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" <[EMAIL PROTECTED]> 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 > _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
