check for exact coefficients; close #600 (#601)

* check for exact coefficients

* typo

* test locally first

* typo

Author: jverzani

Project.toml

@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "4.0.18"
+version = "4.0.19"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

_typos.toml

@@ -1,3 +1,4 @@
 [default.extend-words]
 Pn = "Pn"
-zerod = "zerod"
+zerod = "zerod"
+Comput = "Comput"

src/polynomials/standard-basis/standard-basis.jl

@@ -196,7 +196,14 @@ function Base.divrem(num::P, den::Q) where {B<:StandardBasis,
     m = degree(den)
 
     m == -1 && throw(DivideError())
-    if m == 0 && den[0] ≈ 0 throw(DivideError()) end
+    if m == 0
+        if hasmethod(eps, (S,)) # some way to check if using ≈ or == is appropriate
+            den[0] ≈ 0 && throw(DivideError())
+        else
+            den[0] == 0 && throw(DivideError())
+        end
+    end
+
 
     R = eltype(one(T)/one(S))