I have the following : sage: R.<x> = QQ[] sage: f = prod([R.random_element() for i in range(12)])+1/9939999*R.random_element(degree=24)+73/1298749837*prod([R.random_element(degree=1) for i in range(24)]) sage: f.factor()
(189/2) * (x^24 + 7504997480865664356484601/1685489222385795317475600*x^23 - 86559886260704094481/5934821802648354000*x^22 - 95000942980281728893748543911/1238834578453559558344566000*x^21 - 2931680067766784265971409584453/138749472786798670534591392000*x^20 + 11515525236076630926039622515143/118928119531541717601078336000*x^19 - 13892082133194100527760884036619/227044591832943279056604096000*x^18 - 1023688594047157556459888827191071/29969886121948512835471740672000*x^17 + 23767733432257188084673265898337/237856239063083435202156672000*x^16 + 444451745980658091387501606764119/17125649212542007334555280384000*x^15 - 738829186881482750550278987758409/39959848162598017113962320896000*x^14 - 3878836873081061546191753704623/2179628081596255478943399321600*x^13 + 7160303309088369144242103323/134544943308410832033543168000*x^12 - 57894761695290073256239016830183/119879544487794051341886962688000*x^11 + 1127815928112361886082916771409/4439983129177557457106924544000*x^10 + 1937574800475871259018213/36180952680516582951936000*x^9 - 874200716744023754020688448559/39959848162598017113962320896000*x^8 - 1546411010199459671989/1644588758205299225088000*x^7 + 783060427300243956126025547/1427137434378500611212940032000*x^6 - 90637942795516481/3418457358325451904000*x^5 + 480191813998109156527/138749472786798670534591392000*x^4 + 44405422069/87241880498930803800*x^3 - 2595617455483/2391110940848406790860*x^2 + 2/1878659811*x + 26/20665257921) So, we have a big polynomial with big coefficients... but irreducible. so we look at its roots: sage: r=f.roots(QQbar,multiplicities=False) sage: r[0].minpoly() ... takes a long time. For bigger examples it even gets the following error: sage.libs.pari.gen.PariError: not enough precomputed primes, need primelimit ~ 516569 But the minimal polynomial was given at the construction time! Shouldn't we just compute which is the factor of the given polynomial that contains the root in the cases where the algebraic number is given as a root of a rational polynomial? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
