Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 20
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Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 20 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^34 - 1688006409519343599558860052543/3642441958493277806607614783*t^32 + 336624437237613799793651018080014/3642441958493277806607614783*t^30 - 268069903794378950702890599183782310/25497093709452944646253303481*t^28 + 213661811712597515665803399061644129270/280468030803982391108786338291*t^26 - 801465532123379609245439608446310259130/21574463907998645469906641407*t^24 + 27088153180427119751412883521241051620630/21574463907998645469906641407*t^22 - 1195644098854259433458847765041929288941510/40066861543426055872683762613*t^20 + 20065445200560783376604427345845373377247300/40066861543426055872683762613*t^18 - 236736007146679146492509235640826313106458600/40066861543426055872683762613*t^16 + 1939091720655802763962854669566540067518991150/40066861543426055872683762613*t^14 - 830024167893438157743094796294719681471204050/3082066272571235067129520201*t^12 + 275904163183924589508896060446759870495108650/280187842961021369739047291*t^10 - 630579557455251488763466230565478612215494750/280187842961021369739047291*t^8 + 119272875381963976684197304263899705128449750/40026834708717338534149613*t^6 - 81085286179309389378125105695623670720235250/40026834708717338534149613*t^4 + 22674878655728214539314553393680084053993375/40026834708717338534149613*t^2 - 1255094291201017792255717299740481308128875/40026834708717338534149613
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   34 out of 34
Indefinite weights: 0 out of 34
Negative weights:   0 out of 34
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.5317060638607199116 + 1.8476345130840678833e-448j)  +/-  (4.81e-120, 4.81e-120j)
| (4.3114957943342286437 + 5.346467062139988985e-456j)  +/-  (2.59e-120, 2.59e-120j)
| (5.5317060638607199116 - 1.1306598837486288413e-464j)  +/-  (4.82e-120, 4.82e-120j)
| (10.882659739547817091 - 2.3174398551433472789e-474j)  +/-  (1.4e-122, 1.4e-122j)
| (6.2245499077309610884 + 2.4490206189332322282e-471j)  +/-  (4.3e-120, 4.3e-120j)
| (6.9775085933549047528 - 2.7084519812826565608e-475j)  +/-  (2.91e-120, 2.91e-120j)
| (8.8077944849057180333 + 9.466206143267820262e-476j)  +/-  (2.99e-121, 2.99e-121j)
| (-8.8077944849057180333 - 1.7582547732257086248e-474j)  +/-  (2.89e-121, 2.89e-121j)
| (-6.2245499077309610884 + 1.5770566594400911492e-477j)  +/-  (4.2e-120, 4.2e-120j)
| (3.2762772292662860982 + 1.9761709827233262855e-487j)  +/-  (6.05e-121, 6.05e-121j)
| (0.74196378430272585765 + 3.2634288364493642461e-492j)  +/-  (3.56e-125, 3.56e-125j)
| (7.8149766449547908634 + 3.2996687270643149861e-487j)  +/-  (1.33e-120, 1.33e-120j)
| (-3.7853118295576782359 - 6.15582075491667158e-486j)  +/-  (1.41e-120, 1.41e-120j)
| (-3.2762772292662860982 + 4.2895379257518149255e-488j)  +/-  (5.74e-121, 5.74e-121j)
| (-10.882659739547817091 - 4.8786262762144463923e-493j)  +/-  (1.42e-122, 1.42e-122j)
| (1.4656205133845524345 + 2.939708793300888582e-494j)  +/-  (1.28e-123, 1.28e-123j)
| (-2.3344142183389772393 + 3.0271119065150876743e-490j)  +/-  (6.11e-122, 6.11e-122j)
| (1.9435342584388270312 - 3.826615415480912888e-493j)  +/-  (1.25e-122, 1.25e-122j)
| (-1.9435342584388270312 + 2.0806296498230323069e-491j)  +/-  (1.26e-122, 1.26e-122j)
| (-2.7708378171696855083 - 4.7622633233529726524e-490j)  +/-  (1.92e-121, 1.92e-121j)
| (-6.9775085933549047528 + 2.8323001789412551984e-491j)  +/-  (2.66e-120, 2.66e-120j)
| (0.26842728825432580984 - 7.8873691599431924507e-501j)  +/-  (1.13e-126, 1.13e-126j)
| (4.8924634190478944026 + 5.5137877160088427583e-495j)  +/-  (3.99e-120, 3.99e-120j)
| (-4.8924634190478944026 - 1.0274869479284106861e-497j)  +/-  (4.08e-120, 4.08e-120j)
| (-1.0249796069946131352 + 2.0071252894952965339e-503j)  +/-  (2e-124, 2e-124j)
| (-7.8149766449547908634 + 1.9717068525683898986e-499j)  +/-  (1.19e-120, 1.19e-120j)
| (2.3344142183389772393 + 2.9340685843869667047e-499j)  +/-  (5.39e-122, 5.39e-122j)
| (2.7708378171696855083 - 1.0520957183062256332e-501j)  +/-  (1.94e-121, 1.94e-121j)
| (-0.26842728825432580984 - 7.2604392459127412059e-511j)  +/-  (1.13e-126, 1.13e-126j)
| (-0.74196378430272585765 - 4.9345482465539058215e-512j)  +/-  (3.54e-125, 3.54e-125j)
| (-4.3114957943342286437 - 1.4490264332726412697e-506j)  +/-  (2.65e-120, 2.65e-120j)
| (3.7853118295576782359 + 2.4741938818907323918e-515j)  +/-  (1.21e-120, 1.21e-120j)
| (1.0249796069946131352 + 7.1000306113755147366e-523j)  +/-  (1.94e-124, 1.94e-124j)
| (-1.4656205133845524345 + 3.5629244522538946678e-521j)  +/-  (1.5e-123, 1.5e-123j)
-------------------------------------------------
The weights are:
| (6.0225958243730571088e-08 + 4.4988683028215774917e-455j)  +/-  (9.14e-27, 1.19e-86j)
| (2.0179103056280466623e-05 - 1.2422511389442133494e-454j)  +/-  (1.55e-23, 2.03e-83j)
| (6.0225958243730571088e-08 - 1.005797024750649482e-456j)  +/-  (3.03e-27, 3.96e-87j)
| (2.4956939821234014644e-25 + 5.955840131228185711e-467j)  +/-  (7.59e-38, 9.92e-98j)
| (1.1098145868342957818e-09 + 5.7107494425059880101e-458j)  +/-  (1.98e-29, 2.59e-89j)
| (8.4345026388747828364e-12 - 2.238475204051361947e-459j)  +/-  (1.97e-31, 2.57e-91j)
| (6.4284422727083928745e-18 - 4.569388705217368134e-463j)  +/-  (2.14e-35, 2.79e-95j)
| (6.4284422727083928745e-18 - 2.0000305369860485674e-462j)  +/-  (5.79e-39, 7.56e-99j)
| (1.1098145868342957818e-09 + 9.6900721342109938371e-457j)  +/-  (5.02e-34, 6.56e-94j)
| (0.00095285527048950717508 - 4.2125661984957442241e-453j)  +/-  (1.16e-25, 1.51e-85j)
| (0.11000834375313551475 - 9.7656160265090701308e-451j)  +/-  (2.57e-22, 3.36e-82j)
| (1.954850605407202716e-14 + 5.1225904554631330486e-461j)  +/-  (8.24e-34, 1.08e-93j)
| (0.00015736363889035554196 - 4.3487439140680007749e-453j)  +/-  (1.48e-29, 1.93e-89j)
| (0.00095285527048950717508 + 1.6451055891133774074e-452j)  +/-  (2.41e-28, 3.15e-88j)
| (2.4956939821234014644e-25 + 1.8269894118766165685e-466j)  +/-  (5.12e-43, 6.69e-103j)
| (0.067877810576929225984 - 3.3770047751958426176e-451j)  +/-  (2.56e-22, 3.35e-82j)
| (0.010022406487822284926 + 1.7676654779950046771e-451j)  +/-  (1.99e-26, 2.6e-86j)
| (0.026216307564818840267 + 1.561698259818817385e-451j)  +/-  (3.2e-25, 4.17e-85j)
| (0.026216307564818840267 - 3.2534861136501132308e-451j)  +/-  (1.24e-25, 1.63e-85j)
| (0.0041791582056292709191 - 6.1192616493701095136e-452j)  +/-  (1.14e-27, 1.49e-87j)
| (8.4345026388747828364e-12 - 1.9367498352730020422e-458j)  +/-  (2.78e-37, 3.63e-97j)
| (0.20413064642821842955 + 7.1109566273860730483e-451j)  +/-  (7.94e-26, 1.04e-85j)
| (1.5472068686013390251e-06 + 1.3118830629777812725e-455j)  +/-  (2.93e-33, 3.83e-93j)
| (1.5472068686013390251e-06 - 2.1392992527444073065e-454j)  +/-  (7.77e-34, 1.02e-93j)
| (0.076433320419914800945 - 1.2083411822384527141e-450j)  +/-  (3.27e-28, 4.26e-88j)
| (1.954850605407202716e-14 + 2.9943718395511052397e-460j)  +/-  (5.82e-39, 7.6e-99j)
| (0.010022406487822284926 - 7.1849195788366938544e-452j)  +/-  (3.82e-30, 4.99e-90j)
| (0.0041791582056292709191 + 2.0348561687686694135e-452j)  +/-  (4.64e-31, 6.04e-91j)
| (0.20413064642821842955 - 7.8362741970997844658e-451j)  +/-  (7.58e-29, 9.84e-89j)
| (0.11000834375313551475 + 1.2791136320328953102e-450j)  +/-  (7.65e-29, 9.85e-89j)
| (2.0179103056280466623e-05 + 1.0020968842467641514e-453j)  +/-  (8.48e-34, 1.12e-93j)
| (0.00015736363889035554196 + 8.1513560512530259323e-454j)  +/-  (4.68e-33, 6.19e-93j)
| (0.076433320419914800945 + 8.3055128781283737128e-451j)  +/-  (7.17e-30, 1e-89j)
| (0.067877810576929225984 + 5.8114865791024577816e-451j)  +/-  (2.48e-30, 3e-90j)
