Add checks if triangle relations are satisfied (#15)

* `triangle_equation` function

* necessary exports and usings

* triangle equation test

* bump version 0.1.7

* update `triangle_equation` to not be dependent on `diagm`

* move test

* add triangle test for `IsingBimod`

* format

* format

* move `triangle_equation` definition and export location

Author: borisdevos

Project.toml

@@ -1,7 +1,7 @@
 name = "TensorKitSectors"
 uuid = "13a9c161-d5da-41f0-bcbd-e1a08ae0647f"
 authors = ["Lukas Devos", "Jutho Haegeman"]
-version = "0.1.6"
+version = "0.1.7"
 
 [deps]
 HalfIntegers = "f0d1745a-41c9-11e9-1dd9-e5d34d218721"

src/TensorKitSectors.jl

@@ -15,7 +15,7 @@ export BraidingStyle, NoBraiding, SymmetricBraiding, Bosonic, Fermionic, Anyonic
 export SectorSet, SectorValues, findindex
 export rightone, leftone
 
-export pentagon_equation, hexagon_equation
+export triangle_equation, pentagon_equation, hexagon_equation
 
 export Trivial, Z2Irrep, Z3Irrep, Z4Irrep, ZNIrrep, U1Irrep, SU2Irrep, CU1Irrep
 export ProductSector, TimeReversed

src/sectors.jl

@@ -370,6 +370,27 @@ Return the twist of a sector `a`
 """
 twist(a::Sector) = sum(dim(b) / dim(a) * tr(Rsymbol(a, a, b)) for b in a ⊗ a)
 
+# Triangle equation
+#-------------------------------------------------------------------------------
+# requirement that certain F-moves involving unit objects are trivial
+function triangle_equation(a::I, b::I; kwargs...) where {I<:Sector}
+    for c in ⊗(a, b)
+        F1 = Fsymbol(leftone(a), a, b, c, a, c)
+        F2 = Fsymbol(a, rightone(a), b, c, a, b)
+        F3 = Fsymbol(a, b, rightone(b), c, c, b)
+
+        isapproxone(F) = isapprox(F, one(F); kwargs...)
+        if FusionStyle(I) isa MultiplicityFreeFusion
+            all(isapproxone, (F1, F2, F3)) || return false
+        else
+            N = Nsymbol(a, b, c)
+            tomatrix = Base.Fix2(reshape, (N, N))
+            all(isapproxone ∘ tomatrix, (F1, F2, F3)) || return false
+        end
+    end
+    return true
+end
+
 # Pentagon and Hexagon equations
 #-------------------------------------------------------------------------------
 # Consistency equations for F- and R-symbols

test/multifusion.jl

@@ -114,6 +114,12 @@ Istr = TensorKitSectors.type_repr(I)
         end
     end
 
+    @testset "$Istr: Triangle equation" begin
+        for a in smallset(I), b in smallset(I)
+            @test triangle_equation(a, b; atol=1e-12, rtol=1e-12)
+        end
+    end
+
     @testset "$Istr: Pentagon equation" begin
         objects = collect(values(I))
         for a in objects, b in objects, c in objects, d in objects

test/sectors.jl

@@ -95,6 +95,11 @@ end
         end
     end
 end
+@testset "Sector $Istr: Triangle equation" begin
+    for a in smallset(I), b in smallset(I)
+        @test triangle_equation(a, b; atol=1e-12, rtol=1e-12)
+    end
+end
 @testset "Sector $Istr: Pentagon equation" begin
     for a in smallset(I), b in smallset(I), c in smallset(I), d in smallset(I)
         @test pentagon_equation(a, b, c, d; atol=1e-12, rtol=1e-12)