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#251 About %% ←	↑	→ #254 <code>factor$AN</code> doesn't factor $x^2-2$

#253 factor returns wrong result

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Editor: page Time: 2009/10/18 23:47:58 GMT-7
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I just ran across the following astonishing bug:

\begin{axiom}
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
factor s
\end{axiom}

There are several things to notice, in fact:

- The factorisation is nonsense

- I think that AlgebraicNumber should be able to simplify $\sqrt{2}\sqrt{3}\sqrt{6}$ to $\sqrt{36}$

- shouldn't $sqrt{36}$ be simplified to $6$? Usually, 'sqrt' denotes the positive square root.

Martin

From kratt6 Wed Jan 25 04:50:05 -0600 2006
From: kratt6
Date: Wed, 25 Jan 2006 04:50:05 -0600
Subject: 
Message-ID: <20060125045005-0600@wiki.axiom-developer.org>

In fact, the problem shows already with

\begin{axiom}
s :=x^2-sqrt(2)*sqrt(3)*sqrt(6)
\end{axiom}

and it seems to occur in  'InnerAlgFactor'::

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

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

$\label{eq1}\begin{array}{@{}l} \displaystyle -{{x}^{3}}+{{{-{2 \ {\sqrt{6}}}+{2 \ {\sqrt{3}}}+{3 \ {\sqrt{2}}}}\over 6}\ {{x}^{2}}}+ \ \ \displaystyle {{{{{\left({\sqrt{3}}+{\sqrt{2}}\right)}\ {\sqrt{6}}}-{2 \ {\sqrt{2}}\ {\sqrt{3}}}}\over 6}\ x}-{{{\sqrt{2}}\ {\sqrt{3}}\ {\sqrt{6}}}\over 6}$

(1)

Type: Polynomial(AlgebraicNumber?)

fricas

factor s

$\label{eq2}- 1$

(2)

Type: Factored(Polynomial(AlgebraicNumber?))

There are several things to notice, in fact:

The factorisation is nonsense
I think that AlgebraicNumber? should be able to simplify $\sqrt{2}\sqrt{3}\sqrt{6}$ to $\sqrt{36}$
shouldn't be simplified to ? Usually, sqrt denotes the positive square root.

Martin

... --kratt6, Wed, 25 Jan 2006 04:50:05 -0600 reply

In fact, the problem shows already with

fricas

s :=x^2-sqrt(2)*sqrt(3)*sqrt(6)

$\label{eq3}{{x}^{2}}-{{\sqrt{2}}\ {\sqrt{3}}\ {\sqrt{6}}}$

(3)

Type: Polynomial(AlgebraicNumber?)

and it seems to occur in 'InnerAlgFactor?':

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