Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 19
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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 19 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^33 - 872360169437103021091115023/2495856217653108003195383*t^31 + 658938700460338068546872737143/12479281088265540015976915*t^29 - 624959668593623264474362082924343/137272091970920940175746065*t^27 + 34219750611530818721219158999289259/137272091970920940175746065*t^25 - 250654077180855141828633011491865145/27454418394184188035149213*t^23 + 900308297364693042806082770570484435/3922059770597741147878459*t^21 - 15704757515709116263320063828337714977/3922059770597741147878459*t^19 + 189898734204661971894897774788765528067/3922059770597741147878459*t^17 - 143093424272692843545447606337655841771/356550888236158286170769*t^15 + 8743611889380386209892869759276280665485/3922059770597741147878459*t^13 - 31339865344802557315448172883482762568695/3922059770597741147878459*t^11 + 6194946759310778915531538349515120163545/356550888236158286170769*t^9 - 7387845987458637803702228754706664432895/356550888236158286170769*t^7 + 4141897815661356296102379763005147426435/356550888236158286170769*t^5 - 937953319370154974082928714110788757825/356550888236158286170769*t^3 + 48681266265163995186847505999767891650/356550888236158286170769*t
-------------------------------------------------
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 - 3.1602874029614583718e-455j)  +/-  (2.22e-120, 2.22e-120j)
| (8.9494758104118199863 + 7.3670817684542100016e-467j)  +/-  (4.7e-122, 4.7e-122j)
| (-7.0295411624517818917 - 8.1617524309333015448e-467j)  +/-  (9.93e-121, 9.93e-121j)
| (-3.8167956440339055704 - 1.1407493206186135438e-466j)  +/-  (9.96e-121, 9.96e-121j)
| (-8.9494758104118199863 + 1.1739828245028292197e-471j)  +/-  (4.5e-122, 4.5e-122j)
| (4.8776410825032950944 - 2.5954595291475325046e-470j)  +/-  (2.15e-120, 2.15e-120j)
| (6.248415122484362435 + 5.2756635510542733074e-479j)  +/-  (1.56e-120, 1.56e-120j)
| (-7.9022429256658591383 - 9.1117006775709331233e-488j)  +/-  (3.11e-121, 3.11e-121j)
| (7.0295411624517818917 + 1.7213659365844309373e-487j)  +/-  (9.93e-121, 9.93e-121j)
| (-1.4656205133845524345 - 1.593100932469475344e-492j)  +/-  (6.96e-124, 6.96e-124j)
| (7.9022429256658591383 + 6.707210018408904023e-490j)  +/-  (3.14e-121, 3.14e-121j)
| (-3.2762772292662860982 + 5.3102112590278945527e-491j)  +/-  (3.44e-121, 3.44e-121j)
| (-4.8776410825032950944 - 1.2032791434370672073e-487j)  +/-  (2.25e-120, 2.25e-120j)
| (-6.248415122484362435 - 6.4617520998136948996e-491j)  +/-  (1.69e-120, 1.69e-120j)
| (-0.74196378430272585765 - 5.9471328909747734031e-496j)  +/-  (1.45e-124, 1.45e-124j)
| (0.6754497858806805618 + 2.3089373777333011218e-496j)  +/-  (9.49e-125, 9.49e-125j)
| (2.6762576351716531394 + 1.5825736137974660462e-491j)  +/-  (1.39e-121, 1.39e-121j)
| (3.2762772292662860982 + 3.7900584524150483427e-491j)  +/-  (3.17e-121, 3.17e-121j)
| (4.3114957943342286437 + 1.1807776218263180096e-493j)  +/-  (1.84e-120, 1.84e-120j)
| (-2.6762576351716531394 - 7.2831099130450065586e-502j)  +/-  (1.35e-121, 1.35e-121j)
| (2.3344142183389772393 - 2.5840268582872668616e-501j)  +/-  (8.6e-122, 8.6e-122j)
| (-4.3114957943342286437 - 1.2765981208930226909e-500j)  +/-  (2.02e-120, 2.02e-120j)
| (-0.26842728825432580984 - 1.8590494686174433954e-509j)  +/-  (1.66e-126, 1.66e-126j)
| (-2.0992737568211646264 - 6.0176078234928565165e-505j)  +/-  (2.51e-122, 2.51e-122j)
| (2.0992737568211646264 - 8.0088215710166083256e-505j)  +/-  (2.31e-122, 2.31e-122j)
| (-5.5317060638607199116 + 1.3571502458031410597e-504j)  +/-  (2.34e-120, 2.34e-120j)
| (1.4656205133845524345 + 1.7045282486037818969e-507j)  +/-  (5.94e-124, 5.94e-124j)
| (3.8167956440339055704 + 4.0000703346928904189e-506j)  +/-  (1.02e-120, 1.02e-120j)
| (0.74196378430272585765 + 1.0648405939083510022e-515j)  +/-  (1.45e-124, 1.45e-124j)
| (-0.6754497858806805618 - 1.4633924213326475327e-515j)  +/-  (9.79e-125, 9.79e-125j)
| (-2.3344142183389772393 + 7.4576139712575179333e-520j)  +/-  (7.76e-122, 7.76e-122j)
| (0.26842728825432580984 - 1.2493917059279733795e-523j)  +/-  (1.66e-126, 1.66e-126j)
| (-1.1204318027721798697e-578 + 1.0511519195905571842e-578j)  +/-  (5.07e-577, 5.07e-577j)
-------------------------------------------------
The weights are:
| (6.2138324101753005416e-08 + 8.6713005108746016862e-462j)  +/-  (1.69e-36, 7.74e-96j)
| (1.9495211162262390229e-18 - 6.1697847217400978216e-470j)  +/-  (2.6e-43, 1.19e-102j)
| (6.0872226903508367605e-12 + 1.9792164547962304831e-466j)  +/-  (5.95e-41, 2.72e-100j)
| (0.00013767807204930280251 - 2.3448575959780743193e-460j)  +/-  (2.11e-33, 9.66e-93j)
| (1.9495211162262390229e-18 + 1.4561590170899360698e-470j)  +/-  (2.16e-44, 9.87e-104j)
| (1.6764637478376596062e-06 - 5.1217100365606584442e-461j)  +/-  (2.04e-36, 9.36e-96j)
| (9.9084430748838375798e-10 + 1.1809316191279981841e-463j)  +/-  (1.52e-39, 6.98e-99j)
| (1.0300326755700778521e-14 - 2.9888638809834606201e-468j)  +/-  (1.41e-43, 6.47e-103j)
| (6.0872226903508367605e-12 - 1.6598240505534371275e-465j)  +/-  (1.55e-41, 7.08e-101j)
| (0.086237557678992302338 + 1.7055964307753378508e-457j)  +/-  (1.27e-27, 5.82e-87j)
| (1.0300326755700778521e-14 + 1.693803861964008891e-467j)  +/-  (2.5e-43, 1.15e-102j)
| (0.0010720902258381459934 + 1.4340919659354332948e-459j)  +/-  (1.54e-35, 7.06e-95j)
| (1.6764637478376596062e-06 - 3.2181952741491633248e-462j)  +/-  (9.01e-40, 4.13e-99j)
| (9.9084430748838375798e-10 - 7.1848529877069538423e-465j)  +/-  (3.43e-42, 1.57e-101j)
| (0.6574203622799573268 - 9.193701961117266451e-456j)  +/-  (1.48e-31, 6.77e-91j)
| (-0.56053898150992365437 + 1.536064446587997094e-455j)  +/-  (4.99e-32, 2.29e-91j)
| (0.0069900512246426819825 - 4.8894168384098427037e-458j)  +/-  (4.66e-36, 2.14e-95j)
| (0.0010720902258381459934 + 5.6004684703774856233e-459j)  +/-  (1.28e-37, 5.88e-97j)
| (1.8874846123207666629e-05 + 2.9484493168957546955e-460j)  +/-  (2.18e-39, 9.96e-99j)
| (0.0069900512246426819825 - 1.7009672728889618264e-458j)  +/-  (5.25e-37, 2.4e-96j)
| (-0.0023991596214200767641 + 1.9193448019977316698e-457j)  +/-  (3.37e-36, 1.54e-95j)
| (1.8874846123207666629e-05 + 3.6550384589949322884e-461j)  +/-  (3.95e-40, 1.81e-99j)
| (0.39370722930174903343 - 9.0790635731361675862e-456j)  +/-  (2.33e-34, 1.07e-93j)
| (0.029342806654525620925 - 1.0417724077071098157e-457j)  +/-  (1.54e-36, 7.06e-96j)
| (0.029342806654525620925 - 2.3160672985258578362e-457j)  +/-  (1.34e-36, 6.14e-96j)
| (6.2138324101753005416e-08 + 1.7749945552374874714e-463j)  +/-  (1.17e-42, 5.37e-102j)
| (0.086237557678992302338 + 2.9351608781410211199e-457j)  +/-  (1.99e-36, 9.12e-96j)
| (0.00013767807204930280251 - 1.2782536616870443868e-459j)  +/-  (1.03e-39, 4.69e-99j)
| (0.6574203622799573268 - 1.2042036381001403061e-455j)  +/-  (5.87e-35, 2.67e-94j)
| (-0.56053898150992365437 + 1.2017617718561043339e-455j)  +/-  (3.44e-35, 1.57e-94j)
| (-0.0023991596214200767641 + 7.8014386561918063484e-458j)  +/-  (1.35e-37, 6.21e-97j)
| (0.39370722930174903343 - 1.0005128301478510507e-455j)  +/-  (7.1e-36, 3.11e-95j)
| (-0.22398049750309532533 + 1.2603523507079348216e-455j)  +/-  (5.41e-36, 2.55e-95j)
