factoring over the complex rationals

[clicl...@freenet.de]

Hello,

the Computer Algebra system Derive cannot factor polynomials over the
complex rational numbers. Can the other systems regularly featured on
sci.math.symbolic do this? Can they decompose

-7*x^6 + 10*x^4 + 24*x^3 - 14*x^2 - 27*x - 42 +
#i*(3*x^6 - 9*x^5 + 30*x^4 + 15*x^3 + 17*x^2 - 33*x - 7)

for example? Can the complex problem perhaps be reduced to the real
problem? If so how? This might allow teaching Derive to handle the
complex case too.

Martin.

[G. A. Edgar]

In article <4AF80D68...@freenet.de>, <clicl...@freenet.de>
wrote:

Maple...

p :=

-7*x^6 + 10*x^4 + 24*x^3 - 14*x^2 - 27*x - 42 +

I*(3*x^6 - 9*x^5 + 30*x^4 + 15*x^3 + 17*x^2 - 33*x - 7);

factor(p);

(-7/58+(3/58)*I)*((-7-7*I)+2*x-(8*I)*x-x^2+I*x^2+2*x^3)
*(29*x^3+x^2+(17*I)*x^2-10*x+(4*I)*x+(-32+7*I))

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[Phil Carmody]

Maple = big gun. Never seen anything it couldn't do!

The free Pari/GP pops this out happily:

? factor(f)

[x^3 + (-1/2 + 1/2*I)*x^2 + (1 - 4*I)*x + (-7/2 - 7/2*I) 1]

[x^3 + (1/29 + 17/29*I)*x^2 + (-10/29 + 4/29*I)*x + (-32/29 + 7/29*I) 1]

(Yes, it deliberately bins the content (-7 + 3*I) of the polynomial.)

Phil
--
Any true emperor never needs to wear clothes. -- Devany on r.a.s.f1

[Axel Vogt]

Ok. Maple just replies by rational * integer polynomial, which may be matter of
taste.

All (?) the answers just take the example, but leave open the questions ...