[GAP Forum] transcendental field extensions

[Pasha Zusmanovich]

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?

The questions are related, as the natural way to handle 2 is to define 
an algebra over a transcendental field extension with given parameters.

I am trying to do the following:

gap> x := Indeterminate (Rationals, "x");
x
gap> F := DefaultField (x);
<field in characteristic 0>

but this is a doomed to failure attempt, as one cannot seemingly to do 
anything useful with this field:

gap> DegreeOverPrimeField (F);
Error, no method found! For debugging hints type ?Recovery from 
NoMethodFound
Error, no 2nd choice method found for `DegreeOverPrimeField' on 1 
arguments ca\
lled from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

gap> VectorSpace (F, [[1]]);
Error, no method found! For debugging hints type ?Recovery from 
NoMethodFound
Error, no 1st choice method found for `IsFiniteDimensional' on 1 
arguments cal\
led from
IsFiniteDimensional( V ) called from
IsFinite( R ) called from
triple[3]( F, gens, V, zero ) called from
CheckForHandlingByNiceBasis( R, gens, V, false ); called from
LeftModuleByGenerators( arg[1], arg[2] ) called from
...
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue



Cheers, Pasha.