Two ideas: (1) As in your first construction but replace each field constructed after the forst with the corresponding absolute field.
(2) Let a = sqrt(2)+sqrt(3)+... as a real number and use LLL to find its mimimum polynomial. John Cremona On 10 November 2015 at 06:35, Pierre <[email protected]> wrote: > Hi, > > I'm trying to construct a certain number field, of degree 64 over QQ (well, > I'd like to check that using Sage !). > It is constructed by adding a certain number of square roots. I have first > tried > > F0= QQ > F1.<foo1>= F0.extension( polygen(F0)^2 - 2) ## adding sqrt(2) > F2.<foo2>= F1.extension( polygen(F1)^2 - 5) ## adding sqrt(2) > etc... > > but each step was slower than the previous one, and the last step just > stalled, apparently. (Below are the details of the roots I'd like to add). > > I have tried alternatively to use QQbar, which made the input very easy, > here is the whole thing: > > a= 2 > b= -1 > c= 5 > > ra= QQbar(sqrt(a)) > rc= QQbar(sqrt(c)) > rb= QQbar(sqrt(b)) > > alpha= 1 + ra > gamma= 2 + rc > A= (alpha^2 * gamma)/ ( (alpha+gamma) * (alpha*gamma + b) ) > C= (alpha+gamma)*(alpha*gamma + b) / (b*alpha) > delta= (alpha+gamma)/alpha > > rA= sqrt(A) > rC= sqrt(C) > rdelta= sqrt(delta) > > ## and finally: > > K, gens, phi= number_field_elements_from_algebraics([ra, rb, rc, rA, rC, > rdelta], minimal= True) > > > However this last command takes forever. (This is on SMC.) > > Is there anything else that I could try? > > Thanks ! > Pierre > > > > > > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
