       Re: Factoring a polynomial

• To: mathgroup at smc.vnet.net
• Subject: [mg37106] Re: [mg37102] Factoring a polynomial
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Thu, 10 Oct 2002 03:20:33 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Factoring without specifying the extension does not really make sense.
Of course Mathematica can easily factor yur polynomial into linear
factors over the complex numbers (with the help of Solve), but I
suspect you are really asking for is factoring over the reals. This is
harder and needs more human input. But anyway, Mathematica can do this,
or at least I have done it using Mathematica. In fact if you are
satisfied with a numerical answer Mathematica can do alone and in
seconds:

In:=
Simplify[N[x^6 + (9/14)*x^5 + (9/28)*x^4 + (3/35)*x^3 + (9/700)*x^2 +
(9/8750)*x + 3/87500]]

Out=
1.*(0.010974992601737198 + 0.20255610310498295*x +
x^2)*(0.020476912388332692 +
0.2047691238833268*x + x^2)*(0.15256133957420948 +
0.23553191586883315*x + x^2)

But I have in fact been foolish enough to compute the exact answer too.
I do not propose to post it here for it's absolutely horrible
(expressed in terms of Root objects) and quite useless. However if you
really want to see it I can send it to you privately.

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/

On Wednesday, October 9, 2002, at 06:26 PM, Carlos Felippa wrote:

> From: carlos at colorado.edu (Carlos Felippa)
To: mathgroup at smc.vnet.net
> Date: Wed Oct 9, 2002  6:26:02 PM Asia/Tokyo
> To: mathgroup at smc.vnet.net
> Subject: [mg37106] [mg37102] Factoring a polynomial
>
> Can Mathematica factor the polynomial
>
> p1=x^6+9/14*x^5+9/28*x^4+3/35*x^3+9/700*x^2+9/8750*x+3/87500;
>
> without a priori knowledge of the Extension field?
>
>
>

```

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