diff --git a/docs/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses.md b/docs/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses.md
index 26a3e87818e5..5c05bbefb755 100644
--- a/docs/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses.md
+++ b/docs/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses.md
@@ -54,14 +54,14 @@ polynomial(ring::MPolyQuoRing, c::CohomologyClass)
 ## Methods
 
 ```@docs
-integrate(c::CohomologyClass)
+integrate(c::CohomologyClass; check::Bool = true)
 ```
 
 
 ## Special attributes of toric varieties
 
 ```@docs
-cohomology_ring(v::NormalToricVarietyType)
+cohomology_ring(v::NormalToricVarietyType; check::Bool = true)
 volume_form(v::NormalToricVariety)
 intersection_form(v::NormalToricVariety)
 ```
diff --git a/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl b/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl
index dfa115c6e579..23eca4350f2f 100644
--- a/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl
@@ -1,9 +1,14 @@
 @doc raw"""
-    integrate(c::CohomologyClass)
+    integrate(c::CohomologyClass; check::Bool = true)
 
 Integrate the cohomolgy class `c` over the normal
 toric variety `toric_variety(c)`.
 
+The theory underlying this method requires that the toric variety
+in question is simplicial and complete. The check of completeness
+may take a long time to complete. If desired, this can be switched
+off by setting the optional argument `check` to the value `false`.
+
 # Examples
 ```jldoctest
 julia> dP3 = del_pezzo_surface(NormalToricVariety, 3)
@@ -88,10 +93,12 @@ julia> integrate(cohomology_class(anticanonical_divisor_class(X))^3)
 62
 ```
 """
-function integrate(c::CohomologyClass)
+function integrate(c::CohomologyClass; check::Bool = true)
     # can only integrate if the variety is simplicial, complete
-    @req is_simplicial(toric_variety(c)) && is_complete(toric_variety(c)) "Integration only supported over complete and simplicial toric varieties"
-    
+    if check
+      @req is_simplicial(toric_variety(c)) && is_complete(toric_variety(c)) "Integration only supported over complete and simplicial toric varieties"
+    end
+
     # if the intersection form is known, we can use it
     if has_attribute(toric_variety(c), :_intersection_form_via_exponents)
         intersection_dict = _intersection_form_via_exponents(toric_variety(c))
diff --git a/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/special_attributes.jl b/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/special_attributes.jl
index 0892d9a927a1..e5f2e1861f39 100644
--- a/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/special_attributes.jl
+++ b/src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/special_attributes.jl
@@ -3,7 +3,7 @@
 ########################
 
 @doc raw"""
-    cohomology_ring(v::NormalToricVarietyType)
+    cohomology_ring(v::NormalToricVarietyType; check::Bool = true)
 
 Return the cohomology ring of the simplicial and complete toric variety `v`.
 
@@ -15,12 +15,18 @@ julia> ngens(cohomology_ring(p2))
 3
 ```
 """
-@attr MPolyQuoRing function cohomology_ring(v::NormalToricVarietyType)
+function cohomology_ring(v::NormalToricVarietyType; check::Bool = false)
+  if has_attribute(v, :cohomology_ring)
+    return get_attribute(v, :cohomology_ring)
+  end
+  if check
     @req is_simplicial(v) && is_complete(v) "The cohomology ring is only supported for simplicial and complete toric varieties"
-    R, _ = graded_polynomial_ring(coefficient_ring(v), coordinate_names(v), cached = false)
-    linear_relations = ideal_of_linear_relations(R, v)
-    stanley_reisner = stanley_reisner_ideal(R, v)
-    return quo(R, linear_relations + stanley_reisner)[1]
+  end
+  R, _ = graded_polynomial_ring(coefficient_ring(v), coordinate_names(v), cached = false)
+  linear_relations = ideal_of_linear_relations(R, v)
+  stanley_reisner = stanley_reisner_ideal(R, v)
+  set_attribute!(v, :cohomology_ring, quo(R, linear_relations + stanley_reisner)[1])
+  return get_attribute(v, :cohomology_ring)
 end