Make zero on array of arrays etc apply recursively (#51458)

I wonder if this breaks things, in practice. It shouldn't. Since old
code behavior errored for the cases I am aware of.
As discussed in #38064, this definition is needed to be consistent with
our other linear algebra operations,
and with us considering a vector of vectors etc as a vector space.

Closes #38064

NEWS.md

@@ -111,6 +111,7 @@ New library features
   automatically.
 * `@timed` now additionally returns the elapsed compilation and recompilation time ([#52889])
 * `filter` can now act on a `NamedTuple` ([#50795]).
+* `zero(::AbstractArray)` now applies recursively, so `zero([[1,2],[3,4,5]])` now produces the additive identity `[[0,0],[0,0,0]]` rather than erroring ([#38064]).
 
 Standard library changes
 ------------------------

base/abstractarray.jl

@@ -1217,7 +1217,8 @@ function copymutable(a::AbstractArray)
 end
 copymutable(itr) = collect(itr)
 
-zero(x::AbstractArray{T}) where {T} = fill!(similar(x, typeof(zero(T))), zero(T))
+zero(x::AbstractArray{T}) where {T<:Number} = fill!(similar(x, typeof(zero(T))), zero(T))
+zero(x::AbstractArray) = map(zero, x)
 
 ## iteration support for arrays by iterating over `eachindex` in the array ##
 # Allows fast iteration by default for both IndexLinear and IndexCartesian arrays

test/abstractarray.jl

@@ -1950,3 +1950,14 @@ end
     @test repeat(f, 2, 3, 4) === FillArrays.Fill(3, (8, 6, 4))
     @test repeat(f, inner=(1,2), outer=(3,1)) === FillArrays.Fill(3, (12, 4))
 end
+
+@testset "zero" begin
+    @test zero([1 2; 3 4]) isa Matrix{Int}
+    @test zero([1 2; 3 4]) == [0 0; 0 0]
+
+    @test zero([1.0]) isa Vector{Float64}
+    @test zero([1.0]) == [0.0]
+
+    @test zero([[2,2], [3,3,3]]) isa Vector{Vector{Int}}
+    @test zero([[2,2], [3,3,3]]) == [[0,0], [0, 0, 0]]
+end