Further improve betti_number

- always return an fmpz, even for `i` negative or larger than 2 * dim(v)
- don't store the odd Betti numbers which are always 0
- use this to reduce the storage for Betti numbers by half
- use `get_attribute!` instead of `has_attribute` + `get_attribute`
- remove redundant call to `set_attribute!`
- don't call `dim(v)` repeatedly and add a type assertion
- initialize `f_vector` via a conversion, to ensure its type is inferred correctly

src/ToricVarieties/NormalToricVarieties/methods.jl

@@ -5,35 +5,27 @@
 @doc Markdown.doc"""
     betti_number(v::AbstractNormalToricVariety, i::Int)
 
-Compute the i-th Betti number of the normal toric variety `v`.
+Compute the `i`-th Betti number of the normal toric variety `v`.
 """
 function betti_number(v::AbstractNormalToricVariety, i::Int)
     # check input
-    if i > 2*dim(v) || i < 0
-        return 0
+    d = dim(v)::Int
+    if i > 2*d || i < 0 || isodd(i)
+        return fmpz(0)
     end
-    
+
     # 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)::Vector{fmpz}
-    end
-
+    betti_numbers = get_attribute!(() -> fill(fmpz(-1),d+1), v, :betti_number)::Vector{fmpz}
+
     # 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)
+    k = i >> 1 # i is even, so divide by two and use that as index
+    if betti_numbers[k+1] == -1
+        f_vector::Vector{Int} = pm_object(v).F_VECTOR
+        pushfirst!(f_vector, 1)
+        betti_numbers[k+1] = fmpz(sum((-1)^(i-k) * binomial(i,k) * f_vector[d - i + 1] for i=k:d))
     end
 
     # return result
-    return betti_numbers[i+1]
+    return betti_numbers[k+1]
 end
 export betti_number