On Fri, Jan 13, 2012 at 05:04:09PM +0800, Asst. Prof. Dmitrii (Dima) Pasechnik wrote: > Dear all, > > I need to compute with matrices involving Sqrt(2+Sqrt). > However, GAP does not know how to deal with these. > gap> a:=Sqrt(Sqrt(2)+2); > Error, no method found! For debugging hints type ?Recovery from NoMethodFound > ... > Is there a good workaround?
You can use the identity: Sqrt(Sqrt(2)+2) = E(16)^7-E(16) which you can check in gap: gap> (E(16)^7-E(16))^2 = 2+Sqrt(2); true You can use Alnuth to find such identity: gap> x:=Indeterminate(Rationals,"x");; gap> G:=FieldByPolynomial(x^8+1); <algebraic extension over the Rationals of degree 8> gap> FactorsPolynomialAlgExt( G, (x^2-2)^2-2 ); [ x_1+(-a^5+a^3), x_1+(a^5-a^3), x_1+(-a^7+a), x_1+(a^7-a) ] So up to conjugacy, by taking x_1=E(16) and a = Sqrt(Sqrt(2)+2), you get four solutions. Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
