> Le Mardi 20 janvier 2015 2h48, Palcoux Sebastien <sebastienpalc...@yahoo.fr> > a écrit : > > > Hi, > Is it possible to extend the function Sqrt on the cyclotomic numbers? > See below what's happen if we try, for example, with the number E(5) : > gap> Sqrt(E(5));Error, no method found! For debugging hints type ?Recovery > from NoMethodFoundError, no 1st choice method found for `Sqrt' on 1 arguments > called from<function>( <arguments> ) called from read-eval-loopEntering break > read-eval-print loop ...you can 'quit;' to quit to outer loop, oryou can > 'return;' to continuebrk>
Sqrt(E(5)) is +/- E(5)^3, and more generally Sqrt(E(p)) is +/- E(p)^((p+1)/2) for odd p. gap> (E(5)^3)^2; E(5) However, in the general the square root of a cyclotomic number is not a cyclotomic number, for example Sqrt(2) is a cyclotomic number, but not Sqrt(Sqrt(2)). Cheers, Bill. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
