[PATCH] fix 'iroot' in POLYROOT

[Qian Yun]

(1) -> rootSimp((64*x^12)^(1/12))

6+-+
(1) x\|8
Type: Expression(Integer)
(2) -> rootSimp %

+-+
(2) x\|2
Type: Expression(Integer)

In 'iroot', in the loop, nn is multiple of p, then "nn := nn rem p"
will always be 0 and cause early exit. This is clearly a logical error.

This causes expression to not be simplified at fullest.

- Qian

(Disclaimer: this issue is found by LLM, but the analysis and patch
is thoroughly reviewed by me.)

diff --git a/src/algebra/manip.spad b/src/algebra/manip.spad
index 54dc6b47..69949ac1 100644
--- a/src/algebra/manip.spad
+++ b/src/algebra/manip.spad
@@ -95,15 +95,15 @@
while p <= nn repeat
not ((nn rem p) = 0) =>
p := nextPrime(p)$IntegerPrimesPackage(Z)
if (ru := perfectNthRoot(x,
qcoerce(p)@N)$IntegerRoots(Z)) case Z then
x := ru::Z
e := e*p
- nn := nn rem p
+ nn := nn quo p
else
p := nextPrime(p)$IntegerPrimesPackage(Z)
[(n quo e)::N, x]

if R has imaginary : () -> R then
czroot : (Z, N) -> REC

[Waldek Hebisch]

On Tue, Apr 21, 2026 at 06:45:38AM +0800, Qian Yun wrote:
> (1) -> rootSimp((64*x^12)^(1/12))
>
> 6+-+
> (1) x\|8
> Type: Expression(Integer)
> (2) -> rootSimp %
>
> +-+
> (2) x\|2
> Type: Expression(Integer)
>
> In 'iroot', in the loop, nn is multiple of p, then "nn := nn rem p"
> will always be 0 and cause early exit. This is clearly a logical error.
>
> This causes expression to not be simplified at fullest.
>
> - Qian

Thanks, please commit.

> (Disclaimer: this issue is found by LLM, but the analysis and patch
> is thoroughly reviewed by me.)
>
> diff --git a/src/algebra/manip.spad b/src/algebra/manip.spad
> index 54dc6b47..69949ac1 100644
> --- a/src/algebra/manip.spad
> +++ b/src/algebra/manip.spad
> @@ -95,15 +95,15 @@
> while p <= nn repeat
> not ((nn rem p) = 0) =>
> p := nextPrime(p)$IntegerPrimesPackage(Z)
> if (ru := perfectNthRoot(x,
> qcoerce(p)@N)$IntegerRoots(Z)) case Z then
> x := ru::Z
> e := e*p
> - nn := nn rem p
> + nn := nn quo p
> else
> p := nextPrime(p)$IntegerPrimesPackage(Z)
> [(n quo e)::N, x]
>
> if R has imaginary : () -> R then
> czroot : (Z, N) -> REC
>

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--
Waldek Hebisch