Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 4 13
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Trying to find an order 4 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
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Trying to find an order 13 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
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Ending with final polynomial:
P : 1/2*t^19 - 488132017610946779655512843637863877634608436433372467/3639551744602370430279472853435622423570522511302114*t^18 + 3725425161723309062821218095941844734805551051823062504/233304599012972463479453388040745027151956571237315*t^17 - 10169750149426695543528558803114262347614080529647720462844/9098879361505926075698682133589056058926306278255285*t^16 + 93469318948927074934105706351534949862656861655389727469023/1819775872301185215139736426717811211785261255651057*t^15 - 4972122391574003335796850410804353494952857811561394850085763/3032959787168642025232894044529685352975435426085095*t^14 + 341221610296520551791817075985320668672967926406462441573396006/9098879361505926075698682133589056058926306278255285*t^13 - 437901091302216067838693436423725320909842169260573783551053102/699913797038917390438360164122235081455869713711945*t^12 + 119366623035996436566801234778993126290348734331416756177082120/15553639934198164231963559202716335143463771415821*t^11 - 16165760094040146393647897629726136333708595560105966775690018632/233304599012972463479453388040745027151956571237315*t^10 + 21379378761575587281332229740012389447290459623828367288134848336/46660919802594492695890677608149005430391314247463*t^9 - 34148028257382841119162307668800838697428429749098966757126092848/15553639934198164231963559202716335143463771415821*t^8 + 116649871865136548633560899084688966854634953226274136132165852288/15553639934198164231963559202716335143463771415821*t^7 - 277822244203379574783223127581945353325695009323710231021351536000/15553639934198164231963559202716335143463771415821*t^6 + 448267318594284994956613736772827967049538130142886621501566143744/15553639934198164231963559202716335143463771415821*t^5 - 472130810165583540840702263465594620270183988866779308728341515520/15553639934198164231963559202716335143463771415821*t^4 + 308154924929168106472162980201735758778828840069397615308552238080/15553639934198164231963559202716335143463771415821*t^3 - 114528458019448719348960748534755163783815553203295453205309230080/15553639934198164231963559202716335143463771415821*t^2 + 20505423577114190971352187927222289643149809758901658449450547200/15553639934198164231963559202716335143463771415821*t - 1095897585961766239846695291589092570872922426047343752202147840/15553639934198164231963559202716335143463771415821
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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:
| (51.783253992949438261 - 6.4412293620053840248e-347j)  +/-  (1.6e-120, 1.6e-120j)
| (28.678118395692194891 - 1.806809112550507091e-343j)  +/-  (9.47e-119, 9.47e-119j)
| (23.626634541626926689 - 3.4954770630271162059e-355j)  +/-  (1.36e-118, 1.36e-118j)
| (19.309874944426835663 + 9.1999414190772160681e-367j)  +/-  (1.66e-118, 1.66e-118j)
| (42.026848970557429045 + 3.0903248213404714487e-377j)  +/-  (1.29e-119, 1.29e-119j)
| (10.222557624887292012 + 1.3118616506664797985e-386j)  +/-  (9.54e-119, 9.54e-119j)
| (5.0200908854391305109 - 1.6003252333404538104e-395j)  +/-  (1.25e-120, 1.25e-120j)
| (34.67524319922209637 - 4.739600673595821746e-398j)  +/-  (4.6e-119, 4.6e-119j)
| (0.5857864376269049512 - 1.2043702036814957613e-400j)  +/-  (1.37e-123, 1.37e-123j)
| (1.274433613066887395 + 2.4688927121481740486e-402j)  +/-  (1.67e-122, 1.67e-122j)
| (6.9239565457104964806 - 5.7078457409099920721e-411j)  +/-  (8.06e-120, 8.06e-120j)
| (12.486507079040894342 + 3.418352135848964655e-426j)  +/-  (1.25e-118, 1.25e-118j)
| (3.4142135623730950488 + 4.3252023067410212211e-437j)  +/-  (2.01e-121, 2.01e-121j)
| (8.8710753718250036791 + 1.4882332960371332023e-445j)  +/-  (5.33e-119, 5.33e-119j)
| (2.1300748791567867555 - 9.7993686362775537292e-457j)  +/-  (3.28e-122, 3.28e-122j)
| (1.0406748406401594478 - 1.1945903642367661032e-456j)  +/-  (7.92e-123, 7.92e-123j)
| (0.47193845768537280597 + 9.3036237748836379734e-456j)  +/-  (3.97e-124, 3.97e-124j)
| (0.087124262377269645901 + 5.6909168067984229701e-458j)  +/-  (7.65e-127, 7.65e-127j)
| (15.609030335612394156 + 1.999979316439848895e-457j)  +/-  (1.37e-118, 1.37e-118j)
-------------------------------------------------
The weights are:
| (3.8321797329731878444e-22 + 3.8461328228665450673e-362j)  +/-  (1.08e-53, 2.4e-112j)
| (1.9226610571576532932e-12 + 2.1082992524913580863e-355j)  +/-  (2.3e-49, 5.12e-108j)
| (2.5545306922155584696e-10 - 1.4609014826011063962e-354j)  +/-  (3.19e-48, 7.12e-107j)
| (1.6417702859217826264e-08 + 1.2541818963032138352e-353j)  +/-  (2.48e-47, 5.52e-106j)
| (4.6297944464845399099e-18 - 1.3126368987405079977e-359j)  +/-  (6.01e-53, 1.34e-111j)
| (5.6545082545772008668e-05 - 8.5202446913980964157e-351j)  +/-  (4.01e-45, 8.95e-104j)
| (0.011644829017462966079 + 8.7890865361658842285e-350j)  +/-  (2.78e-42, 6.19e-101j)
| (5.739803828899468356e-15 + 1.7915341271414835308e-357j)  +/-  (1.39e-51, 3.11e-110j)
| (-0.076558092697712869365 - 1.8152708389060169081e-347j)  +/-  (5.12e-38, 1.14e-96j)
| (0.10011232444602682447 - 1.0309764035903845086e-347j)  +/-  (5.11e-38, 1.14e-96j)
| (0.001987728617560286075 - 3.5252992741001167002e-350j)  +/-  (5e-44, 1.12e-102j)
| (1.0584269630867942821e-05 + 1.1960612180177553715e-351j)  +/-  (1.21e-46, 2.7e-105j)
| (0.047585978236911238618 - 2.7813478789776861488e-349j)  +/-  (4.41e-43, 9.97e-102j)
| (0.00023058952979161526661 + 1.9017125767365368641e-350j)  +/-  (3.91e-45, 8.81e-104j)
| (0.13293218761302182697 + 1.2566282881633618604e-348j)  +/-  (2.14e-42, 4.9e-101j)
| (0.18737453714516435332 + 1.5097830338013127121e-347j)  +/-  (1.94e-41, 4.46e-100j)
| (0.38940345244149501899 + 1.2910468753334633091e-347j)  +/-  (1.62e-41, 3.73e-100j)
| (0.20521875143376840952 - 5.88542807973792029e-349j)  +/-  (1.06e-42, 2.43e-101j)
| (5.6818924935618098028e-07 - 1.1946711604186437553e-352j)  +/-  (3.64e-48, 7.83e-107j)
