Review: return a single root, add tests

src/Rings/AbelianClosure.jl

@@ -850,11 +850,19 @@ end
 # which is already implemented for QQAbElem directly
 
 function Oscar.sqrt(a::QQAbElem)
-  return Oscar.roots(a, 2)
+  sqrt = Oscar.roots(a, 2)
+  if is_empty(sqrt)
+    error("Element $a does not have a square root")
+  end
+  return sqrt[1]
 end
 
 function Oscar.cbrt(a::QQAbElem)
-  return Oscar.roots(a, 3)
+  cbrt = Oscar.roots(a,3)
+  if is_empty(cbrt)
+    error("Element $a does not have a cube root")
+  end
+  return cbrt[1]
 end
 
 

test/Rings/AbelianClosure.jl

@@ -264,6 +264,10 @@ end
     @test length(roots(x^15-2^15)) == 15
 
     @test order(z(5)) == 5
+
+    @test cbrt(K(8)) == 2
+    @test_throws ErrorException("Element 4 does not have a cube root") cbrt(K(4))
+
   end
 
   @testset "Automorphism" begin
@@ -292,6 +296,9 @@ end
       @test ((a - x)//y)^2 == n
     end
 
+    @test sqrt(K(2)) == -z(8)^3 + z(8)
+    @test_throws ErrorException("Element zeta(4) + 1 does not have a square root") sqrt(z(4)+1)
+
     @test Oscar.AbelianClosure.quadratic_irrationality_info(z(5)) === nothing
 
     @testset for d in -50:50