oldk1331 wrote:
>
> 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'.
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
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