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 Submitted by : (unknown) at: 2007-11-17T22:15:40-08:00 (11 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : Axiom Aldor Interface Axiom Compiler Axiom Library Axiom Interpreter Axiom Documentation Axiom User Interface building Axiom from source lisp system MathAction Doyen CD Reduce Axiom on Windows Axiom on Linux Severity : critical serious normal minor wishlist Status : open closed rejected not reproducible fix proposed fixed somewhere duplicate need more info Optional subject :   Optional comment :

I just ran across the following astonishing bug:

fricas
s :=-x^3+1/6*(-2*sqrt(6)+2*sqrt(3)+3*sqrt(2))*x^2+1/6*((sqrt(3)+sqrt(2))*sqrt(6)-2*sqrt(2)*sqrt(3))*x-sqrt(2)*sqrt(3)*sqrt(6)/6 (1)
Type: Polynomial(AlgebraicNumber?)
fricas
factor s (2)
Type: Factored(Polynomial(AlgebraicNumber?))

This is the same problem as 191ExquoAndThereforeGcdCannotHandleUPXEXPRINT. Namely, the roots sqrt(2), sqrt(3) and sqrt(6) are dependent, which cause problems because sqrt(6)^2 = 6 = 23 = sqrt(2)^2sqrt(3)^2 but we do not know if sqrt(6) = sqrt(2)sqrt(3) or sqrt(6) = -sqrt(2)sqrt(3). This effectively creates ring with zero divisors, while factoring/GCD routines assume a field.

There are several things to notice, in fact:

• The factorisation is nonsense
• I think that AlgebraicNumber? should be able to simplify to • shouldn't be simplified to ? Usually, sqrt denotes the positive square root.

Martin

In fact, the problem shows already with

fricas
s :=x^2-sqrt(2)*sqrt(3)*sqrt(6) (3)
Type: Polynomial(AlgebraicNumber?)

and it seems to occur in 'InnerAlgFactor?':

  \begin{axiom}
)tr InnerAlgFactor  )ma
factor(s)
\end{axiom}


Status: open => duplicate

 Subject:   Be Bold !! ( 14 subscribers )
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