[GAP Forum] transcendental field extensions

[Alexander Hulpke]

Dear GAP Forum,

On Mar 31, 2007, at 3/31/07 10:51, Pasha Zusmanovich wrote:

> Dear people,
>
> I have two related questions:
>
> 1. Is it possible to define transcendental field extensions in GAP?
> 2. Is it possible to make calculations in algebras with parametric  
> coefficients?

To my knowledge the answer is no. Let me briefly add what is there  
and what is missing:

GAP implements arithmetic for the quotient field of the polynomial  
ring in countable many indeterminates. However it does not really  
implement the field itself as an object, thus it is not possible to  
use for example vector space functionality for this.

What is missing is part simple-minded code that defines these  
objects. However I fear that there will be secondary functionality  
(e.g. basis over a prime field) that is missing as well, thus little  
functionality would be available.

Best,

    Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke