Starting with polynomial:
P : 2*t
Extension levels are: 1 4 62
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 62 Kronrod extension for:
P2 : 2*t^5 - 10*t^3 + 15/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^67 - 37081342617759730339696957543708050816471959120964229307/17611964765029972453417171637800543410212110687536561*t^65 + 531825459382203866087985604240553620777459357698800502530285/510746978185869201149097977496215758896151209938560269*t^63 - 109613742491747109034142001488482948179779505707335459109057535/340497985457246134099398651664143839264100806625706846*t^61 + 806179792437814745169539598005998956300401946604971748893522075/11542304591771055393199954293699791161494942597481588*t^59 - 9009452747077409412239720525822106195031598869940949763384461915/796021006329038302979307192668951114585858110171144*t^57 + 2266120773162966831334826483170538647275764397612659674155190685505/1592042012658076605958614385337902229171716220342288*t^55 - 453827913905719563883624291398329287501178814724821122645280203996025/3184084025316153211917228770675804458343432440684576*t^53 + 73664978256866972065107790273657577198405085313155681893976435351204825/6368168050632306423834457541351608916686864881369152*t^51 - 9815666166226296460575317928501756363236140592528260609461240650445395625/12736336101264612847668915082703217833373729762738304*t^49 + 1083534567282960974160263181959428517976244564026047665295304384828251425125/25472672202529225695337830165406435666747459525476608*t^47 - 99736520788445897994897157560147567077992056850164124053871571827395005557125/50945344405058451390675660330812871333494919050953216*t^45 + 7689187763259674009687897529314894313802418020713406216194117335537077483276875/101890688810116902781351320661625742666989838101906432*t^43 - 497867723207184410855221138085264369198788491037915291587894531248568719560749375/203781377620233805562702641323251485333979676203812864*t^41 + 27109348734695200010587076914690391024532227856044880365100454003995545063047003125/407562755240467611125405282646502970667959352407625728*t^39 - 1241359732158007418757676849660048667204201419412614657184778015476548036808911108125/815125510480935222250810565293005941335918704815251456*t^37 + 23872320639642513964373331408207781968138595144519640895001181053553184908913763333125/815125510480935222250810565293005941335918704815251456*t^35 - 384679779348018697993144042518652110087173097710742418734542592337822236838009340071875/815125510480935222250810565293005941335918704815251456*t^33 + 41403295344077142713656301662227785619922731962538430856143205704416088681099321778971875/6521004083847481778006484522344047530687349638522011648*t^31 - 925605393054451891116651619363767041258023636759691845915629900723067417658897175219421875/13042008167694963556012969044688095061374699277044023296*t^29 + 17084094471314952135435377422542935611942494657830865260119150384030073729873637179647603125/26084016335389927112025938089376190122749398554088046592*t^27 - 258281274756099809977840731666079738719081728046359880820845567437270389774332031202681690625/52168032670779854224051876178752380245498797108176093184*t^25 + 3167133076928915253093500943167507557793829747551041352279508523237947525500596141682446171875/104336065341559708448103752357504760490997594216352186368*t^23 - 31121083322920347430184469555595941267836858511884087586570574382898849222967734706144739296875/208672130683119416896207504715009520981995188432704372736*t^21 + 241412934380815841307509888806505308036543964392441452254129298727554830693416691079012793359375/417344261366238833792415009430019041963990376865408745472*t^19 - 1451084964060144039414587755536566266943342017824338748359201015713639501258371204329693016234375/834688522732477667584830018860038083927980753730817490944*t^17 + 6601535804482724745007204452444510277416325557937989192906159427432560482151992178947226458484375/1669377045464955335169660037720076167855961507461634981888*t^15 - 22054351889757846831862328930893458062276315251769311748441316633296321529717674553524966201484375/3338754090929910670339320075440152335711923014923269963776*t^13 + 51989603682124470829894338936520832535972768314466652297164117553333947899722807388784961893515625/6677508181859821340678640150880304671423846029846539927552*t^11 - 81881875034915875620583579837122357368136753342566105638886992373003774942309484586727960201953125/13355016363719642681357280301760609342847692059693079855104*t^9 + 79633667262119971457614501049315396039042858068589330725483357656761934717096588401534323312734375/26710032727439285362714560603521218685695384119386159710208*t^7 - 42303090060921177655981987484104611973622403277999507582460199431870334075230215842621563882109375/53420065454878570725429121207042437371390768238772319420416*t^5 + 19771967520806277939824949230047225176698178039626859507324581100557143354143629347836444948046875/213680261819514282901716484828169749485563072955089277681664*t^3 - 1246679625980249332935359478454768162693741581530239066635354896244432718400275531573457398828125/427360523639028565803432969656339498971126145910178555363328*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-4.5589496506943858366 - 5.4920499134910117422e-1213j)  +/-  (6.43e-496, 6.43e-496j)
| (-10.00976282785181362 - 2.8708824883662490387e-1211j)  +/-  (4.42e-498, 4.42e-498j)
| (-9.4903604277911324388 - 3.5663342960952237981e-1238j)  +/-  (4.12e-497, 4.12e-497j)
| (7.8169965354109933989 - 1.284578771974174584e-1273j)  +/-  (5.83e-495, 5.83e-495j)
| (4.5589496506943858366 + 1.2782593312297719035e-1298j)  +/-  (7.14e-496, 7.14e-496j)
| (8.5998723908682315869 + 4.8969017751365473011e-1315j)  +/-  (9.51e-496, 9.51e-496j)
| (10.637533036577660298 - 7.6300385490392801401e-1332j)  +/-  (1.88e-499, 1.88e-499j)
| (-10.637533036577660298 - 1.1515269782534568708e-1337j)  +/-  (1.8e-499, 1.8e-499j)
| (-1.2194881648764165459 - 7.1580426800898420659e-1349j)  +/-  (1.17e-504, 1.17e-504j)
| (2.0201828704560856329 - 1.9592445063643268486e-1345j)  +/-  (7.71e-502, 7.71e-502j)
| (2.2919518823260967702 - 2.312434183695528994e-1344j)  +/-  (6.29e-501, 6.29e-501j)
| (7.4510882211710887052 - 1.1303736279462865843e-1337j)  +/-  (9.28e-495, 9.28e-495j)
| (10.00976282785181362 + 4.9446711305355544341e-1346j)  +/-  (4.45e-498, 4.45e-498j)
| (-3.121387335966697129 + 1.0920129622124698813e-1348j)  +/-  (1.17e-498, 1.17e-498j)
| (-7.4510882211710887052 + 1.4934656555694889501e-1344j)  +/-  (9.72e-495, 9.72e-495j)
| (3.9744093476382716099 - 7.0008146850193833267e-1346j)  +/-  (8.41e-497, 8.41e-497j)
| (-6.7556491251762591135 - 1.7257857723068053483e-1344j)  +/-  (1.57e-494, 1.57e-494j)
| (9.4903604277911324388 + 1.6899729543097627242e-1345j)  +/-  (4.01e-497, 4.01e-497j)
| (-6.0970833700977506588 + 9.1230784736648716997e-1345j)  +/-  (1.36e-494, 1.36e-494j)
| (5.159144023115416532 + 9.8418777846232929024e-1343j)  +/-  (3.32e-495, 3.32e-495j)
| (-9.0270454008929144424 - 1.5936301136326827206e-1352j)  +/-  (2.49e-496, 2.49e-496j)
| (2.8424832268778822931 - 5.7918860183304602164e-1357j)  +/-  (2.32e-499, 2.32e-499j)
| (-3.9744093476382716099 - 4.4538118055465726115e-1353j)  +/-  (8.03e-497, 8.03e-497j)
| (4.2649069823456925142 - 8.4952190674682230454e-1351j)  +/-  (2.33e-496, 2.33e-496j)
| (-8.1985739927646404735 - 4.071686909646811777e-1351j)  +/-  (2.49e-495, 2.49e-495j)
| (-5.778613117917044023 - 2.9198273480186558971e-1351j)  +/-  (8.92e-495, 8.92e-495j)
| (5.4661939691022944951 + 4.2397672401990546691e-1349j)  +/-  (5.32e-495, 5.32e-495j)
| (6.4224267706415456161 + 4.6332490537372252198e-1367j)  +/-  (1.53e-494, 1.53e-494j)
| (-5.4661939691022944951 + 2.9415804008046108534e-1386j)  +/-  (5.77e-495, 5.77e-495j)
| (9.0270454008929144424 - 8.4243486183283833995e-1403j)  +/-  (2.48e-496, 2.48e-496j)
| (6.0970833700977506588 - 1.2347899622397485059e-1436j)  +/-  (1.29e-494, 1.29e-494j)
| (3.6871545508640481953 + 2.0129484758508231027e-1452j)  +/-  (2.13e-497, 2.13e-497j)
| (-6.4224267706415456161 - 1.8371912137155908523e-1454j)  +/-  (1.58e-494, 1.58e-494j)
| (-7.0980037894566765331 - 6.9124658822996988511e-1469j)  +/-  (1.27e-494, 1.27e-494j)
| (-1.4837540391244350153 - 1.2461631319251345849e-1488j)  +/-  (1.18e-503, 1.18e-503j)
| (-5.159144023115416532 + 2.2870867027219742546e-1483j)  +/-  (3.26e-495, 3.26e-495j)
| (6.7556491251762591135 - 7.5997375905323483672e-1498j)  +/-  (1.57e-494, 1.57e-494j)
| (0.95857246461381850711 + 3.1643636183253697636e-1540j)  +/-  (9.87e-506, 9.87e-506j)
| (4.8568908785349931865 - 1.0435110144440252345e-1533j)  +/-  (1.59e-495, 1.59e-495j)
| (-4.2649069823456925142 + 8.7264230189771712337e-1552j)  +/-  (2.43e-496, 2.43e-496j)
| (-2.566036456635366968 - 6.6022820429647761677e-1561j)  +/-  (3.98e-500, 3.98e-500j)
| (-3.6871545508640481953 - 4.5405618304251078083e-1561j)  +/-  (2.1e-497, 2.1e-497j)
| (1.7507461158578957939 + 3.5619397427665752049e-1566j)  +/-  (1.08e-502, 1.08e-502j)
| (1.4837540391244350153 + 1.4869657499781945282e-1571j)  +/-  (1.3e-503, 1.3e-503j)
| (8.1985739927646404735 - 6.956013030232766855e-1579j)  +/-  (2.5e-495, 2.5e-495j)
| (-2.0201828704560856329 + 1.5779978937254213344e-1603j)  +/-  (7.83e-502, 7.83e-502j)
| (-3.4028857148349135342 + 4.662856887297931485e-1599j)  +/-  (5.15e-498, 5.15e-498j)
| (2.566036456635366968 - 1.6730472722315190251e-1601j)  +/-  (3.91e-500, 3.91e-500j)
| (0.70239264249807928747 + 1.8041678079561837244e-1607j)  +/-  (9.42e-507, 9.42e-507j)
| (-8.5998723908682315869 - 1.5209173260346371048e-1594j)  +/-  (9.7e-496, 9.7e-496j)
| (-1.7507461158578957939 - 1.5767168253360971538e-1611j)  +/-  (1.04e-502, 1.04e-502j)
| (-0.95857246461381850711 + 2.0529045566667493311e-1614j)  +/-  (1.02e-505, 1.02e-505j)
| (-4.8568908785349931865 - 4.4345167029320040212e-1603j)  +/-  (1.45e-495, 1.45e-495j)
| (1.2194881648764165459 - 3.805522803989356402e-1618j)  +/-  (1.18e-504, 1.18e-504j)
| (-2.8424832268778822931 - 8.3477398595130335782e-1613j)  +/-  (2.38e-499, 2.38e-499j)
| (-7.8169965354109933989 + 9.3073744465716329613e-1607j)  +/-  (5.23e-495, 5.23e-495j)
| (-0.70239264249807928747 + 2.033769301579510647e-1635j)  +/-  (9.42e-507, 9.42e-507j)
| (-2.2919518823260967702 - 1.065965821201143901e-1628j)  +/-  (6.09e-501, 6.09e-501j)
| (3.121387335966697129 - 6.0893360852883889667e-1623j)  +/-  (1.14e-498, 1.14e-498j)
| (0.45403112465218736197 + 1.072395969499104024e-1645j)  +/-  (6.76e-508, 6.76e-508j)
| (1.3740892810960496186e-1645 + 2.30559881823378038e-1645j)  +/-  (1.8e-1643, 1.8e-1643j)
| (7.0980037894566765331 + 6.0319834671931711694e-1657j)  +/-  (1.28e-494, 1.28e-494j)
| (-0.2191641585382305832 - 2.7931736193402068613e-1698j)  +/-  (4.76e-509, 4.76e-509j)
| (5.778613117917044023 - 2.0756069459130759045e-1692j)  +/-  (8.8e-495, 8.8e-495j)
| (0.2191641585382305832 - 3.0105167901021977607e-1728j)  +/-  (4.76e-509, 4.76e-509j)
| (3.4028857148349135342 + 1.3704102436221975687e-1708j)  +/-  (5.25e-498, 5.25e-498j)
| (-0.45403112465218736197 + 2.4842793614440004394e-1722j)  +/-  (6.78e-508, 6.78e-508j)
-------------------------------------------------
The weights are:
| (1.5711788973708590356e-10 - 4.271357478108806054e-1222j)  +/-  (2.31e-167, 6.68e-414j)
| (9.6576639017594168627e-45 - 2.8278096222832826691e-1241j)  +/-  (3.25e-190, 9.42e-437j)
| (2.1042500091248123929e-40 + 5.1171448551534517257e-1239j)  +/-  (1.12e-188, 3.24e-435j)
| (6.1037920757724933517e-28 - 5.0480563918306713442e-1233j)  +/-  (1.58e-185, 4.59e-432j)
| (1.5711788973708590356e-10 - 9.4637949402119574133e-1224j)  +/-  (2.61e-171, 7.57e-418j)
| (1.769583944124657615e-33 - 6.7291166426509625654e-1236j)  +/-  (2.02e-188, 5.84e-435j)
| (2.9414723260744653663e-50 - 1.572243441211500303e-1244j)  +/-  (3.25e-195, 9.42e-442j)
| (2.9414723260744653663e-50 + 3.9306148682659542343e-1244j)  +/-  (8.92e-195, 2.58e-441j)
| (0.033503196237054558705 - 2.6046536697868313081e-1218j)  +/-  (3.82e-140, 1.11e-386j)
| (0.0025784353056688313803 + 1.9544003664359333163e-1219j)  +/-  (5.09e-153, 1.47e-399j)
| (0.00080556092947676602569 - 8.7668507604431295323e-1220j)  +/-  (3.47e-156, 1e-402j)
| (1.567340223476833187e-25 + 9.1353315696167218319e-1232j)  +/-  (2.72e-185, 7.88e-432j)
| (9.6576639017594168627e-45 + 1.0580112672503549074e-1241j)  +/-  (1.46e-193, 4.23e-440j)
| (9.2789301782266409189e-06 + 2.7851632347702757839e-1220j)  +/-  (6.55e-167, 1.9e-413j)
| (1.567340223476833187e-25 - 3.7935830337846273643e-1231j)  +/-  (3.72e-188, 1.08e-434j)
| (2.248961181679049977e-08 - 1.5398001510549041628e-1222j)  +/-  (1.18e-172, 3.41e-419j)
| (2.8780118160890616406e-21 - 8.1513857662573347082e-1229j)  +/-  (4.97e-186, 1.44e-432j)
| (2.1042500091248123929e-40 - 1.7961553375714719061e-1239j)  +/-  (2.87e-193, 8.33e-440j)
| (1.3010803359100585212e-17 - 9.4901022871908496748e-1227j)  +/-  (4.76e-184, 1.38e-430j)
| (4.7379301623293995303e-13 - 3.901266505351327942e-1225j)  +/-  (4.88e-180, 1.41e-426j)
| (1.0191854681833896361e-36 - 4.330865378343277775e-1237j)  +/-  (2.79e-193, 8.07e-440j)
| (4.8524180647953499216e-05 - 1.4367532100506910154e-1220j)  +/-  (1.91e-168, 5.55e-415j)
| (2.248961181679049977e-08 - 2.2478633904182638693e-1221j)  +/-  (1.96e-176, 5.68e-423j)
| (2.0775855635132555598e-09 + 4.0017172514669182032e-1223j)  +/-  (5.25e-176, 1.52e-422j)
| (1.4170452232338625052e-30 - 7.547987079687119455e-1234j)  +/-  (2.43e-191, 7.04e-438j)
| (5.5982917483883817505e-16 + 8.6744396327802759554e-1226j)  +/-  (1.04e-183, 3.02e-430j)
| (1.8444394995010147381e-14 + 6.7122049363251711435e-1226j)  +/-  (1.67e-182, 4.83e-429j)
| (2.2654739299896211807e-19 - 1.5913232849230741482e-1228j)  +/-  (7.4e-187, 2.14e-433j)
| (1.8444394995010147381e-14 - 7.4170559271458960739e-1225j)  +/-  (2.2e-184, 6.37e-431j)
| (1.0191854681833896361e-36 + 1.424313870142072901e-1237j)  +/-  (9.34e-195, 2.7e-441j)
| (1.3010803359100585212e-17 + 1.3698386913810552533e-1227j)  +/-  (1.01e-185, 2.92e-432j)
| (2.0095041208227980917e-07 + 5.4174061525767238452e-1222j)  +/-  (3.4e-177, 9.86e-424j)
| (2.2654739299896211807e-19 + 9.3775876358882463372e-1228j)  +/-  (7.41e-188, 2.15e-434j)
| (2.5810815606181717462e-23 + 6.0817743806515335929e-1230j)  +/-  (3.28e-190, 9.49e-437j)
| (0.016584392464732980604 + 1.584045148658311921e-1218j)  +/-  (6.56e-170, 1.9e-416j)
| (4.7379301623293995303e-13 + 6.3167658824540501323e-1224j)  +/-  (4.28e-185, 1.24e-431j)
| (2.8780118160890616406e-21 + 1.5825700215921804965e-1229j)  +/-  (8.16e-190, 2.36e-436j)
| (0.058272420577317316361 + 2.6772872157650504921e-1218j)  +/-  (1.99e-169, 5.76e-416j)
| (9.6346917475955478481e-12 + 2.0258030145497304964e-1224j)  +/-  (3.26e-183, 9.44e-430j)
| (2.0775855635132555598e-09 + 1.2008658305002838494e-1221j)  +/-  (1.75e-183, 5.07e-430j)
| (0.00021454936926273810265 + 1.3145143743540265855e-1219j)  +/-  (1.15e-179, 3.34e-426j)
| (2.0095041208227980917e-07 + 5.1241966885344163666e-1221j)  +/-  (1.2e-182, 3.48e-429j)
| (0.00705981733616530313 - 4.0887778524128526388e-1219j)  +/-  (1.41e-175, 4.09e-422j)
| (0.016584392464732980604 + 8.0613727558578418565e-1219j)  +/-  (1.44e-174, 4.18e-421j)
| (1.4170452232338625052e-30 + 2.1533832330341087748e-1234j)  +/-  (1.57e-195, 4.54e-442j)
| (0.0025784353056688313803 + 5.0647657399078295139e-1219j)  +/-  (9.41e-179, 2.73e-425j)
| (1.4928386156447057713e-06 - 1.2053953246112693112e-1220j)  +/-  (2.64e-182, 7.64e-429j)
| (0.00021454936926273810265 + 3.6767974013807170035e-1220j)  +/-  (3.52e-180, 1.02e-426j)
| (0.087151581502857160674 - 4.5566185638218102653e-1218j)  +/-  (4.14e-175, 1.2e-421j)
| (1.769583944124657615e-33 + 2.1912630874440444391e-1235j)  +/-  (3.31e-198, 9.58e-445j)
| (0.00705981733616530313 - 9.1869923193598856851e-1219j)  +/-  (2.66e-179, 7.71e-426j)
| (0.058272420577317316361 + 4.1029010735668619187e-1218j)  +/-  (1.36e-178, 3.94e-425j)
| (9.6346917475955478481e-12 - 6.4021479225550425545e-1223j)  +/-  (2.03e-186, 5.88e-433j)
| (0.033503196237054558705 - 1.5052754553677482302e-1218j)  +/-  (1.65e-179, 4.79e-426j)
| (4.8524180647953499216e-05 - 6.1953046667713334066e-1220j)  +/-  (2.33e-182, 6.76e-429j)
| (6.1037920757724933517e-28 + 1.9175437450819894464e-1232j)  +/-  (1.4e-195, 4.06e-442j)
| (0.087151581502857160674 - 6.2164075139638859e-1218j)  +/-  (1.33e-179, 3.85e-426j)
| (0.00080556092947676602569 - 2.6493555552862971068e-1219j)  +/-  (1.58e-181, 4.58e-428j)
| (9.2789301782266409189e-06 + 5.2131120205070935206e-1221j)  +/-  (1.88e-185, 5.42e-432j)
| (0.11143483502990671624 + 7.3727661980887865007e-1218j)  +/-  (1.16e-180, 3.26e-427j)
| (0.12138990474364430447 + 1.2882768544229092488e-1217j)  +/-  (3.24e-181, 9.23e-428j)
| (2.5810815606181717462e-23 - 1.3246989868745317917e-1230j)  +/-  (1.14e-195, 3.3e-442j)
| (0.12164073724143879715 - 1.1887026405330222776e-1217j)  +/-  (3.14e-182, 8.21e-429j)
| (5.5982917483883817505e-16 - 1.0234421164391668728e-1226j)  +/-  (5.74e-192, 1.66e-438j)
| (0.12164073724143879715 - 1.0796550019183056438e-1217j)  +/-  (2.33e-182, 6.08e-429j)
| (1.4928386156447057713e-06 - 1.7502422485020436978e-1221j)  +/-  (7.86e-187, 2.4e-433j)
| (0.11143483502990671624 + 9.0037195568358989872e-1218j)  +/-  (1.17e-182, 2.72e-429j)
