[GAP Forum] A question on fields

[Nicola Sottocornola]

Hi,

I have to determine if a given rational function f belongs to the  
field generated by two other functions g and h. Can GAP do this?

  Consider this trivial example:


gap>x:=Indeterminate(Rationals,1);;y:=Indeterminate(Rationals,2);;

gap> F:=Field(x+y,x-y);
<field in characteristic 0>

gap> p:=x^2-y^2;
x_1^2-x_2^2

gap> p in F;
Error, no method found! For debugging hints type ?Recovery from  
NoMethodFound
Error, no 2nd choice method found for  
`GeneratorsOfLeftOperatorRingWithOne' on 1 arguments called from
GeneratorsOfLeftOperatorRingWithOne( A ) called from
GeneratorsOfLeftOperatorRing( A ) called from
Basis( V ) called from
Enumerator( D ) called 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
brk>


Thanks, Nicola