diff --git a/docs/src/refs.bib b/docs/src/refs.bib
index 0f1d5e40..67caf6b3 100644
--- a/docs/src/refs.bib
+++ b/docs/src/refs.bib
@@ -13,6 +13,19 @@ @Article{GHLMP96
   doi           = {10.1007/BF01190329}
 }
 
+@Article{Kem21,
+  author        = {Kempner, Aubrey J.},
+  title         = {Polynomials and their residue systems},
+  mrnumber      = {1501173},
+  journal       = {Trans. Amer. Math. Soc.},
+  fjournal      = {Transactions of the American Mathematical Society},
+  volume        = {22},
+  number        = {2},
+  pages         = {240--266},
+  year          = {1921},
+  doi           = {10.2307/1989020}
+}
+
 @Book{OSCAR,
   bibkey        = {OSCAR},
   title         = {The Computer Algebra System OSCAR: Algorithms and Examples},
@@ -24,19 +37,3 @@ @Book{OSCAR
   month         = {8},
   url           = {https://link.springer.com/book/9783031621260}
 }
-
-@Article{MR1501173,
-    author = {Kempner, Aubrey J.},
-     title = {Polynomials and their residue systems},
-   journal = {Trans. Amer. Math. Soc.},
-  fjournal = {Transactions of the American Mathematical Society},
-    volume = {22},
-      year = {1921},
-    number = {2},
-     pages = {240--266},
-      issn = {0002-9947,1088-6850},
-   mrclass = {11C08 (13P99)},
-  mrnumber = {1501173},
-       doi = {10.2307/1989020},
-       url = {https://doi.org/10.2307/1989020},
-}
diff --git a/src/GenericCyclotomics.jl b/src/GenericCyclotomics.jl
index 5fad9b4d..cc223405 100644
--- a/src/GenericCyclotomics.jl
+++ b/src/GenericCyclotomics.jl
@@ -61,7 +61,7 @@ end
     kempner(m::Int64)
 
 Return the minimal non-negative integer `k` such that `k!` is a multiple of `m`. This is called the `m`-th Kempner number.
-Details about the Kempner numbers and how to compute them can be found in [MR1501173](@cite).
+Details about the Kempner numbers and how to compute them can be found in [Kem21](@cite).
 
 # Examples
 ```jldoctest
@@ -417,8 +417,13 @@ function (R::GenericCycloRing)(f::Dict{UPolyFrac, UPoly}; simplify::Bool=true)
 	if !simplify
 		return GenericCyclo(f, R)
 	end
+	
+	if length(f) == 1 && is_one(numerator(first(first(f))))
+		return GenericCyclo(f, R)
+	end
 
 	# congruence preparation
+	# 68 allocations
 	if R.congruence !== nothing
 		q=gen(base_ring(R), 1)
 		substitute=R.congruence[2]*q+R.congruence[1]
@@ -426,17 +431,23 @@ function (R::GenericCycloRing)(f::Dict{UPolyFrac, UPoly}; simplify::Bool=true)
 	end
 
 	# reduce numerators modulo denominators
+	# 757 allocations -> 444
 	L=NTuple{4, UPoly}[]
 	for (g,c) in f
-		if !iszero(c)
-			if R.congruence === nothing
-				gp=g
-			else
-				gp=evaluate(numerator(g), [1], [substitute])//evaluate(denominator(g), [1], [substitute])
-			end
-			a,r=divrem(numerator(gp),denominator(gp))
-			push!(L,(c,denominator(gp),r,a))
-		end
+		iszero(c) && continue
+
+        n = numerator(g, false)
+        d = denominator(g, false)
+        if R.congruence !== nothing
+            if !is_constant(n) n=evaluate(n, [1], [substitute]) end
+            if !is_constant(d) d=evaluate(d, [1], [substitute]) end
+        end
+        if is_one(n)
+          a,r=zero(n),n
+        else
+          a,r=divrem(n,d)
+        end
+        push!(L,(c,d,r,a))
 	end
 
 	# return early if `L` is empty
@@ -463,22 +474,22 @@ function (R::GenericCycloRing)(f::Dict{UPolyFrac, UPoly}; simplify::Bool=true)
 	fp=Dict{UPolyFrac, UPoly}()
 	for (c,g_2,r,a) in L
 		# normalize the polynomial part of the exponent
-		ap=normal_form(change_base_ring(ZZ,d*a), d)
+		ap=normal_form(change_base_ring(ZZ,d*a), d)  # 32 allocations
 
 		# normalize the constant part
 		t=constant_coefficient(ap)
-		app=change_base_ring(base_ring(base_ring(R)), ap-t, parent=base_ring(R))
-		S,x=ZZ[:x]
-		p=mod(x^t,cyclotomic_polynomial(d,S))
+		app=change_base_ring(base_ring(base_ring(R)), ap-t, parent=base_ring(R))  # 25 allocations
+		SSSS,x=ZZ[:x]
+		p=mod(x^t,cyclotomic_polynomial(d,SSSS))
 
 		# distribute the normalized constant part
 		for (i,cp) in enumerate(coefficients(p))
 			tp=i-1
-			g=1//d*app+r//g_2+tp//d
+			g=1//d*app+r//g_2+tp//d   # 153 allocations
 			if R.congruence === nothing
 				gp=g
 			else
-				gp=evaluate(numerator(g), [1], [substitute_inv])//evaluate(denominator(g), [1], [substitute_inv])
+				gp=evaluate(numerator(g), [1], [substitute_inv])//evaluate(denominator(g), [1], [substitute_inv])  # 692 allocations
 			end
 			if haskey(fp,gp)
 				fp[gp]+=cp*c