define nsymbol

src/abstractsector.jl

@@ -4,7 +4,12 @@
 using BlockArrays: blocklengths
 using LabelledNumbers: LabelledInteger, label, label_type, labelled, unlabel, unlabel_type
 using GradedUnitRanges:
-  GradedUnitRanges, blocklabels, fuse_blocklengths, gradedrange, tensor_product
+  GradedUnitRanges,
+  blocklabels,
+  fuse_blocklengths,
+  fusion_product,
+  gradedrange,
+  tensor_product
 
 abstract type AbstractSector end
 
@@ -47,6 +52,13 @@ quantum_dimension(::AbelianStyle, ::AbstractSector) = 1
 quantum_dimension(::AbelianStyle, g::AbstractUnitRange) = length(g)
 quantum_dimension(::NotAbelianStyle, g::AbstractUnitRange) = sum(block_dimensions(g))
 
+function nsymbol(s1::AbstractSector, s2::AbstractSector, s3::AbstractSector)
+  full_space = fusion_product(s1, s2)
+  i = findfirst(==(s3), blocklabels(full_space))
+  isnothing(i) && return labelled(0, s3)
+  return blocklengths(full_space)[i]
+end
+
 # ===============================  Fusion rule interface  ==================================
 ⊗(c1::AbstractSector, c2::AbstractSector) = fusion_rule(c1, c2)
 

test/test_fusion_rules.jl

@@ -1,5 +1,6 @@
 using GradedUnitRanges:
   dual, fusion_product, space_isequal, gradedrange, flip, tensor_product
+using LabelledNumbers: label
 using SymmetrySectors:
   ⊗,
   Fib,
@@ -11,6 +12,7 @@ using SymmetrySectors:
   U1,
   Z,
   block_dimensions,
+  nsymbol,
   quantum_dimension,
   trivial
 using Test: @inferred, @test, @testset, @test_throws
@@ -29,6 +31,8 @@ using Test: @inferred, @test, @testset, @test_throws
     @test (@inferred q ⊗ q) == q
     @test (@inferred q ⊗ z0) == z0
     @test (@inferred z1 ⊗ q) == z1
+    @test nsymbol(q, q, q) == 1
+    @test label(nsymbol(q, q, q)) == q
 
     # using GradedUnitRanges interface
     @test space_isequal(fusion_product(z0, z0), gradedrange([z0 => 1]))
@@ -49,6 +53,11 @@ using Test: @inferred, @test, @testset, @test_throws
     @test q1 ⊗ q2 == U1(3)
     @test q2 ⊗ q1 == U1(3)
     @test (@inferred q1 ⊗ q2) == q3  # no better way, see Julia PR 23426
+
+    @test nsymbol(q1, q2, q3) == 1
+    @test label(nsymbol(q1, q2, q3)) == q3
+    @test nsymbol(q1, q1, q3) == 0
+    @test label(nsymbol(q1, q1, q3)) == q3
   end
 
   @testset "O2 fusion rules" begin
@@ -263,6 +272,9 @@ end
     @test space_isequal(
       fusion_product(dual(g5), dual(g6)), gradedrange([s1 => 2, f3 => 1, c3 => 1, ad8 => 1])
     )
+
+    @test nsymbol(ad8, ad8, ad8) == 2
+    @test label(nsymbol(ad8, ad8, ad8)) == ad8
   end
 
   @testset "Mixed GradedUnitRange - Sector fusion rules" begin