On Wed, Oct 21, 2009 at 12:03:15AM +0200, Michał Olejnik wrote: > Hello, > > I'm a beginner to GAP, so forgive me if my question is trivial. > > I would like to know if there is an easy way in GAP to write a function > which will check wheter passed number is an algebraic number of degree N. Is > something like that available in GAP or one of the extending packages?
How do you input your number ? GAP has no floating point numbers, so in that case it is probably simpler to use the algdep function of PARI/GP, for example: ? algdep(cos(2*Pi/7),3) %1 = 8*x^3 + 4*x^2 - 4*x - 1 Now, GAP has LLL, so it is possible to write an algdep routine for numbers given by a rational approximation (which is what floating points numbers are anyway) in GAP: Algdep:= function(x,n,prec) local M,p,q,Q,qerr; p:=NumeratorRat(x); q:=DenominatorRat(x); Q:=q^(n-1); qerr:=1/(q*prec); M:=IdentityMat(n+1); M[n+1]:=List([0..n],e->EuclideanQuotient(p^e*q^(n-e),Q)*qerr); return LLLReducedBasis(TransposedMat(M),"linearcomb").transformation[1]; end; Algdep(x,n,prec) is looking for a polynomial of degree <=n whose root alpha verify |alpha-x|<prec. Examples: Algdep(778085762274086750445/1247952668920125525979,3,10^-20); [ -1, -4, 4, 8 ] Algdep(1908304252230311410894/2155165470608815381879,6,10^-20); [ -1, 6, 24, -32, -80, 32, 64 ] Algdep(Fibonacci(101)/Fibonacci(100),2,10^-30); [ -1, -1, 1 ] Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
