fix generic conv (#497)

* fix generic conv

* fix test

Author: GiggleLiu

src/polynomials/standard-basis.jl

@@ -100,8 +100,9 @@ end
 ## put here, not with type definition, in case reuse is possible
 ## `conv` can be used with matrix entries, unlike `fastconv`
 function conv(p::Vector{T}, q::Vector{S}) where {T,S}
+    (isempty(p) || isempty(q)) && return promote_type(T, S)[]
     as = [p[1]*q[1]]
-    z = 0 * as[1]
+    z = zero(as[1])
     n,m = length(p)-1, length(q)-1
     for i ∈ 1:n+m
         Σ = z

test/StandardBasis.jl

@@ -442,6 +442,30 @@ end
 
     end
 
+    @testset "generic arithmetics" begin
+        P = Polynomial
+        # define a set algebra
+        struct Setalg  # not a number
+            content::Vector{Int}
+        end
+        Base.:(+)(a::Setalg, b::Setalg) = Setalg(a.content ∪ b.content)
+        Base.:(*)(a::Setalg, b::Setalg) = Setalg(vec([x * y for x in a.content, y in b.content]))
+        Base.zero(::Setalg) = Setalg(Int[])
+        Base.one(::Setalg) = Setalg(Int[1])
+        Base.zero(::Type{Setalg}) = Setalg(Int[])
+        Base.one(::Type{Setalg}) = Setalg(Int[1])
+        Base.:(==)(a::Setalg, b::Setalg) = a.content == b.content
+
+        a = Setalg([1])
+        b = Setalg([4,2])
+        pNULL = P(Setalg[])
+        p0 = P([a])
+        p1 = P([a, b, b])
+        @test pNULL * p0 == pNULL
+        @test pNULL * p1 == pNULL
+        @test p0 * p1 == p1
+    end
+
     @testset for P in Ps # ensure promotion of scalar +,*,/
         p = P([1,2,3])
         @test p + 0.5 ==ᵟ P([1.5, 2.0, 3.0])