OK, after some debugging, I have made a patch:
--- a/src/algebra/manip.spad
+++ b/src/algebra/manip.spad
@@ -349,7 +349,7 @@ AlgebraicManipulations(R, F) : Exports ==
Implementation where
rootKerSimp(op, x, n) == inroot(op, x, n)
-- l is a list of nth-roots, returns a list of records of the form
--- [a^(1/n1), a^(1/n2), ...], [n1, n2, ...]]
+-- [[a^(1/n1), a^(1/n2), ...], [n1, n2, ...]]
-- such that the whole list covers l exactly
breakup l ==
empty? l => empty()
@@ -386,21 +386,22 @@
-- replaces (a^(1/n))^m in p by a power of a simpler radical of a if
-- n and m have a common factor
radeval(p, k) ==
a := first(arg := argument k)
n := (retract(second arg)@Integer)::NonNegativeInteger
ans : F := 0
q := univariate(p, k)
while (d := degree q) > 0 repeat
- term :=
+ term : F :=
-- 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
+ (d = n) => a
+ ((g := gcd(d, n)) = 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
First part is just a comment fix.
The second part fixs function 'radeval', bug happens when
simplify calls rootProduct calls radeval.
As we can see from the comments above, when 'm=n',
'(a^(1/n))^m' should simplify to 'a' instead of '(a^(1/1))^1'.
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