## Axiom Computer Algebra System - Bugs: bug #8086, rootsOf(2*z^4 + z^3 - z - 2)...

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## bug #8086: rootsOf(2*z^4 + z^3 - z - 2) wrong

 Submitted by: Martin Rubey Submitted on: Wed 10 Mar 2004 09:06:43 AM UTC Category: algebra Severity: 3 - Normal Item Group: code bug Status: None Privacy: Public Assigned to: None Originator Name: kratt6 Open/Closed: Open Release: 14.6.2003 Reproducibility: None Fixed Release: Error message: Example of code trigerring the bug: rootsOf(2*z^4 + z^3 - z - 2) wrong rootsOf(2*z^4 + z^3 - z - 2, z) correct rootsOf(z^4 + z^3 + z - 1) wrong rootsOf(z^4 + z^3 + z - 1,z) correct Internal cause:

Sat 22 May 2004 01:48:36 PM UTC, comment #1:

Maybe I should have added why rootsOf(2*z^4 + z^3 - z - 2) is wrong:
2z^4+z^3-z-2=(z^2-1)(2*z^2+z+2),
thus no two roots are equal, contrary to axioms result.

Martin

Martin Rubey <kratt6>
Wed 10 Mar 2004 09:06:43 AM UTC, original submission:

a fresh Axiom says

(1) -> rootsOf(2*z^4 + z^3 - z - 2,z)

- 2%z2 - 2%z1 - 2%z0 - 1
(1) [%z0,%z1,%z2,------------------------]
2
Type: List Expression Integer

(2) -> rootsOf(2*z^4 + z^3 - z - 2)
PolynomialFunctions2
AlgebraicManipulations
IndexedDirectProductOrderedAbelianMonoidSup
IndexedDirectProductOrderedAbelianMonoid
SetCategory&
Evalable&
RetractableTo&
BasicType&
InnerEvalable&
CommuteUnivariatePolynomialCategory
PseudoRemainderSequence
UnivariatePolynomialSquareFree
HeuGcd
InnerModularGcd
EuclideanModularRing
ModularDistinctDegreeFactorizer
ModularRing
ListToMap

(2) [%z4,%z5,%z5,- %z5]
Type: List AlgebraicNumber

which is wrong.

Same thing for zerosOf, same thing for z^4+z^3+z-1

Martin Rubey <kratt6>

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• -unavailable- added by axiom (Updated the item)
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