diff --git a/src/mtables.jl b/src/mtables.jl
index fcf0f23..6b9fac0 100644
--- a/src/mtables.jl
+++ b/src/mtables.jl
@@ -92,6 +92,23 @@ function complete!(mt::MTable)
     return mt
 end
 
+function MA.operate!(
+    ms::UnsafeAddMul{<:MTable},
+    res::AbstractCoefficients,
+    v::AbstractCoefficients,
+    w::AbstractCoefficients,
+)
+    for (kv, a) in nonzero_pairs(v)
+        for (kw, b) in nonzero_pairs(w)
+            c = ms.structure(kv, kw)
+            for (k, v) in nonzero_pairs(c)
+                res[ms.structure[k]] += v * a * b
+            end
+        end
+    end
+    return res
+end
+
 function MA.operate!(
     ms::UnsafeAddMul{<:MTable},
     res::AbstractSparseVector,
diff --git a/test/abstract_coeffs.jl b/test/abstract_coeffs.jl
index c5b6536..efc6826 100644
--- a/test/abstract_coeffs.jl
+++ b/test/abstract_coeffs.jl
@@ -1,51 +1,3 @@
-struct ACoeffs{T} <: SA.AbstractCoefficients{UInt32,T}
-    vals::Vector{T}
-end
-
-# convienience:
-ACoeffs(v::AbstractVector) = ACoeffs{valtype(v)}(v)
-
-# AbstractCoefficients API
-
-## Basic API
-Base.keys(ac::ACoeffs) = (k for (k, v) in pairs(ac.vals) if !iszero(v))
-Base.values(ac::ACoeffs) = (v for v in ac.vals if !iszero(v))
-SA.canonical(ac::ACoeffs) = ac
-function SA.star(b::SA.AbstractBasis, ac::ACoeffs)
-    return ACoeffs([ac.vals[star(b, k)] for k in keys(ac)])
-end
-
-# for preallocation in arithmetic
-function Base.similar(ac::ACoeffs, ::Type{T}) where {T}
-    # it is needed to zero as uninitialized values may not be cleared by
-    # MA.operate!(zero, ac)
-    return ACoeffs(zeros(T, size(ac.vals)))
-end
-
-# the default arithmetic implementation uses this access
-Base.getindex(ac::ACoeffs, idx) = ac.vals[idx]
-Base.setindex!(ac::ACoeffs, val, idx) = ac.vals[idx] = val
-
-# a very basic * using ms.structure;
-# TODO: this is so generic that it should be included in SA
-# but then it hijacks the more refined version
-function MA.operate!(
-    ms::SA.UnsafeAddMul,
-    res::ACoeffs,
-    v::SA.AbstractCoefficients,
-    w::SA.AbstractCoefficients,
-)
-    for (kv, a) in SA.nonzero_pairs(v)
-        for (kw, b) in SA.nonzero_pairs(w)
-            c = ms.structure(kv, kw)
-            for (k, v) in SA.nonzero_pairs(c)
-                res[ms.structure[k]] += v * a * b
-            end
-        end
-    end
-    return res
-end
-
 @testset "Abstract coefficients" begin
     G = PermGroup(perm"(1,2,3)", perm"(1,2)")
     RG = StarAlgebra(G, SA.DiracBasis{UInt8}(G))
diff --git a/test/runtests.jl b/test/runtests.jl
index 8e9866c..3d87d80 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -22,6 +22,9 @@ end
 # implementations of the free monoid over an alphabet
 include("test_example_words.jl")
 
+# example implementation of abstract coefficients
+include("test_example_acoeffs.jl")
+
 @testset "StarAlgebras" begin
     # proof of concept
     using PermutationGroups
diff --git a/test/test_example_acoeffs.jl b/test/test_example_acoeffs.jl
new file mode 100644
index 0000000..3a21966
--- /dev/null
+++ b/test/test_example_acoeffs.jl
@@ -0,0 +1,27 @@
+struct ACoeffs{T} <: SA.AbstractCoefficients{UInt32,T}
+    vals::Vector{T}
+end
+
+# convienience:
+ACoeffs(v::AbstractVector) = ACoeffs{valtype(v)}(v)
+
+# AbstractCoefficients API
+
+## Basic API
+Base.keys(ac::ACoeffs) = (k for (k, v) in pairs(ac.vals) if !iszero(v))
+Base.values(ac::ACoeffs) = (v for v in ac.vals if !iszero(v))
+SA.canonical(ac::ACoeffs) = ac
+function SA.star(b::SA.AbstractBasis, ac::ACoeffs)
+    return ACoeffs([ac.vals[star(b, k)] for k in keys(ac)])
+end
+
+# for preallocation in arithmetic
+function Base.similar(ac::ACoeffs, ::Type{T}) where {T}
+    vals = similar(ac.vals, T)
+    MA.operate!(zero, vals)
+    return ACoeffs(vals)
+end
+
+# the default arithmetic implementation uses this access
+Base.getindex(ac::ACoeffs, idx) = ac.vals[idx]
+Base.setindex!(ac::ACoeffs, val, idx) = ac.vals[idx] = val