Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 4 21
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : 1/2*t^6 - 162/13*t^5 + 101*t^4 - 4208/13*t^3 + 5436/13*t^2 - 2928/13*t + 552/13
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^27 - 2107742642895019151354087032446706788605995066775852893973961656307599104456761674635045430008550275981809551/7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374*t^26 + 571314877897894113773277938841628099022315107866313176099989435432870001996440097477863056516633341823408116349/7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374*t^25 - 94755674414245602837617805326885354251034458630386171532203270506199514377919439895508295246263903516317472752109/7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374*t^24 + 91624114674411681257817536043551560876470464849391615210141709363189019703200986155925326146129305081442282836099438/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^23 - 7595960272591846634198770057752285217650560916735827512472071170457810448680357622852528023932092386364229445439826614/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^22 + 476024303187980002466544326320460699826175704848210188834071233498901353714319667716857915417118433636922080133623141386/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^21 - 23087518830329745563759074396936245055600159763816229483392923922077830692043569217003295790741811865964352169615407776130/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^20 + 880216485078692334984775414248364295569446082601466882209392757533663090132845321280927333118875475675673727520619781505280/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^19 - 26650166018047684841983907448047840700228659567973039504597661284620808039344427237247940024055199357033429375530183997928160/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^18 + 644841219575933053446019632575867726448699199451994153619999665839038935818617308432004586634195076808517736788062514724823280/60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179*t^17 - 735915150304861830207535770519946268013507598091542958772901849664119492403542784747427021912985750241008540640745337397781360/3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187*t^16 + 11456580163409518187335359947662423349900514379053709511809790385079371045137636917068033059933873009186426487015018641677593600/3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187*t^15 - 142903077068457564617894778554337527702651281731281685988670804458966512930431571856975669678935968760273119957970915154217241600/3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187*t^14 + 1423031858466719220218481840505344233744061294942573087274655073403864934496268779613193169892579988333145166598805549943169203200/3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187*t^13 - 865201713605469805645653688324191243371619267355508345761940813668928869761185779647474889125006162721027975587593255034574003200/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^12 + 5384125675116576789102444493554813690139070273682396310739227067196119706832753656960309241543954679569635122480679122401230028800/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^11 - 26098151011235107265614053320272248423350244118321222826305932301999681061964319209791761661647927530859544805223878512892598272000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^10 + 97189868840324065894215123289342898984549898960214902929540703366745674031160992567100117830183390162419157597863103308857398272000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^9 - 273259476999235619969979341101140332007084328406766602750039568426350960884384750921784984054219821998315659910423516341479855104000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^8 + 567468589400340337794907387655041328297271502625141911800959361011455587715038620163309595444136887234483030009140914306190876672000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^7 - 846725866268912041424810528130366470100405571409037501856873140115144134758807340957536080593105665046355926488909912809370001408000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^6 + 876694950132921721699027848529402609044792431988310289194971966329323465702506518958391747261609742718180295009223156741384232960000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^5 - 602255297607819882878262170851815924489218721847488786735727667778312653596551061971380470732723081163603543730799793591613480960000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^4 + 258280935610501654864394565297147502158215289195282930956611399829081875972039679027859685770127871329249094515227967379067371520000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t^3 - 401108029116655448590632837275528786784893374858119592663970846787634319555373166398004886019926882424851956423629348748001280000/1754294659001700674470211797278330010485315084730760401922150746017878154756486385296074800434268390907*t^2 + 7286009829899536808405541736027886156319152563448789165009841343481020691168765028332840714057806662448980229986928030611210240000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399*t - 241068167028784022903912219647334839532208794188377200222687830549756409775208043157918876057900388769873641943421237239808000000/275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (81.738227155150041633 - 3.326341822941415709e-572j)  +/-  (1.02e-245, 1.02e-245j)
| (70.203974845903916393 + 1.2034250041281889016e-572j)  +/-  (1.53e-244, 1.53e-244j)
| (61.302149703325273812 - 1.9321101261647830577e-594j)  +/-  (8.08e-244, 8.08e-244j)
| (53.854300793197091054 - 3.0802919785777455408e-630j)  +/-  (3.03e-243, 3.03e-243j)
| (41.702746311846765951 - 3.4495859397661473247e-662j)  +/-  (1.17e-242, 1.17e-242j)
| (2.4156731847914784107 + 1.0774601584549636146e-675j)  +/-  (2.04e-248, 2.04e-248j)
| (10.304321206059799183 - 1.0453462921001711519e-683j)  +/-  (2.94e-244, 2.94e-244j)
| (27.899962320902530978 + 6.6118693390750356451e-710j)  +/-  (1.75e-242, 1.75e-242j)
| (8.4270662797019607144 - 1.7477226181381817712e-727j)  +/-  (1.03e-244, 1.03e-244j)
| (36.612881335955409706 + 2.3446392115492258125e-730j)  +/-  (1.65e-242, 1.65e-242j)
| (1.6215202542937050877 - 1.6205411302840792777e-746j)  +/-  (2.35e-249, 2.35e-249j)
| (14.953860654933482427 + 2.8627812227030331212e-741j)  +/-  (1.77e-243, 1.77e-243j)
| (20.771447410140803265 + 2.7964695288859880792e-740j)  +/-  (7.4e-243, 7.4e-243j)
| (1.0406748406401594478 + 5.1628383128930343481e-759j)  +/-  (3.82e-250, 3.82e-250j)
| (24.158203922208911827 + 2.4974374928081543131e-755j)  +/-  (1.19e-242, 1.19e-242j)
| (6.9239565457104964806 + 1.1669750815464596369e-768j)  +/-  (3.46e-245, 3.46e-245j)
| (5.7438299459931175054 - 2.5236837702603132163e-770j)  +/-  (1.07e-245, 1.07e-245j)
| (12.486507079040894342 - 1.3235410474689583726e-768j)  +/-  (7.29e-244, 7.29e-244j)
| (4.565860331513633365 + 3.1362933390169333742e-777j)  +/-  (1.69e-246, 1.69e-246j)
| (0.27234840934504231023 - 3.8342254797864964131e-785j)  +/-  (2.09e-252, 2.09e-252j)
| (32.03475130215503633 + 2.3363306170759596368e-780j)  +/-  (1.84e-242, 1.84e-242j)
| (0.5857864376269049512 - 1.7294695682884210477e-801j)  +/-  (9.68e-251, 9.68e-251j)
| (17.71061473844342315 + 1.9800564747218727916e-793j)  +/-  (3.91e-243, 3.91e-243j)
| (47.401264462033071204 + 6.2038098663062391538e-806j)  +/-  (6.43e-243, 6.43e-243j)
| (0.052098078836124356136 - 4.3944119450997510184e-829j)  +/-  (1.3e-254, 1.3e-254j)
| (3.4142135623730950488 + 1.1638537126904387767e-822j)  +/-  (2.1e-247, 2.1e-247j)
| (0.47193845768537280597 - 9.7363385469511156672e-827j)  +/-  (4.07e-251, 4.07e-251j)
-------------------------------------------------
The weights are:
| (4.3853740274048619586e-35 - 7.5532749656456741201e-606j)  +/-  (5.64e-105, 2.52e-225j)
| (3.2098118736731170708e-30 - 2.0802718281306319219e-602j)  +/-  (2.05e-103, 9.16e-224j)
| (1.9212319405871206568e-26 + 4.8222262421245869389e-601j)  +/-  (2.41e-102, 1.08e-222j)
| (2.8192796577693965438e-23 - 1.4192689439476767811e-599j)  +/-  (1.71e-101, 7.65e-222j)
| (4.1600360560465697664e-18 - 6.2101007617795659582e-597j)  +/-  (6.75e-100, 3.02e-220j)
| (0.080525475008651929521 + 3.8310561385866637802e-586j)  +/-  (8.64e-76, 3.86e-196j)
| (6.8194786206695886169e-05 + 8.618551865967635487e-589j)  +/-  (5.83e-89, 2.6e-209j)
| (3.0040657075729752027e-12 + 1.0778082650366678551e-593j)  +/-  (1.94e-97, 8.67e-218j)
| (0.00037331619834976476504 - 4.3924279778057296651e-588j)  +/-  (4.72e-88, 2.11e-208j)
| (6.0580933090392130112e-16 + 9.0609148807234708038e-596j)  +/-  (2.01e-99, 8.99e-220j)
| (0.13508046059006038029 - 9.3005176441349493473e-586j)  +/-  (4.34e-78, 1.94e-198j)
| (8.3619521326268178091e-07 + 2.8191931204173499544e-590j)  +/-  (2.1e-93, 9.39e-214j)
| (3.0681375737116024068e-09 + 6.9164074990031059009e-592j)  +/-  (4.98e-96, 2.23e-216j)
| (0.17424110104347014782 + 2.1654299419240812416e-585j)  +/-  (1.27e-80, 5.7e-201j)
| (1.1468916302966899853e-10 - 9.228351700589674265e-593j)  +/-  (5.58e-97, 2.49e-217j)
| (0.0012760830838326488749 + 1.7705158119226859395e-587j)  +/-  (4.8e-90, 2.15e-210j)
| (0.0036598083769066767138 - 4.4156143375750907017e-587j)  +/-  (1.38e-89, 6.18e-210j)
| (8.7833627385326606415e-06 - 1.5985248398005510225e-589j)  +/-  (2.21e-93, 9.9e-214j)
| (0.012419211950810428519 + 8.5779869171284633806e-587j)  +/-  (1.47e-89, 6.56e-210j)
| (0.2377713260565938198 - 2.9276295751527776652e-585j)  +/-  (2.48e-87, 1.11e-207j)
| (5.3168638581887594516e-14 - 1.0794406593141523625e-594j)  +/-  (4.81e-100, 2.15e-220j)
| (0.2659955430798009871 - 9.1956348393892395678e-585j)  +/-  (2.49e-88, 1.12e-208j)
| (5.9105946928511226288e-08 - 4.627185878692420034e-591j)  +/-  (4.5e-96, 2.01e-216j)
| (1.5679975729450534227e-20 + 3.3751303115470828944e-598j)  +/-  (6.35e-104, 2.84e-224j)
| (0.12650072868711947018 + 3.4867141223567725715e-586j)  +/-  (4.23e-90, 1.91e-210j)
| (0.03579278236575006429 - 1.7083866732431565861e-586j)  +/-  (2.07e-91, 9.01e-212j)
| (-0.073713713077336318679 + 1.0271285245735908188e-584j)  +/-  (3.31e-89, 1.51e-209j)
