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#253 factor returns wrong result ←	↑	→ #255 install DoyenWiki from DoyenCD

#254 <code>factor$AN</code> doesn't factor $x^2-2$

Edit detail for #254 <code>factor$AN</code> doesn't factor $x^2-2$ revision 1 of 2

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Editor: test1 Time: 2015/06/19 15:42:37 GMT+0
Note:

changed:
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I think that this is also a bug:
\begin{axiom}
factor(x^2-2::POLY AN)
\end{axiom}

I'd expect $(x-\sqrt{2})(x+\sqrt{2})$.

In fact, over algebraic numbers (and over Expression)
'factor' if specified to factor over a subfield generated
by coefficients of the polynomial.  More precisely, 'factor'
only uses kernels present in the coefficients and will not
introduce new roots.  OTOH 'split' will build appropriate
extension.

I think that this is also a bug:

fricas

factor(x^2-2::POLY AN)

$\label{eq1}{{x}^{2}}- 2$

(1)

Type: Factored(Polynomial(AlgebraicNumber?))

I'd expect $(x-\sqrt{2})(x+\sqrt{2})$ .

In fact, over algebraic numbers (and over Expression) factor if specified to factor over a subfield generated by coefficients of the polynomial. More precisely, factor only uses kernels present in the coefficients and will not introduce new roots. OTOH split will build appropriate extension.