Cache betti numbers of normal toric varieties

Change name of method: ith_betti_number -> betti_number

docs/src/ToricVarieties/NormalToricVarieties.md

@@ -108,7 +108,7 @@ nef_cone(v::NormalToricVariety)
 dim(v::AbstractNormalToricVariety)
 dim_of_torusfactor(v::AbstractNormalToricVariety)
 euler_characteristic(v::AbstractNormalToricVariety)
-ith_betti_number(v::AbstractNormalToricVariety, i::Int)
+betti_number(v::AbstractNormalToricVariety, i::Int)
 ```
 
 ### Rings and ideals

src/ToricVarieties/NormalToricVarieties/methods.jl

@@ -1,21 +1,39 @@
 ############################
-# Dimensions
+# Betti numbers
 ############################
 
 @doc Markdown.doc"""
-    ith_betti_number(v::AbstractNormalToricVariety, i::Int)
+    betti_number(v::AbstractNormalToricVariety, i::Int)
 
 Compute the i-th Betti number of the normal toric variety `v`.
 """
-function ith_betti_number(v::AbstractNormalToricVariety, i::Int)
-    if isodd(i)
+function betti_number(v::AbstractNormalToricVariety, i::Int)
+    # check input
+    if i > 2*dim(v) || i < 0
         return 0
     end
-    k = div(i, 2)
-    f_vector = Vector{Int}(pm_object(v).F_VECTOR)
-    pushfirst!(f_vector, 1)
-    betti_number = sum((-1)^(i-k) * binomial(i,k) * f_vector[dim(v) - i + 1] for i=k:dim(v))
-    return betti_number
 
+    # extract vector of currently-known Betti numbers (or create it if necessary)
+    if !has_attribute(v, :betti_number)
+        betti_numbers = fill(fmpz(-1),2*dim(v)+1)
+    else
+        betti_numbers = get_attribute(v, :betti_number)
+    end
+
+    # compute the Betti number if needed
+    if betti_numbers[i+1] == -1
+        if isodd(i)
+            betti_numbers[i+1] = fmpz(0)
+        else
+            k = div(i, 2)
+            f_vector = Vector{Int}(pm_object(v).F_VECTOR)
+            pushfirst!(f_vector, 1)
+            betti_numbers[i+1] = fmpz(sum((-1)^(i-k) * binomial(i,k) * f_vector[dim(v) - i + 1] for i=k:dim(v)))
+        end
+        set_attribute!(v, :betti_number, betti_numbers)
+    end
+
+    # return result
+    return get_attribute(v, :betti_number)[i+1]
 end
-export ith_betti_number
+export betti_number

test/ToricVarieties/runtests.jl

@@ -63,11 +63,11 @@ P2 = toric_projective_space(2)
     @test hastorusfactor(P2) == false
     @test isorbifold(P2) == true
     @test issimplicial(P2) == true
-    @test ith_betti_number(P2, 0) == 1
-    @test ith_betti_number(P2, 1) == 0
-    @test ith_betti_number(P2, 2) == 1
-    @test ith_betti_number(P2, 3) == 0
-    @test ith_betti_number(P2, 4) == 1
+    @test betti_number(P2, 0) == 1
+    @test betti_number(P2, 1) == 0
+    @test betti_number(P2, 2) == 1
+    @test betti_number(P2, 3) == 0
+    @test betti_number(P2, 4) == 1
     S = cox_ring(P2)
     @test ngens(S) == 3
     @test length(stanley_reisner_ideal(P2).gens) == 1
@@ -93,11 +93,11 @@ H5 = hirzebruch_surface(5)
     @test dim(H5) == 2
     @test dim_of_torusfactor(H5) == 0
     @test euler_characteristic(H5) == 4
-    @test ith_betti_number(H5, 0) == 1
-    @test ith_betti_number(H5, 1) == 0
-    @test ith_betti_number(H5, 2) == 2
-    @test ith_betti_number(H5, 3) == 0
-    @test ith_betti_number(H5, 4) == 1
+    @test betti_number(H5, 0) == 1
+    @test betti_number(H5, 1) == 0
+    @test betti_number(H5, 2) == 2
+    @test betti_number(H5, 3) == 0
+    @test betti_number(H5, 4) == 1
     @test length(affine_open_covering(H5)) == 4
     @test fan(H5).pm_fan.FAN_DIM == 2
     @test rank(torusinvariant_divisor_group(H5)) == 4
@@ -139,11 +139,11 @@ blowup_variety = blowup_on_ith_minimal_torus_orbit(P2, 1)
     @test hastorusfactor(blowup_variety) == false
     @test isorbifold(blowup_variety) == true
     @test issimplicial(blowup_variety) == true
-    @test ith_betti_number(blowup_variety, 0) == 1
-    @test ith_betti_number(blowup_variety, 1) == 0
-    @test ith_betti_number(blowup_variety, 2) == 2
-    @test ith_betti_number(blowup_variety, 3) == 0
-    @test ith_betti_number(blowup_variety, 4) == 1
+    @test betti_number(blowup_variety, 0) == 1
+    @test betti_number(blowup_variety, 1) == 0
+    @test betti_number(blowup_variety, 2) == 2
+    @test betti_number(blowup_variety, 3) == 0
+    @test betti_number(blowup_variety, 4) == 1
     @test euler_characteristic(blowup_variety) == 4
     @test rank(picard_group(blowup_variety)) == 2
 end
@@ -159,15 +159,15 @@ v = H5 * P2
     @test hastorusfactor(v) == false
     @test isorbifold(v) == true
     @test issimplicial(v) == true
-    @test ith_betti_number(v, 0) == 1
-    @test ith_betti_number(v, 1) == 0
-    @test ith_betti_number(v, 2) == 3
-    @test ith_betti_number(v, 3) == 0
-    @test ith_betti_number(v, 4) == 4
-    @test ith_betti_number(v, 5) == 0
-    @test ith_betti_number(v, 6) == 3
-    @test ith_betti_number(v, 7) == 0
-    @test ith_betti_number(v, 8) == 1
+    @test betti_number(v, 0) == 1
+    @test betti_number(v, 1) == 0
+    @test betti_number(v, 2) == 3
+    @test betti_number(v, 3) == 0
+    @test betti_number(v, 4) == 4
+    @test betti_number(v, 5) == 0
+    @test betti_number(v, 6) == 3
+    @test betti_number(v, 7) == 0
+    @test betti_number(v, 8) == 1
 end
 
 @testset "ComparisonWithProjectiveSpace" begin