> Does it handle the following? 
>
> r1 := sqrt(x) 
> r2 := x^(2/3) 
> r3 := x^(3/4) 
> r12 := x^(1/12) 
> simplify(r1*r2*r3*r12) 
> -- 
>                               Waldek Hebisch 
>

No, it does not.  I make a change in the patch:

--- a/src/algebra/manip.spad
+++ b/src/algebra/manip.spad
@@ -391,11 +391,12 @@ AlgebraicManipulations(R, F) : Exports == 
Implementation where
         ans : F := 0
         q := univariate(p, k)
         while (d := degree q) > 0 repeat
-          term :=
---            one?(g := gcd(d, n)) => monomial(1, k, d)
-            ((g := gcd(d, n)) = 1) => monomial(1, k, d)
-            monomial(1, kernel(operator k, [a, (n quo g)::F], height k), d 
quo g)
-          ans := ans + leadingCoefficient(q)::F * term::F
+          term :F :=
+            g := gcd(d, n)
+            (g = n) => a^(d quo g)
+            (g = 1) => monomial(1, k, d)::F
+            monomial(1, kernel(operator k, [a, (n quo g)::F], height k), d 
quo g)::F
+          ans := ans + leadingCoefficient(q)::F * term
           q := reductum q
         leadingCoefficient(q)::F + ans

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