[Q] how to solve and evalutate a polynomial?

youngsu · Thu Aug 11, 2005 5:32 pm

if i have a polynomial f (ex : poly f = x2 - 1 )

i want to have f(1) ( f(1) = (1)^2-1 = 0 )
and want to solve f(x) = 0

How can i do this?

email: marine917i@gmail.com
Posted in old Singular Forum on: 2004-10-11 19:23:40+02

Re: [Q] how to solve and evalutate a polynomial?

levandov · Thu Aug 11, 2005 8:29 pm

Hi,

Quote:

> if i have a polynomial f (ex : poly f = x2 - 1 )
>
> i want to have f(1) ( f(1) = (1)^2-1 = 0 )
> and want to solve f(x) = 0
>
> How can i do this?

First of all you have define a ring (which includes a definition of a ground field and an ordering on monomials).
In your case let the ground field be Q, then your ring definition will be

Code:

ring r = 0,(x),dp;

Then you define your polynomial.

Code:

poly f = x^2 -1;

For evaluation there is a command "subst"

Code:

poly f1 = subst(f,x,1);

For "solving" you can use either factorization (for one polynomial)

Code:

factorize(f);

or, for systems of equations, see the library "solve.lib".

In any case, you find the detailed information in the documentation, available both on-line (for instance, at http://www.singular.uni-kl.de/Manual/2-0-5/index.htm) and in every distribution you dowload.

Best regards,