#7097: bug in polynomial factorization over number fields
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Reporter: cremona | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-4.1.3
Component: algebra | Keywords: polynomial factor root number field
Reviewer: | Author:
Merged: |
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Comment(by mhansen):
It looks like Maxima does this:
{{{
(%i9) f;
(%o9) 8*x^9+42*x^6+6*x^3-1
(%i10) h;
(%o10)
a^24-12*a^23+72*a^22-286*a^21+849*a^20-2022*a^19+4034*a^18-6894*a^17
+10182*a^16-13048*a^15+14532*a^14-13974*a^13+11365*a^12-7578*a^11
+4038*a^10-1766*a^9+762*a^8-408*a^7+236*a^6-126*a^5+69*a^4-38*a^3
+18*a^2-6*a+1
(%i11) factor(f, h);
(%o11) (3158212*x-3260097*a^22+35861067*a^21-197810817*a^20+722970825*a^19
-1980508347*a^18+4374189477*a^17-8119721106*a^16
+12884806062*a^15-17542341771*a^14+20537782665*a^13
-20658463789*a^12+17502836649*a^11-11908953451*a^10
+6086953981*a^9-2239289340*a^8+778181412*a^7-505969453*a^6
+338959407*a^5-155204647*a^4+79628015*a^3-57339525*a^2
+26692783*a-6545352)
*(3158212*x+188516*a^22-2073676*a^21+11590464*a^20-43325980*a^19
+122225476*a^18-278937216*a^17+535796097*a^16
-882319104*a^15+1254071028*a^14-1544093240*a^13
+1646197106*a^12-1500956232*a^11+1138302192*a^10
-689737648*a^9+322105959*a^8-122939196*a^7+58570992*a^6
-45023100*a^5+32705982*a^4-17015624*a^3+5914800*a^2
-1247596*a+2111017)
*(3158212*x+3637129*a^22-40008419*a^21+220991745*a^20-809622785*a^19
+2224959299*a^18-4932063909*a^17+9191313300*a^16
-14649444270*a^15+20050483827*a^14-23625969145*a^13
+23950858001*a^12-20504749113*a^11+14185557835*a^10
-7466429277*a^9+2883501258*a^8-1024059804*a^7+623111437*a^6
-429005607*a^5+220616611*a^4-113659263*a^3+69169125*a^2
-29187975*a+10767386)
*(3376128628*x-13037418309*a^23+147986265103*a^22-842436166379*a^21
+3179679952500*a^20-8992812318199*a^19
+20481211157658*a^18-39183513868608*a^17
+64201696547469*a^16-90642645538435*a^15
+110634699001317*a^14-116846928947581*a^13
+105515418570210*a^12-78998183270169*a^11
+47113502861424*a^10-21976590852910*a^9
+8895376932597*a^8-4325369983083*a^7+2567289532461*a^6
-1378351513869*a^5+720259899784*a^4-435299125839*a^3
+222726821994*a^2-94507315024*a+19159220127)
*(3376128628*x-6387038940*a^23+73350186008*a^22-421620000598*a^21
+1604591400717*a^20-4568987819322*a^19
+10461603417962*a^18-20101918099398*a^17
+33066824065209*a^16-46858866959908*a^15
+57379037846352*a^14-60764137178426*a^13
+55013146367973*a^12-41280470420502*a^11
+24608001215702*a^10-11382737677922*a^9
+4526140881603*a^8-2209906206144*a^7+1347712439108*a^6
-715822479258*a^5+359494446867*a^4-218463619790*a^3
+116078029422*a^2-46409847590*a+8745186851)
*(3376128628*x-263340429*a^23+4770936780*a^22-37531645806*a^21
+181956914439*a^20-627692491480*a^19+1675167744677*a^18
-3655686220725*a^17+6748030279365*a^16
-10698769298897*a^15+14629386661812*a^14
-17273544259614*a^13+17573023624705*a^12
-15147774806946*a^11+10628171669139*a^10
-5718069302755*a^9+2236895473851*a^8-737433500223*a^7
+412745999502*a^6-309054161436*a^5+167184773693*a^4
-83494234294*a^3+51866715375*a^2-30222204871*a
+8665827713)
*(3376128628*x+263340429*a^23-1285893087*a^22-803834817*a^21
+29502848934*a^20-145163320445*a^19+441995678266*a^18
-1020322330188*a^17+1931951582949*a^16
-3075088381381*a^15+4123376691387*a^14
-4681345409271*a^13+4510874165736*a^12
-3562757570835*a^11+2102499569980*a^10-788884502934*a^9
+156904830609*a^8-94442429205*a^7+128135345755*a^6
-53293444647*a^5-1271006050*a^4-1628113741*a^3
+9429236850*a^2+1687619844*a-1668846425)
*(3376128628*x+6387038940*a^23-73551709612*a^22+423836760242*a^21
-1616981606733*a^20+4615303291942*a^19
-10592262451806*a^18+20400101983302*a^17
-33639590092902*a^16+47802066082084*a^15
-58719639775284*a^14+62414772851986*a^13
-56772931074287*a^12+42884992632510*a^11
-25824846258950*a^10+12120067223634*a^9
-4870472151774*a^8+2341328206668*a^7-1410324829556*a^6
+763952173158*a^5-394457141625*a^4+236653321846*a^3
-122400950622*a^2+47743527714*a-11001864024)
*(3376128628*x+13037418309*a^23-151874356004*a^22+885205166290*a^21
-3415920127905*a^20+9858299075364*a^19
-22859692648289*a^18+44455890187329*a^17
-74027210465169*a^16+106302901463065*a^15
-132068666212380*a^14+142103089963586*a^13
-131118885773279*a^12+100917760071966*a^11
-62277864187039*a^10+29958203750023*a^9
-11977839777399*a^8+5420089913559*a^7-3233395658614*a^6
+1836958507752*a^5-956099056943*a^4+556800877986*a^3
-296668616619*a^2+125709260299*a-30669555761)
/5831063333391611960658932226137207117687009423878679719420581600168485617664
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7097#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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