The old Google Groups will be going away soon, but your browser is incompatible with the new version.
Message from discussion Quotients of polynomials

From:
To:
Cc:
Followup To:
Subject:
 Validation: For verification purposes please type the characters you see in the picture below or the numbers you hear by clicking the accessibility icon.

More options Oct 12 2011, 8:50 am
From: Florent Hivert <Florent.Hiv...@lri.fr>
Date: Wed, 12 Oct 2011 14:50:15 +0200
Local: Wed, Oct 12 2011 8:50 am
Subject: Re: [sage-algebra] Re: Quotients of polynomials

On Wed, Oct 12, 2011 at 05:27:02AM -0700, Urs Hackstein wrote:
> My membership in sage-support ist still pending.

> "Complicated" means here that the whole term is more than three pages
> long. Starting from a fraction with products of constants, values and
> variables in the numerator and denominator you subsitute some of the
> values in the numerator and the denominator by fractions with products
> of constants, values and variables, then you substitute some of the
> variables in all of the numerators and denominators by fractions
> with ... again and so on. Thus the only pattern of the form f is given
> is that there are only basic arithmetic operations in its definition.

> Of course, I could choose a set of numerical values for our constants
> and evaluate f in some points (this gives us float points) and get the
> coefficients by interpolation. But we are looking for a description of
> the coefficients as functions of some other variables, so numerical
> values for the coefficients don't help us.

> By the way, there is another question more elementary: How can I
> compute in \mathbb{C}(t) (i.e. the quotient field of the polynomial
> ring) using sage?

Nothing particular to do: just divide polynomials, the fraction field is
automatically created.

sage: P.<t> = CC[]
sage: P
Univariate Polynomial Ring in t over Complex Field with 53 bits of precision
sage: F = (t/t).parent()
sage: F
Fraction Field of Univariate Polynomial Ring in t over Complex Field with 53 bits of precision

You can alternatively define

sage: P.fraction_field()
Fraction Field of Univariate Polynomial Ring in t over Complex Field with 53
bits of precision

Cheers,

Florent