deps]
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"

src/CategoryFramework/AbstractMethods.jl

@@ -152,37 +152,17 @@ function decompose_by_endomorphism_ring(X::Object, E = End(X))
     _images = [image(f)[1] for f ∈ idems]
 
     # Check for matrix algebras
-    images = []
-    for x ∈ _images
-        H = End(x)
-        R = endomorphism_ring(x, H)
-        d = dim(R)
-        if is_squarefree(d) || is_commutative(R) 
-            push!(images, x)
-            continue
-        end
-
-        G = gens(R)
-
-        if maximum(degree.(minpoly.(G))) == d
-            push!(images, x)
-            continue
-        end
-
-        y,k = _simple_end_as_matrix_algebra(x, H) 
-        push!(images,[y for _ ∈ 1:k]...)
-    end
-
-
+    images = [_decompose_by_simple_endomorphism_ring(i) for i ∈ _images]
+
 
     tuples = Tuple{typeof(X), Int}[]
 
-    for Y ∈ images
+    for (Y,k) ∈ images
         i = findfirst(Z -> is_isomorphic(Z[1],Y)[1], tuples)
         if i === nothing
-            push!(tuples, (Y,1))
+            push!(tuples, (Y,k))
         else
-            tuples[i] = (Y, tuples[i][2] + 1)
+            tuples[i] = (Y, tuples[i][2] + k)
         end
     end
 
@@ -319,29 +299,33 @@ function minpoly(f::Morphism)
     end
 end 
 
-function _simple_end_as_matrix_algebra(X::Object, E = End(X))
-
-    B = gens(E)
-
-    if length(B) == 1 return  (X,1) end
-
-    for f ∈ B
-       eig_spaces = eigenvalues(f)
-        if length(eig_spaces) == 0 
-            continue
-
-        elseif length(eig_spaces) == 1 && dim(collect(values(eig_spaces))[1]) == dim(X)
-            continue
-        end
-
-
-        return (collect(values(eig_spaces))[1], length(eig_spaces))
+function _decompose_by_simple_endomorphism_ring(X::Object, E = End(X))
+    K = base_ring(X)
+    R = endomorphism_ring(X, E)
+    CR,_ = center(R)
+    dR = dim(R)
+    if !is_square(div(dR,dim(CR))) || is_commutative(R) 
+        return (X,1)
     end
+
+    G = basis(E)
 
-    if is_simple(X) 
-        return (X,1)
+    n,_ = size(matrix(G[1]))
+    mats = matrix.(G)
+
+    for i ∈ 1:n
+        m = matrix(K,n,length(G), hcat([M[i,:] for M ∈ mats]...))
+
+        d,N = nullspace(m)
+
+        if d > 0 
+            Y,y = kernel(sum(collect(N[:,1]) .* G))
+            Z,k = _decompose_by_simple_endomorphism_ring(Y, End(Y))
+            return (Z, sqrt(dR // int_dim(End(Z))))
+        end
     end
-    error("Could not decompose")  
+
+    return (X,1)
 end
 
 

src/Examples/Haagerup/HaagerupH3.jl

@@ -20,6 +20,13 @@ function HaagerupH3(K::Field = QQ; p1 = 1, p2 = 1)
 
     r13 = sqrt(K(13))
 
+    try
+        sqrt(6*(1 + r13))
+        sqrt((-3 + r13)//2)
+    catch
+        r13 = -r13
+    end
+
     H = SixJCategory(K,["𝟙", "α", "α∗", "ρ", "αρ", "α∗ρ"])
 
     mult = Array{Int,3}(undef,6,6,6)

src/Examples/TambaraYamagami/TambaraYamagami.jl

@@ -180,10 +180,12 @@ end
 
     Ising()
 
-Construct the Ising category over ``ℚ̅``.
+Construct the Ising category over ``ℚ(√2)``.
 """
 function Ising()
-    Ising(QQBar, sqrt(QQBar(2)), 1)
+    _,x = QQ[:x]
+    K,r2 = number_field(x^2-2, "√2")
+    Ising(K, r2, 1)
 end
 
 """ 

src/TensorCategories.jl

@@ -28,7 +28,8 @@ import Oscar: +, @alias, @attributes, AbstractSet, AcbField, StructureConstantAl
     set_attribute!, size, solve, sparse_matrix, splitting_field,
     stabilizer, sub, subst, symbols, symmetric_group, tensor_power, tensor_product, tr,
     trivial_subgroup, unit, zero, zero_matrix, ∘, ⊕, ⊗, AbsSimpleNumField,
-    number_of_rows, number_of_columns, is_squarefree, is_commutative, gens
+    number_of_rows, number_of_columns, is_squarefree, is_commutative,
+    gens, center
 
 import Graphs: SimpleDiGraph, weakly_connected_components,
             SimpleGraph,connected_components

src/TensorCategoryFramework/Center/Center.jl

@@ -948,7 +948,7 @@ end
 function simples_by_induction!(C::CenterCategory, log = true)
     S = CenterObject[]
     d = dim(C.category)^2
-
+    C.induction_gens = object_type(category(C))[]
     simpls = simples(C.category)
 
     FI_simples = []
@@ -1166,7 +1166,16 @@ end
 function extension_of_scalars(C::CenterCategory, L::Field)
     CL = _extension_of_scalars(C,L, category(C)⊗L)
 
-    CL.simples = vcat([indecomposable_subobjects(extension_of_scalars(s, L, CL)) for s ∈ simples(C)]...)
+    CL.simples = vcat([[x for (x,_) ∈ decompose(extension_of_scalars(s, L, CL))] for s ∈ simples(C)]...)
+
+    if isdefined(C, :inductions)
+        CL.inductions = Dict(extension_of_scalars(x, L, category(CL)) =>
+                        extension_of_scalars(Ix, L, CL) for (x,Ix) ∈ C.inductions)
+    end
+
+    if isdefined(C, :induction_gens)
+        CL.induction_gens = [extension_of_scalars(is, L, category(CL)) for is ∈ C.induction_gens]
+    end
 
     return CL
 end