Starting with polynomial:
P : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Extension levels are: 4 20
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Trying to find an order 20 Kronrod extension for:
P1 : 1/24*t^4 - 2/3*t^3 + 3*t^2 - 4*t + 1
Solvable: 1
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Ending with final polynomial:
P : 1/24*t^24 - 36460779972381514189483596866260184512935031/1755824032118495530019523335416138678722384*t^23 + 141214171976040521194355093311265958089858797859/29849008546014424010331896702074357538280528*t^22 - 19531344603447273232591121774137111769857593352387/29849008546014424010331896702074357538280528*t^21 + 612319393985924868609865250055036092476229450501551/9949669515338141336777298900691452512760176*t^20 - 2598379071456968363350024535725684345473303071586505/621854344708633833548581181293215782047511*t^19 + 131974190268146835673632280472508628074174439456478855/621854344708633833548581181293215782047511*t^18 - 10256263992674018606612994181983874371051153332211942495/1243708689417267667097162362586431564095022*t^17 + 18192500674853488498447364414055121981136784944404632405/73159334671603980417480138975672444946766*t^16 - 214720200043291767569304865193488056978093087193315635360/36579667335801990208740069487836222473383*t^15 + 3985797524527430578348030811096021491355861759750930445600/36579667335801990208740069487836222473383*t^14 - 58251804751911928231675860304542729725841874175828988885600/36579667335801990208740069487836222473383*t^13 + 669129367094822792453712306175073471403709632831575607511200/36579667335801990208740069487836222473383*t^12 - 6014307698258418434113346820725331168231989195081374237593600/36579667335801990208740069487836222473383*t^11 + 41996175696276850510919121578500095416893678799448638590694400/36579667335801990208740069487836222473383*t^10 - 225511536301137974794371066438280648232917273366630580227296000/36579667335801990208740069487836222473383*t^9 + 918683981699759165121834315734133002297110825865732791778976000/36579667335801990208740069487836222473383*t^8 - 2789159393513635180195893171446674093824102372968827953061632000/36579667335801990208740069487836222473383*t^7 + 6164714518423756673400808574440770611208159540446004400601856000/36579667335801990208740069487836222473383*t^6 - 9609997618785284807372605053645368593350839835863397424783104000/36579667335801990208740069487836222473383*t^5 + 10100624737040602872320181433774074038047249403399332200218880000/36579667335801990208740069487836222473383*t^4 - 6681574198984780353971585654939602624444865929182514148167680000/36579667335801990208740069487836222473383*t^3 + 2476704466216494126394635107483694297726856142254965478748160000/36579667335801990208740069487836222473383*t^2 - 410843574158458048690634712704236258209136217469723584686080000/36579667335801990208740069487836222473383*t + 17256103529595147657522061297666610887990222684712138373120000/36579667335801990208740069487836222473383
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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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (63.288603270425101175 - 1.4406288188881311333e-298j)  +/-  (1.3e-117, 1.3e-117j)
| (31.287775966501736895 + 2.0734957946454456401e-298j)  +/-  (7.59e-116, 7.59e-116j)
| (54.735115350854751017 + 5.0443283763677629962e-303j)  +/-  (6.07e-117, 6.07e-117j)
| (47.611516828225274048 + 1.9218414715276796302e-310j)  +/-  (2.24e-116, 2.24e-116j)
| (19.747288365243134448 - 7.5192111183009735653e-321j)  +/-  (4.27e-116, 4.27e-116j)
| (36.075990118580057943 + 3.6255882065750472055e-327j)  +/-  (7.23e-116, 7.23e-116j)
| (41.469905309192415671 - 1.157410923000745393e-335j)  +/-  (4.83e-116, 4.83e-116j)
| (23.180400847447973763 - 1.5275252281909483494e-347j)  +/-  (6.22e-116, 6.22e-116j)
| (27.011229691099590602 - 2.0294006243316996739e-359j)  +/-  (8.16e-116, 8.16e-116j)
| (4.5366202969211279833 + 6.8342886113454034788e-368j)  +/-  (1.81e-119, 1.81e-119j)
| (74.421168425276914176 + 2.0699677095964642825e-369j)  +/-  (1.13e-118, 1.13e-118j)
| (5.9406772784677419282 + 1.8462091866667903197e-366j)  +/-  (7.31e-119, 7.31e-119j)
| (2.1949308417498391644 + 1.3914596353177889944e-375j)  +/-  (8.5e-121, 8.5e-121j)
| (16.676203076484479277 - 2.2781036935036002789e-374j)  +/-  (2.02e-116, 2.02e-116j)
| (7.5465534606644834009 + 1.3423505356589074661e-384j)  +/-  (3.5e-118, 3.5e-118j)
| (3.3043880465359073738 + 1.1513908954718380342e-389j)  +/-  (2.96e-120, 2.96e-120j)
| (1.5661963465136231571 - 2.5889187683468421259e-394j)  +/-  (2.33e-121, 2.33e-121j)
| (0.3225476896193923118 + 1.5918555606927429198e-397j)  +/-  (2.11e-125, 2.11e-125j)
| (13.940347095993820432 - 1.8498461635783371409e-394j)  +/-  (9.3e-117, 9.3e-117j)
| (1.7457611011583465757 + 4.932340058684313513e-409j)  +/-  (6.29e-121, 6.29e-121j)
| (11.519203615194836109 + 3.7785712297265064762e-405j)  +/-  (3.64e-117, 3.64e-117j)
| (0.79631048050062854964 + 6.4195874018537332407e-420j)  +/-  (9.05e-124, 9.05e-124j)
| (0.06114850179939435374 - 1.018657197073394166e-420j)  +/-  (4.64e-127, 4.64e-127j)
| (9.3950709123011331292 + 1.0126090109046036655e-413j)  +/-  (1.17e-117, 1.17e-117j)
-------------------------------------------------
The weights are:
| (3.1144389751029105668e-27 - 3.8658246456320711729e-320j)  +/-  (1.04e-43, 1.09e-99j)
| (1.1667594643089310597e-13 - 1.3413636996632695127e-311j)  +/-  (2.18e-37, 2.28e-93j)
| (1.3099753239917164364e-23 + 4.3239782250438121704e-318j)  +/-  (1.5e-42, 1.57e-98j)
| (1.3833890708214945937e-20 - 2.5327861434608801565e-316j)  +/-  (1.65e-41, 1.73e-97j)
| (8.6167126566641444184e-09 + 1.2739075099747540428e-309j)  +/-  (1.19e-35, 1.24e-91j)
| (1.0904400366619606679e-15 - 3.8392639781178700542e-313j)  +/-  (1.03e-39, 1.08e-95j)
| (5.6059676804645232768e-18 + 1.0261284759248240682e-314j)  +/-  (7.42e-41, 7.78e-97j)
| (3.1060194342718526518e-10 - 2.5887351922124115204e-310j)  +/-  (1.16e-37, 1.21e-93j)
| (7.5167407042568169247e-12 + 5.8444321594822694845e-311j)  +/-  (2.04e-38, 2.14e-94j)
| (0.014079932192279641488 - 7.1236776245884111358e-306j)  +/-  (4.51e-31, 4.74e-87j)
| (6.3869763168626801701e-32 + 1.0028567456111476405e-322j)  +/-  (7.84e-49, 8.23e-105j)
| (0.0039412479833091159 + 2.9316349768373439469e-306j)  +/-  (6.49e-33, 6.81e-89j)
| (0.13396997612069406909 - 9.121963015747279472e-305j)  +/-  (2.7e-29, 2.83e-85j)
| (1.6594235589676898014e-07 - 5.9953462915110643917e-309j)  +/-  (2.13e-37, 2.23e-93j)
| (0.00090832771543492911953 - 1.0914669263208682023e-306j)  +/-  (8.39e-35, 8.8e-91j)
| (0.042335110186887336836 + 1.7596419392123879444e-305j)  +/-  (3.03e-32, 3.19e-88j)
| (0.32216854689231695329 - 2.1645421093993333533e-304j)  +/-  (2.5e-31, 2.62e-87j)
| (0.26535087251973736194 - 9.7659691742654912366e-306j)  +/-  (9.7e-32, 1.02e-87j)
| (2.2732120871343187189e-06 + 2.5951729443079176446e-308j)  +/-  (1.85e-37, 1.94e-93j)
| (-0.19421682901124015768 + 2.7813677203793677219e-304j)  +/-  (5.83e-32, 6.14e-88j)
| (2.2554601853461042626e-05 - 1.0165369774320145444e-307j)  +/-  (3.59e-37, 3.77e-93j)
| (0.26362528082435564976 + 2.411682457031542843e-305j)  +/-  (7.7e-34, 8.39e-90j)
| (0.14764776273711467647 + 2.5985833751269835219e-306j)  +/-  (1.27e-34, 1.41e-90j)
| (0.00016476914786481885789 + 3.5535809407088097877e-307j)  +/-  (1.52e-36, 1.59e-92j)
