Jan Draisma asked:
> I would like to construct the field F=Q(t), where t is an
> indeterminate, and Q is the field of rational numbers, to construct
> vector spaces over F, to compute coefficients of an element with
> respect to a basis, and even work with split simple Lie algebras over
> this field. Is any of this possible?
At the moment GAP 4 implements polynomial rings in countably many
indeterminates and it is possible to take quotients of such polynomials.
However the quotient field itself is not yet implemented and thus I cannot see
any easy way of defining algebras over it.
Sorry for not being able to provide more help,