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

[Dima Pasechnik]

GAP cannot deal with non-rational expressions involving indeterminants.
Realistically, you most probably would not be able to go much further than
k=15, say. So you can just use another CAS to write these polynomials out
explicitly and feed them into GAP.

HTH,
Dmitrii

On 3/18/06 1:33 PM, "marta asaeda" <marta31 at gmail.com> wrote:

> 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
>