Starting with polynomial:
P : t
Extension levels are: 1 4 12 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P3 : t^17 - 6536/53*t^15 + 617205/106*t^13 - 7144995/53*t^11 + 172854825/106*t^9 - 539111430/53*t^7 + 3204996795/106*t^5 - 1892565675/53*t^3 + 1129052925/106*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 354696408756689972035341792798958782630145129488255160445782133908844667752745790678583782583677/361947278787276079606380737395009697201726430023372024265004165160073849850080265365484966647*t^49 + 37321986895249883451351006435242722675118320856984416653385007057664987829927553050200084292749121219/84695663236222602627893092550432269145203984625469053678010974647457280864918782095523482195398*t^47 - 10232320370317224721146809214888878221154063070175806037821070009173496514466781783958634302296345184035/84695663236222602627893092550432269145203984625469053678010974647457280864918782095523482195398*t^45 + 638987315580134318602311874719572080010883069339617741700959063140321335276138979037371627195925535697055/28231887745407534209297697516810756381734661541823017892670324882485760288306260698507827398466*t^43 - 65952669946675402033554793565451275740381048501295372894087538678844184814998134728852403033214868962107991165/21428002798764318464856952415259364093736608110243670580536776585806692058824451870167440995435694*t^41 + 6750447333553301089186055254357449690277569309657451435503214077385371566169921146745701240042008937541585153665/21428002798764318464856952415259364093736608110243670580536776585806692058824451870167440995435694*t^39 - 197766103829307963551215226102760017653352691632560366792156085202205360523719100280528162412794365583267091795/7962840133320073751340376222690213338437981460514184533830091633521624696701765838040669266234*t^37 + 2523394053217598097456913507765128689886756900999495973929219978872271991570410389462236396335928403123884174705225/1648307907597255266527457878096874161056662162326436198502828968138976312217265528474418538110438*t^35 - 11160111960381113571174483775056913412210396340051286482081352546180262016466279763889397906355527526057831920922075/149846173417932296957041625281534014641514742029676018045711724376270573837933229861310776191858*t^33 + 71795152406092846133846978118838515346907084928227981984181473784335227708334157023030038078114629045363579615037375/24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643*t^31 - 2203020059703572222501315036983886923939524097340230658668252787438330865855475011845440955339781571895709501618923375/24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643*t^29 + 53688031276435117347878917711835536445617092199030614640048881178985073030049195506079560463260779771297010893020807625/24974362236322049492840270880255669106919123671612669674285287396045095639655538310218462698643*t^27 - 38346731162749672770576812670817877254662578513519509323176161610448756524325710856679034235414118517636347003495150375/924976379123038870105195217787247003959967543393061839788343977631299838505760678156239359209*t^25 + 25282469009710782895435774258476188029444273259276235159129492556476604920598775515212741206315654675281493244309015625/40216364309697342178486748599445521911302936669263558251667129462230427761120029485053885183*t^23 - 298703427390338629770826801652916819794278231946966846478700781601851111593028188879845578051073428610462413630276520625/40216364309697342178486748599445521911302936669263558251667129462230427761120029485053885183*t^21 + 905145227368793648768775990423296971120116837940027995343590928694375414546091058315548544072712496903928745167833072500/13405454769899114059495582866481840637100978889754519417222376487410142587040009828351295061*t^19 - 6228266507541905087432976809193712778491097291595901054167036255461010928387880964522420749051674655479536653510763473750/13405454769899114059495582866481840637100978889754519417222376487410142587040009828351295061*t^17 + 63504972849781442462809123110125771853169606491706965755185662594051782620480169757264963832047554590030736312583244515625/26810909539798228118991165732963681274201957779509038834444752974820285174080019656702590122*t^15 - 77749119371633040371441984733476231509086055001312426492522199306165984131948835035316114265440878636430042650500552571875/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^13 + 198202775119120067346020611038100050418432821581832124086762158018332215746161766728135670042876189141606308455467398278125/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^11 - 333260299449137705786273694957357432298545064688873198121098046259414702081963354388716386352714774068669298295467902340625/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^9 + 343799035553830506326843076746090901585877881045553832538321708972669868247874505092234407935562655509649599231626142428125/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^7 - 195441984601232991153874180297031047863381298236607370328457942037008319939633541146253022889590943324773095040543785703125/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^5 + 51560998543633382826717179703722561934567634865412661772416994527114867396403421548903382124570800130780467216865153453125/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t^3 - 4414983813377993531404338743133537642138401133764684337047409149473624080545938214303116635706852445978240064237895078125/8936969846599409372997055244321227091400652593169679611481584324940095058026673218900863374*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   51 out of 51
Indefinite weights: 0 out of 51
Negative weights:   0 out of 51
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.230568656931763495 + 1.4733166892087168831e-884j)  +/-  (6.62e-245, 6.62e-245j)
| (-10.230568656931763495 + 5.6247387524345469085e-884j)  +/-  (6.84e-245, 6.84e-245j)
| (8.8685627208355121731 + 1.979420245867923824e-883j)  +/-  (6.7e-244, 6.7e-244j)
| (-2.4568166379024949948 + 2.4417922221541909644e-888j)  +/-  (6.03e-248, 6.03e-248j)
| (9.5225312318247327711 - 6.3958538539913696928e-884j)  +/-  (2.52e-244, 2.52e-244j)
| (-4.5407393558732796134 + 2.1579335198944982252e-884j)  +/-  (7.85e-245, 7.85e-245j)
| (-9.5225312318247327711 + 4.9680475216178746528e-884j)  +/-  (2.66e-244, 2.66e-244j)
| (-11.976738888664075454 + 3.902788093031707659e-886j)  +/-  (7.28e-247, 7.28e-247j)
| (11.02244221636490531 - 1.2667698494377971912e-885j)  +/-  (1.13e-245, 1.13e-245j)
| (-8.2537081181302142544 - 2.4471091136514813207e-881j)  +/-  (1.37e-243, 1.37e-243j)
| (11.976738888664075454 + 5.2108611122207982896e-887j)  +/-  (7.04e-247, 7.04e-247j)
| (3.263277679107196058 - 1.1559875647153203906e-886j)  +/-  (1.73e-246, 1.73e-246j)
| (8.2537081181302142544 - 2.8020517498519700782e-883j)  +/-  (1.56e-243, 1.56e-243j)
| (5.0128235072121870258 - 2.3853309737043156579e-885j)  +/-  (2.41e-244, 2.41e-244j)
| (-11.02244221636490531 + 2.2309924821702740937e-886j)  +/-  (9.88e-246, 9.88e-246j)
| (4.5407393558732796134 - 1.0117044021758740502e-884j)  +/-  (7.8e-245, 7.8e-245j)
| (6.4380508734772030705 - 3.0039016523603461227e-882j)  +/-  (9.51e-243, 9.51e-243j)
| (-8.8685627208355121731 + 3.0589978753783505108e-883j)  +/-  (7.29e-244, 7.29e-244j)
| (-4.0922203353591217352 - 4.3620704475077631126e-889j)  +/-  (2.56e-245, 2.56e-245j)
| (-6.0017196349345120672 + 1.1301579864826756916e-889j)  +/-  (2.41e-243, 2.41e-243j)
| (4.0922203353591217352 - 3.9630866618532921931e-911j)  +/-  (2.76e-245, 2.76e-245j)
| (-7.1161159517738442054 + 1.0260114213587334337e-916j)  +/-  (4.55e-243, 4.55e-243j)
| (2.4568166379024949948 + 2.0221471139799869482e-942j)  +/-  (5.77e-248, 5.77e-248j)
| (5.5024926885277373775 + 4.2149666317620558964e-937j)  +/-  (7.81e-244, 7.81e-244j)
| (-7.6699435270746899559 + 2.9693508806478371385e-943j)  +/-  (2.76e-243, 2.76e-243j)
| (6.0017196349345120672 + 4.0585030951030456336e-952j)  +/-  (2.64e-243, 2.64e-243j)
| (6.6454015073373845862 - 3.0030782308202257104e-953j)  +/-  (1.09e-242, 1.09e-242j)
| (7.1161159517738442054 + 1.0114158920521615176e-957j)  +/-  (4.85e-243, 4.85e-243j)
| (-1.7367610169088183293 - 1.8525437011665904161e-966j)  +/-  (1.26e-249, 1.26e-249j)
| (-0.66258025043351322197 + 3.8088959279831778495e-969j)  +/-  (2.09e-252, 2.09e-252j)
| (-3.6699364715253227764 - 7.6711678584511421457e-959j)  +/-  (8.1e-246, 8.1e-246j)
| (1.3556261799742658658 - 9.2695449994944886889e-973j)  +/-  (1.45e-250, 1.45e-250j)
| (0.96078224600702180467 + 9.8504357669734595692e-974j)  +/-  (1.38e-251, 1.38e-251j)
| (3.6699364715253227764 + 2.7825314509101055061e-966j)  +/-  (7.69e-246, 7.69e-246j)
| (-2.8569700138728056542 + 1.8574675771703635574e-965j)  +/-  (3.33e-247, 3.33e-247j)
| (-2.0871529758705234569 + 1.9788203190321967242e-972j)  +/-  (9.91e-249, 9.91e-249j)
| (-6.6454015073373845862 + 2.1059595191350136386e-967j)  +/-  (1.03e-242, 1.03e-242j)
| (2.8569700138728056542 - 8.8920330838746979403e-995j)  +/-  (3.25e-247, 3.25e-247j)
| (-3.263277679107196058 + 1.2345844712528706569e-991j)  +/-  (1.68e-246, 1.68e-246j)
| (-6.4380508734772030705 - 4.766352044154154597e-992j)  +/-  (8.93e-243, 8.93e-243j)
| (-0.39527171068739030607 - 5.4495821066588082067e-1013j)  +/-  (2.15e-253, 2.15e-253j)
| (-5.5024926885277373775 + 1.6462742315748550412e-1003j)  +/-  (8.22e-244, 8.22e-244j)
| (-1.4762997819423636749e-1036 - 1.1341509680501806843e-1036j)  +/-  (9.49e-1035, 9.49e-1035j)
| (1.7367610169088183293 + 3.4160345823540458322e-1011j)  +/-  (1.5e-249, 1.5e-249j)
| (0.39527171068739030607 - 9.0835496796194337555e-1015j)  +/-  (2.14e-253, 2.14e-253j)
| (-1.3556261799742658658 + 1.1050220308070313547e-1012j)  +/-  (1.3e-250, 1.3e-250j)
| (-0.96078224600702180467 - 1.1751312625865906933e-1014j)  +/-  (1.23e-251, 1.23e-251j)
| (7.6699435270746899559 + 2.0007333207532103637e-1006j)  +/-  (2.53e-243, 2.53e-243j)
| (0.66258025043351322197 - 4.7189568919556885106e-1016j)  +/-  (1.97e-252, 1.97e-252j)
| (2.0871529758705234569 - 3.6826229080906555721e-1013j)  +/-  (1.03e-248, 1.03e-248j)
| (-5.0128235072121870258 + 1.8280482004925215049e-1012j)  +/-  (2.48e-244, 2.48e-244j)
-------------------------------------------------
The weights are:
| (5.549515044188048608e-24 + 3.9703428378827758403e-902j)  +/-  (1.4e-77, 5.64e-199j)
| (5.549515044188048608e-24 - 4.0259981721067108483e-902j)  +/-  (8.89e-79, 3.59e-200j)
| (2.1043298951962875868e-18 + 1.6137632380283818686e-898j)  +/-  (5.52e-75, 2.23e-196j)
| (0.0075864292541468357784 - 3.5008270609416905097e-887j)  +/-  (3.25e-50, 1.31e-171j)
| (5.5124467537038658614e-21 - 3.1368484399919617442e-900j)  +/-  (2.97e-76, 1.2e-197j)
| (6.1331370578829731268e-06 + 4.4966608375980671968e-889j)  +/-  (2.99e-63, 1.21e-184j)
| (5.5124467537038658614e-21 + 4.4750803819832565262e-900j)  +/-  (5.22e-78, 2.11e-199j)
| (3.1235510775836419166e-32 - 3.1726322248973676549e-907j)  +/-  (2.44e-83, 9.84e-205j)
| (1.409579495580142068e-27 - 2.5692111078080057918e-904j)  +/-  (5.06e-81, 2.04e-202j)
| (3.8462674852894204921e-16 - 5.5115360600436335143e-896j)  +/-  (2.28e-76, 9.2e-198j)
| (3.1235510775836419166e-32 + 4.6430118482625608103e-907j)  +/-  (1.95e-83, 7.87e-205j)
| (0.00078718039097882611209 - 4.636589919645360359e-888j)  +/-  (4.53e-62, 1.83e-183j)
| (3.8462674852894204921e-16 - 5.7086199796975956818e-897j)  +/-  (3.09e-76, 1.25e-197j)
| (6.7182307293422415479e-07 + 1.765013797499929178e-890j)  +/-  (1.25e-69, 5.05e-191j)
| (1.409579495580142068e-27 + 2.0744286002098525005e-904j)  +/-  (1.37e-83, 5.52e-205j)
| (6.1331370578829731268e-06 + 2.5446030012407521315e-889j)  +/-  (2.55e-68, 1.03e-189j)
| (1.1178502165276802732e-10 + 1.9229028262388180782e-892j)  +/-  (8.25e-74, 3.33e-195j)
| (2.1043298951962875868e-18 - 4.2615996009920713439e-898j)  +/-  (1.12e-79, 4.54e-201j)
| (4.0090377949882109638e-05 - 1.3233634795994483645e-888j)  +/-  (1.96e-69, 7.89e-191j)
| (2.9891721772791405995e-09 + 1.1255059067604099408e-891j)  +/-  (2.24e-75, 9.03e-197j)
| (4.0090377949882109638e-05 - 8.1508490578872384913e-889j)  +/-  (3.38e-69, 1.36e-190j)
| (2.1525602153085794323e-12 - 7.8367745102146067466e-894j)  +/-  (8.37e-78, 3.38e-199j)
| (0.0075864292541468357784 - 3.0757489055128963479e-887j)  +/-  (1.17e-64, 4.73e-186j)
| (5.2737396090219674513e-08 + 2.2311898400438868744e-891j)  +/-  (2.25e-73, 9.1e-195j)
| (3.8200379943266041062e-14 + 4.9433769653721228991e-895j)  +/-  (3.36e-79, 1.36e-200j)
| (2.9891721772791405995e-09 - 1.7062259813230124842e-891j)  +/-  (7.06e-75, 2.85e-196j)
| (3.3213460167422355427e-11 + 6.6584262293734512549e-892j)  +/-  (1.28e-76, 5.17e-198j)
| (2.1525602153085794323e-12 - 9.7586787892750943892e-894j)  +/-  (2.59e-78, 1.04e-199j)
| (0.031901246150458237378 - 1.3610484281940239186e-886j)  +/-  (4.86e-68, 1.96e-189j)
| (0.070498432303402575472 + 8.193997576981981765e-886j)  +/-  (2.88e-66, 1.16e-187j)
| (0.00019522417507380207787 + 2.6723271505036541058e-888j)  +/-  (1.24e-74, 5.02e-196j)
| (0.063213397666095293719 + 2.196851707059351278e-886j)  +/-  (1.26e-66, 5.09e-188j)
| (0.094418664361639046157 - 4.7133962532800079708e-886j)  +/-  (1.57e-66, 6.35e-188j)
| (0.00019522417507380207787 + 1.9843947297930547131e-888j)  +/-  (2.76e-72, 1.11e-193j)
| (0.0027387190696952555119 + 1.4448164228639420012e-887j)  +/-  (7.33e-73, 2.96e-194j)
| (0.015870992332698221218 + 7.6989963450669555591e-887j)  +/-  (1.63e-70, 6.57e-192j)
| (3.3213460167422355427e-11 + 1.5647685266299317831e-892j)  +/-  (2.85e-81, 1.15e-202j)
| (0.0027387190696952555119 + 1.1731367711052813157e-887j)  +/-  (1.51e-73, 6.08e-195j)
| (0.00078718039097882611209 - 6.1314825084578678479e-888j)  +/-  (5.21e-75, 2.1e-196j)
| (1.1178502165276802732e-10 - 3.9821708046913282821e-892j)  +/-  (4.5e-81, 1.82e-202j)
| (0.13048726031696414004 - 7.892626475231114185e-886j)  +/-  (7.25e-72, 3.01e-193j)
| (5.2737396090219674513e-08 - 6.3740508461970107072e-891j)  +/-  (1.98e-80, 8.07e-202j)
| (0.16451100553401834115 + 6.1462039781667536206e-886j)  +/-  (2.52e-72, 1.05e-193j)
| (0.031901246150458237378 - 1.2821190868864134045e-886j)  +/-  (1.04e-74, 4.31e-196j)
| (0.13048726031696414004 - 7.8287009249377349105e-886j)  +/-  (8.1e-73, 3.37e-194j)
| (0.063213397666095293719 + 2.2832192322597038519e-886j)  +/-  (5.21e-74, 2.16e-195j)
| (0.094418664361639046157 - 4.8237180586683840381e-886j)  +/-  (1.86e-73, 7.73e-195j)
| (3.8200379943266041062e-14 + 2.2490837465275599909e-895j)  +/-  (7.13e-85, 2.97e-206j)
| (0.070498432303402575472 + 8.0762147819700123237e-886j)  +/-  (8.32e-74, 3.51e-195j)
| (0.015870992332698221218 + 7.0581342870428917555e-887j)  +/-  (9.17e-76, 3.86e-197j)
| (6.7182307293422415479e-07 + 5.9263016776146991015e-890j)  +/-  (4.83e-80, 1.89e-201j)
