redefine scalar_div to avoid undesirable type conversion (#496)

* redefine scalar_div to avoid undesirable type conversion

* guard for 0 poly

* both are method errors

* use _convert

Project.toml

@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "3.2.9"
+version = "3.2.10"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

src/common.jl

@@ -1048,8 +1048,11 @@ end
 scalar_mult(p1::AbstractPolynomial, p2::AbstractPolynomial) = error("scalar_mult(::$(typeof(p1)), ::$(typeof(p2))) is not defined.") # avoid ambiguity, issue #435
 
 # scalar div
-Base.:/(p::P, c::S) where {P <: AbstractPolynomial,S} = scalar_div(p, c)
-scalar_div(p::AbstractPolynomial, c) = scalar_mult(p, inv(c))
+Base.:/(p::AbstractPolynomial, c) = scalar_div(p, c)
+function scalar_div(p::P, c::S) where {S, T, X, P<:AbstractPolynomial{T, X}}
+    iszero(p) && return zero(⟒(P){Base.promote_op(/,T,S), X})
+    _convert(p, coeffs(p) ./ Ref(c))
+end
 
 ## Polynomial p*q
 ## Polynomial multiplication formula depend on the particular basis used. The subtype must implement

test/StandardBasis.jl

@@ -284,7 +284,8 @@ end
             @test_throws MethodError q * p == P(conv([a,b], [a,b, c])) # Ok, no * for T
 
             # poly powers
-            @test_throws MethodError p^2 == p * p # Ok, no * for T
+            @test_throws MethodError p^2  # Ok, no * for T
+            @test_throws MethodError p * p
 
             # evaluation
             @test p(s) == a + b * s + c * s * s
@@ -525,6 +526,11 @@ end
             @test p - p == 0*p
         end
     end
+
+    # issue #495, (scalar div fix)
+    𝐐 = Rational{Int}
+    v = Polynomial{𝐐}([0//1])
+    @test eltype(integrate(v)) == 𝐐
 end
 
 @testset "Divrem" begin