Dear All,
This bug seems to be in the previous version 4.XX too.
I can definitely reproduce the same error on my DfW version 5.06 English version.
I hope version 6 would correct this.
Tze Beng
-----Original Message-----
From: DERIVE computer algebra system [mailto:[log in to unmask]] On Behalf Of Ignacio Larrosa Caņestro
Sent: 13 November 2003 08:28
To: [log in to unmask]
Subject: Error when factoring
I get the polinomial correctly
x^8 - 40x^6 + 352x^4 - 960x^2 + 576 (#1)
by squaring from three times, isolating th roots.
x = sqrt(2) + sqrt(3) + sqrt(5)
But when I factorize #1 in radicals with Derive, it put:
(x + <(20·<6 + 4·<114))·(x - <(20·<6 + 4·<114))·(x + <(20·<6 - 4·<114))·(x -
<(20·<6 - 4·<114))·(x^2 + x·<(40·<6 - 48) + 24)·(x^2 - x·<(40·<6 - 48) + 24)
= 0
('<' is 'sqrt')
And in complex,
(x + <(20·<6 + 4·<114))·(x - <(20·<6 + 4·<114))·(x + <(20·<6 - 4·<114))·(x -
<(20·<6 - 4·<114))·(x + <(10·<6 - 12) + î·<(36 - 10·<6))·(x + <(10·<6 -
12) - î·<(36 - 10·<6))·(x - <(10·<6 - 12) + î·<(36 - 10·<6))·(x - <(10·<6 -
12) - î·<(36 - 10·<6)) = 0
getting four real roots, any of them sqrt(2) + sqrt(3) + sqrt(5), and four
complex conjugates ones.
But substituing x ---> sqrt(t), we get
t^4 - 40·t^3 + 352·t^2 - 960·t + 576
that derive factorice correctly to:
(t + 2·<15 + 2·<10 - 2·<6 - 10)·(t + 2·<15 - 2·<10 + 2·<6 - 10)·(t - 2·<15 +
2·<10 + 2·<6 - 10)·(t - 2·<15 - 2·<10 - 2·<6 - 10)
or, aproximating
(t - 0.8284574727)·(t - 3.679609142)·(t - 6.522431886)·(t - 28.96950149)
getting four linear real factors, as It expects.
My version of Derive is 5.06 in Spanish.
Saludos,
Ignacio Larrosa Caņestro
A Coruņa (Espaņa)
[log in to unmask]
|