Thank Vincent ! I've tried to do it your way, but it is still computing after more than an hour (unless my SageMathCloud page needs refreshing, I'm always confused about that...)
How long did it take for you? (you've erased the output of the %time command, i think) On Tuesday, November 10, 2015 at 3:29:37 PM UTC+1, vdelecroix wrote: > > Hi, > > This computation takes long time but Sage is able to do it. Doing it > step by step, you can observe the relation between the degree of the > field and the time needed to generate it. > > sage: a=2 > sage: b=-1 > sage: c=5 > sage: ra = QQbar(a).sqrt(); ra.exactify() > sage: rb = QQbar(b).sqrt(); rb.exactify() > sage: rc = QQbar(c).sqrt(); rc.exactify() > sage: K, gens, phi= number_field_elements_from_algebraics( > ....: [ra,rb,rc], minimal=True) > sage: g = phi(K.gen()) > > sage: alpha= 1 + ra > sage: gamma= 2 + rc > sage: A= (alpha^2 * gamma)/ ( (alpha+gamma) * (alpha*gamma + b) ) > sage: A.exactify() > sage: C= (alpha+gamma)*(alpha*gamma + b) / (b*alpha) > sage: C.exactify() > sage: rA = A.sqrt() > sage: rA.exactify() > sage: rC = C.sqrt() > sage: rC.exactify() > sage: K2,gens2,phi2 = number_field_elements_from_algebraics( > ....: [rA,rC], minimal=True) > sage: g2 = phi2(K2.gen()) > sage: K3,gens3,phi3 = number_field_elements_from_algebraics( > ....: [g,g2], minimal=True) > sage: g3 = phi3(K3.gen()) > > > sage: delta= (alpha+gamma)/alpha > sage: delta.exactify() > sage: rdelta = delta.sqrt() > sage: rdelta.exactify() > sage: %time K4,gens4,phi4 = number_field_elements_from_algebraics( > ....: [g3,rdelta], minimal=True) > sage: K4 > Number Field in a with defining polynomial y^64 - 32*y^63 + 536*y^62 - > 6160*y^61 + 53904*y^60 - 379232*y^59 + 2220272*y^58 - 11096704*y^57 + > 48371100*y^56 - 187534480*y^55 + 658036744*y^54 - 2118167168*y^53 + > 6310029040*y^52 - 17496563168*y^51 + 45354462568*y^50 - > 110086558656*y^49 + 249092068530*y^48 - 518760267056*y^47 + > 970049745040*y^46 - 1540658021296*y^45 + 1726215748448*y^44 + > 261617504256*y^43 - 9416895523976*y^42 + 37922732526336*y^41 - > 112535439872616*y^40 + 286729191976224*y^39 - 657670378395560*y^38 + > 1379644802117040*y^37 - 2644268269215664*y^36 + 4577567236779360*y^35 - > 6965533209709168*y^34 + 8539207658489472*y^33 - 5319331244483781*y^32 - > 12389886738998320*y^31 + 65118197751618896*y^30 - > 193580564430962864*y^29 + 472080249239522272*y^28 - > 1019160749338571136*y^27 + 2001763007703523512*y^26 - > 3634327413042005888*y^25 + 6153857939241808968*y^24 - > 9737320234062776416*y^23 + 14333546151266502616*y^22 - > 19364810168265444560*y^21 + 23281715700145502160*y^20 - > 23008604561491319328*y^19 + 13767163228246461264*y^18 + > 8765359686368418944*y^17 - 43200366094147621118*y^16 + > 77999223597440406896*y^15 - 90519472303245161928*y^14 + > 54028667281044557920*y^13 + 41367302912532250064*y^12 - > 168969147746602154528*y^11 + 261672020286578277832*y^10 - > 244896792544276915584*y^9 + 104844130048796679732*y^8 + > 105596980415747506608*y^7 - 299690125602975518832*y^6 + > 385834615403528683056*y^5 - 319833171820701032864*y^4 + > 76406760284299949376*y^3 + 197175416506143879144*y^2 - > 277360083651780693056*y + 182754695501929110289 > > > On 10/11/15 08:35, Pierre 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.
