Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 14
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Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 14 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
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Ending with final polynomial:
P : t^23 - 162172376436644/910428501785*t^21 + 11646855547613196/910428501785*t^19 - 439398131988492519/910428501785*t^17 + 9529093728525786696/910428501785*t^15 - 24508861097128292430/182085700357*t^13 + 16995837407490115902/16553245487*t^11 - 75300371316250818192/16553245487*t^9 + 186327422204203087353/16553245487*t^7 - 242940895669979487162/16553245487*t^5 + 152434641505163676750/16553245487*t^3 - 35261234801507861055/16553245487*t
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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
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The nodes are:
| (-4.515990402576288729 - 3.6666967117203710591e-332j)  +/-  (1.49e-122, 1.49e-122j)
| (-6.2954952329564191026 + 1.5007590803657883614e-336j)  +/-  (7.75e-123, 7.75e-123j)
| (-7.4095174326865003618 - 3.3050656773463606592e-340j)  +/-  (1.51e-123, 1.51e-123j)
| (-3.7313022243357029508 + 7.4233167366910874677e-349j)  +/-  (9.12e-123, 9.12e-123j)
| (2.997526806230110589 - 2.8248719710241935483e-358j)  +/-  (4.63e-123, 4.63e-123j)
| (6.2954952329564191026 - 6.668555605398057778e-365j)  +/-  (7.12e-123, 7.12e-123j)
| (5.3603418042691438892 + 3.9989178962602971061e-365j)  +/-  (1.36e-122, 1.36e-122j)
| (7.4095174326865003618 - 1.2570178852835183402e-366j)  +/-  (1.73e-123, 1.73e-123j)
| (-2.997526806230110589 + 5.1398833902071408788e-365j)  +/-  (4.47e-123, 4.47e-123j)
| (1.7839144719330184867 + 8.6271236102719954935e-369j)  +/-  (6.19e-124, 6.19e-124j)
| (0.74196378430272585765 - 3.7242825108210529258e-374j)  +/-  (2.75e-125, 2.75e-125j)
| (2.3344142183389772393 + 1.1998173296634029232e-373j)  +/-  (1.7e-123, 1.7e-123j)
| (-1.7839144719330184867 + 6.6997269674515240749e-378j)  +/-  (5.94e-124, 5.94e-124j)
| (-1.1394584722652275305 + 6.1456142107450070462e-378j)  +/-  (4.62e-124, 4.62e-124j)
| (1.1394584722652275305 - 5.8433708889050886668e-378j)  +/-  (4.81e-124, 4.81e-124j)
| (-2.3344142183389772393 + 5.3522254909152213004e-379j)  +/-  (1.73e-123, 1.73e-123j)
| (-5.3603418042691438892 + 5.3719027905141743199e-380j)  +/-  (1.43e-122, 1.43e-122j)
| (3.2283069654532297596e-381 - 4.7717451527461072256e-381j)  +/-  (1.33e-379, 1.33e-379j)
| (-1.0379709584894152952 - 1.2298312249345637179e-382j)  +/-  (3.1e-124, 3.1e-124j)
| (-0.74196378430272585765 - 7.45585180116579254e-383j)  +/-  (2.55e-125, 2.55e-125j)
| (4.515990402576288729 + 2.5568314269612778712e-387j)  +/-  (1.44e-122, 1.44e-122j)
| (1.0379709584894152952 - 2.2454214949959241823e-399j)  +/-  (3.22e-124, 3.22e-124j)
| (3.7313022243357029508 + 4.0360412056252234042e-413j)  +/-  (1e-122, 1e-122j)
-------------------------------------------------
The weights are:
| (1.2068119560454270888e-05 - 1.4292715502118691322e-336j)  +/-  (3.13e-42, 1.15e-103j)
| (9.8828858144380079229e-10 + 5.4229960385061887312e-340j)  +/-  (1.17e-45, 4.29e-107j)
| (6.1056972409052184424e-13 - 4.2027847078313830668e-342j)  +/-  (1.99e-47, 7.32e-109j)
| (0.00028718145427405634799 + 6.4612401501365536846e-336j)  +/-  (2.1e-41, 7.71e-103j)
| (0.0031495732523168322476 - 6.2474439732741494743e-336j)  +/-  (5.7e-42, 2.1e-103j)
| (9.8828858144380079229e-10 - 8.9258170004635643653e-341j)  +/-  (1.16e-48, 4.26e-110j)
| (2.0279481479290354915e-07 + 2.7654602985515810856e-339j)  +/-  (1.72e-47, 6.32e-109j)
| (6.1056972409052184424e-13 + 1.0197388322676939086e-342j)  +/-  (1.88e-50, 6.9e-112j)
| (0.0031495732523168322476 - 3.0913024869567370137e-335j)  +/-  (2.35e-43, 8.64e-105j)
| (0.042150126675066029845 - 2.8333968097281345413e-334j)  +/-  (3.51e-41, 1.29e-102j)
| (0.29555701041663664253 + 3.5250087678412144521e-333j)  +/-  (2.99e-40, 1.1e-101j)
| (0.015933695113129631616 + 5.237505549455357886e-335j)  +/-  (1.69e-42, 6.22e-104j)
| (0.042150126675066029845 - 6.5335428460977986651e-334j)  +/-  (5.58e-42, 2.05e-103j)
| (0.36591663023632685868 + 1.1733679625381104232e-332j)  +/-  (1.72e-40, 6.32e-102j)
| (0.36591663023632685868 + 7.0054806170412195135e-333j)  +/-  (5.8e-41, 2.13e-102j)
| (0.015933695113129631616 + 1.6446386736371972226e-334j)  +/-  (3.31e-43, 1.22e-104j)
| (2.0279481479290354915e-07 - 3.234752501241850803e-338j)  +/-  (4.95e-48, 1.83e-109j)
| (0.2804087677714696538 - 1.443958652833383879e-333j)  +/-  (6.79e-42, 2.52e-103j)
| (-0.36321087293675927651 - 1.5360615455995905231e-332j)  +/-  (2.1e-41, 7.74e-103j)
| (0.29555701041663664253 + 4.9110243273450655986e-333j)  +/-  (1.49e-42, 5.96e-104j)
| (1.2068119560454270888e-05 - 4.899266113016117979e-338j)  +/-  (2.68e-48, 9.72e-110j)
| (-0.36321087293675927651 - 9.6191723147756108713e-333j)  +/-  (1.08e-42, 4.63e-104j)
| (0.00028718145427405634799 + 6.1475383098909708446e-337j)  +/-  (3.28e-47, 1.17e-108j)
