Add sqrt and cbrt functions for QQAbElem (#3096)

src/Rings/AbelianClosure.jl

@@ -846,6 +846,25 @@ function Oscar.order(a::QQAbElem)
   return o
 end
 
+# Convenient sqrt and cbrt functions as simple wrappers around the roots function,
+# which is already implemented for QQAbElem directly
+
+function Oscar.sqrt(a::QQAbElem)
+  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)
+  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))^3 == K(8)
+    @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))^2 == K(2)
+    @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