[GAP Forum] 1/sqrt(polynomial) not recognized

[marta asaeda]

Hello,

I am having a problem: I would like to find galois group for each
polynomial in a sequence of polynomials parametrized by n. It is given
by a  recursive formula, so it does involve non-polynomials for
expression in terms of n. I have this (  I'm mixing mathematica and
gap notations just for this message):

A[x]:=(1/Sqrt(x^2 - 4*x))*(x^2 - 4*x + 3 - (2 - x)*((2 - x - Sqrt(x^2
- 4*x))/2))
B[x]:=(-1/Sqrt(x^2 - 4*x))*(x^2 - 4*x + 3 - (2 - x)*((2 - x + Sqrt(x^2
- 4*x))/2))

a := (2 - x + Sqrt[x^2 - 4x])/2
b := (2 - x - Sqrt[x^2 - 4x])/2

P[n_, x_] := A[x]a^(n - 1) + B[x]b^(n - 1)

R[k_, x_] :=
    (-2+x)^2(3-5x+x^2) P[2(k - 1), x] - (8-14x+7x^2-x^3) P[2(k - 1) - 1, x]

R[k,x] is a polynomial for any positive integer k. I would like to
give the list of galois groups for each k, say, 5<k<100, or 1000, just
as much as it is doable by gap in a few days. If I just set it at
night, go to bed, and see 1000 of galois groups spitted out, that will
be wonderful.  However, it seems gap is having problem dealing with
1/Sqrt(x^2 - 4*x). I just tried to teach A, B, a, b one by one, so I
did like

gap> x:=Indeterminate(Rationals);
gap> Ax:=(1/Sqrt(x^2 - 4*x))*(x^2 - 4*x + 3 - (2 - x)*((2 - x -
Sqrt(x^2 - 4*x))/2));

then I get error message like
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `Sqrt' on 1 arguments called from
Error( no_method_found ); 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


Could anyone please tell me what I should do ?

Thank you ~

marta