Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 18
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Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 18 Kronrod extension for:
P2 : t^14 - 477/7*t^12 + 11241/7*t^10 - 112815/7*t^8 + 68715*t^6 - 108945*t^4 + 46845*t^2 - 2835
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^32 - 145880276916639796403374251/419448786873338114517800*t^30 + 1690260013507913278170899361837/32297556589247034817870600*t^28 - 145325868536576333709704149190181/32297556589247034817870600*t^26 + 317792788693620937263898185934755/1291902263569881392714824*t^24 - 11637126235344435787790483341866075/1291902263569881392714824*t^22 + 19028882673288851051971116120765393/83889757374667622903560*t^20 - 3664949469168123464050991266713353403/922787331121343851939160*t^18 + 44616380610825570683052977964784550829/922787331121343851939160*t^16 - 74804183090863790563102920048120107763/184557466224268770387832*t^14 + 423410312254280518150564647398840816841/184557466224268770387832*t^12 - 142488140088505333256723661438683784051/16777951474933524580712*t^10 + 328454090406804103160453789439733850061/16777951474933524580712*t^8 - 62459293157586099964924761942781562619/2396850210704789225816*t^6 + 42572530290889973607125231398040112105/2396850210704789225816*t^4 - 11917688480399429337305848980747769785/2396850210704789225816*t^2 + 659823981998511440734350428572845975/2396850210704789225816
-------------------------------------------------
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:
| (-5.5317060638607199116 + 5.347430619293319213e-367j)  +/-  (2.56e-120, 2.56e-120j)
| (-7.8624962137071014161 - 6.2076910365142588067e-369j)  +/-  (3.51e-121, 3.51e-121j)
| (7.8624962137071014161 - 1.6433622511925837811e-369j)  +/-  (3.64e-121, 3.64e-121j)
| (-4.8891513280702986943 - 3.5908880787308661493e-368j)  +/-  (2.34e-120, 2.34e-120j)
| (-8.8994501314713857333 - 3.013249921786975039e-370j)  +/-  (4.76e-122, 4.76e-122j)
| (8.8994501314713857333 + 3.0550713705290741238e-370j)  +/-  (4.73e-122, 4.73e-122j)
| (1.9495339563816251988 + 4.7258153256424042222e-372j)  +/-  (1.24e-122, 1.24e-122j)
| (2.7647027747369714116 - 7.8238505505197706976e-369j)  +/-  (1.41e-121, 1.41e-121j)
| (-6.2335219305467143595 - 1.4188815664654430578e-368j)  +/-  (1.85e-120, 1.85e-120j)
| (-7.0012943577162672854 - 3.2060241491645398491e-369j)  +/-  (9.28e-121, 9.28e-121j)
| (1.4656205133845524345 + 4.870659997254391987e-372j)  +/-  (1.34e-123, 1.34e-123j)
| (3.2762772292662860982 - 4.9012676984141272203e-368j)  +/-  (4.27e-121, 4.27e-121j)
| (-1.9495339563816251988 + 7.5319161737225093426e-375j)  +/-  (1.07e-122, 1.07e-122j)
| (1.0218092793672526883 - 2.661907712322230273e-372j)  +/-  (1.83e-124, 1.83e-124j)
| (3.7896494882343626548 - 6.5635320967194989876e-373j)  +/-  (9.31e-121, 9.31e-121j)
| (4.8891513280702986943 + 1.6500101113436149656e-383j)  +/-  (2.18e-120, 2.18e-120j)
| (2.3344142183389772393 - 2.0560324270400714708e-393j)  +/-  (5.01e-122, 5.01e-122j)
| (-1.0218092793672526883 - 1.5539810137339963652e-397j)  +/-  (2.09e-124, 2.09e-124j)
| (-2.3344142183389772393 + 5.2191062503546119551e-396j)  +/-  (5.29e-122, 5.29e-122j)
| (-4.3114957943342286437 - 9.9078620776365143763e-395j)  +/-  (1.87e-120, 1.87e-120j)
| (4.3114957943342286437 + 1.1118623215577680062e-396j)  +/-  (1.76e-120, 1.76e-120j)
| (6.2335219305467143595 - 3.7004645027378634208e-408j)  +/-  (1.89e-120, 1.89e-120j)
| (-3.2762772292662860982 + 1.5642912794547868336e-419j)  +/-  (4.54e-121, 4.54e-121j)
| (-2.7647027747369714116 - 5.0209002264416866751e-419j)  +/-  (1.59e-121, 1.59e-121j)
| (7.0012943577162672854 + 6.7521341372291346669e-418j)  +/-  (1.12e-120, 1.12e-120j)
| (5.5317060638607199116 + 1.3180937002492086804e-428j)  +/-  (2.56e-120, 2.56e-120j)
| (0.26842728825432580984 - 3.1397903218940337595e-435j)  +/-  (1.43e-126, 1.43e-126j)
| (-0.26842728825432580984 + 5.5870462209517756479e-435j)  +/-  (1.43e-126, 1.43e-126j)
| (-3.7896494882343626548 + 4.3670763779298858452e-431j)  +/-  (9.81e-121, 9.81e-121j)
| (-0.74196378430272585765 + 2.6387945506208687157e-437j)  +/-  (3.34e-125, 3.34e-125j)
| (-1.4656205133845524345 + 1.1286599505254965904e-435j)  +/-  (1.34e-123, 1.34e-123j)
| (0.74196378430272585765 - 6.7907056557537446402e-438j)  +/-  (3.34e-125, 3.34e-125j)
-------------------------------------------------
The weights are:
| (6.0795468869808927002e-08 + 1.2972928041503381932e-373j)  +/-  (3.31e-32, 1.19e-91j)
| (1.3928689238056110879e-14 + 5.3314412077310596226e-379j)  +/-  (3.1e-37, 1.11e-96j)
| (1.3928689238056110879e-14 + 1.6025473810761648106e-379j)  +/-  (7.97e-39, 2.87e-98j)
| (1.5725732046705490252e-06 - 9.1376516301349653071e-373j)  +/-  (2.03e-31, 7.31e-91j)
| (3.0211486237565001668e-18 - 2.25122167601940053e-381j)  +/-  (2.61e-39, 9.41e-99j)
| (3.0211486237565001668e-18 - 8.3829425340554403769e-382j)  +/-  (9e-41, 3.24e-100j)
| (0.026162183935436707454 - 2.1791434006689692362e-370j)  +/-  (9.17e-24, 3.3e-83j)
| (0.0042731876087688043403 - 2.4935424818010156149e-370j)  +/-  (1.06e-27, 3.82e-87j)
| (1.0664854258111884894e-09 + 2.5463778528521235188e-375j)  +/-  (4.57e-35, 1.65e-94j)
| (7.3093644396397136569e-12 - 4.5041644133875322443e-377j)  +/-  (1.88e-36, 6.76e-96j)
| (0.068571425125434216162 - 1.0381370141748178172e-370j)  +/-  (4.49e-23, 1.62e-82j)
| (0.00096659232841869508151 + 1.4058229034858826322e-370j)  +/-  (5.46e-31, 1.97e-90j)
| (0.026162183935436707454 - 1.2503447816460166384e-369j)  +/-  (1.27e-27, 4.59e-87j)
| (0.076570487227320059613 + 1.1277188523048900217e-369j)  +/-  (1.1e-23, 3.98e-83j)
| (0.00015467800388788332597 + 2.0169682972084116572e-371j)  +/-  (5.04e-33, 1.81e-92j)
| (1.5725732046705490252e-06 + 1.3459098200486883235e-373j)  +/-  (1.43e-36, 5.16e-96j)
| (0.0096712922963073126487 + 2.4222081591837972001e-370j)  +/-  (5.05e-29, 1.82e-88j)
| (0.076570487227320059613 - 4.2397008765338943782e-369j)  +/-  (2.25e-26, 8.12e-86j)
| (0.0096712922963073126487 + 7.1400229504782264752e-370j)  +/-  (2.85e-31, 1.03e-90j)
| (1.9963301526817856023e-05 + 4.26332018283068277e-372j)  +/-  (1.96e-35, 7.05e-95j)
| (1.9963301526817856023e-05 - 1.7778847393511293155e-372j)  +/-  (2.96e-35, 1.07e-94j)
| (1.0664854258111884894e-09 + 3.3682406511288785231e-376j)  +/-  (2.57e-40, 9.26e-100j)
| (0.00096659232841869508151 + 6.5566718590011234796e-371j)  +/-  (3.74e-35, 1.35e-94j)
| (0.0042731876087688043403 - 2.4993686974119935967e-370j)  +/-  (4.32e-34, 1.56e-93j)
| (7.3093644396397136569e-12 - 9.9232306641102984488e-378j)  +/-  (4.56e-42, 1.64e-101j)
| (6.0795468869808927002e-08 - 7.7666664579010742398e-375j)  +/-  (3.1e-39, 1.12e-98j)
| (0.20418455708527829005 + 1.7679133521884577295e-369j)  +/-  (1.15e-32, 4.14e-92j)
| (0.20418455708527829005 - 2.3588936831665010856e-369j)  +/-  (7.78e-33, 2.81e-92j)
| (0.00015467800388788332597 - 1.7523612330419208567e-371j)  +/-  (1.04e-36, 3.76e-96j)
| (0.10942399864513895115 + 4.3080684078604968288e-369j)  +/-  (1.29e-33, 4.7e-93j)
| (0.068571425125434216162 + 2.1132481852502344176e-369j)  +/-  (3.23e-34, 1.17e-93j)
| (0.10942399864513895115 - 1.813839540202234611e-369j)  +/-  (6.99e-34, 2.24e-93j)
