       Re: Simplifying polynomial and rounding problems

• To: mathgroup at smc.vnet.net
• Subject: [mg82913] Re: [mg82801] Simplifying polynomial and rounding problems
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Sat, 3 Nov 2007 03:25:00 -0500 (EST)
• References: <13454456.1194022919313.JavaMail.root@m35>

```You can approximate the polynomial with, for instance:

a1 = 1.0000000000000002 - 0.6721560269293043 s^2 -
0.32784397307069685 s^4;
a2 = Rationalize[a1, 10^-14]
a2 // Factor

1 - (8292319 s^2)/12336896 - (4044577 s^4)/12336896

-(((-1 + s) (1 + s) (12336896 + 4044577 s^2))/12336896)

1 is an exact root of a2, and the approximation error is

a1 - a2 // InputForm

2.220446049250313*^-16 - 2.220446049250313*^-15*
s^2 + 9.992007221626409*^-16*s^4

Depending on your application and the value of s, that may -- or may not
-- be small enough (in theory).

In practice, I doubt that you know the coefficients to more than six
digits in the first place.

Bobby

On Wed, 31 Oct 2007 06:14:15 -0500, Isaac Martinez G.
<isaac.martinez at sbcglobal.net> wrote:

> I am having problems with Mathematica precision/accuracy (or whatever
> you call it)
> I have the following expression
> A1=1.0000000000000002-0.6721560269293043s^2 - 0.32784397307069685s^4
> Now when I factorize:
> There are a couple of (-1+s)(1+s) factors or something very close to 1.
> Like 0.999999999999999997+s
> I want to elliminate those factors but due to the fact that it is not
> really 1, but 0.999999999999999997 Mathematica does not always cancel
> those factors neither with A1/((-1.+s)(1.+s)) nor A1/((-1+s)(1+s)).
> How can I avoid the problem of 1 versus 0.999999999999999997
> I am doing directional coupler design and I do need to elliminate some
> factors from an ABCD matrix where 5 to 6 decimal places is just fine in
> the last step.
> I have tried
> Factor[]
> Cancel[]
> FactorList[]
> but I always have this problem and it screws up my program.
> Sorry, I am  new to Mathematica
>
> I am new to Mathematica.....
>
>

--
DrMajorBob at bigfoot.com

```

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