Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 8
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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 8 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^17 - 979083/11003*t^15 + 163166982/55015*t^13 - 2614614867/55015*t^11 + 107801282178/275075*t^9 - 454972876533/275075*t^7 + 922004635734/275075*t^5 - 157900293621/55015*t^3 + 44369803107/55015*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: 1
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   17 out of 17
Indefinite weights: 0 out of 17
Negative weights:   0 out of 17
Extension rule has valid weights: 1
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The nodes are:
| (2.948175424779571609 - 6.3584428643078192352e-133j)  +/-  (4.88e-60, 4.88e-60j)
| (-4.6974733674682695184 + 1.1094620760355021557e-131j)  +/-  (4.93e-60, 4.93e-60j)
| (-3.7313022243357029508 - 5.1593288506115241614e-136j)  +/-  (5.78e-60, 5.78e-60j)
| (4.6974733674682695184 + 3.0834001665591130013e-140j)  +/-  (3.94e-60, 3.94e-60j)
| (-5.8752140359939481631 + 1.0244761064039810346e-137j)  +/-  (1.2e-60, 1.2e-60j)
| (3.7313022243357029508 + 1.4957771020754846049e-139j)  +/-  (5.89e-60, 5.89e-60j)
| (-1.9313893809255380161e-138 + 5.2483407090367880873e-139j)  +/-  (3.4e-137, 3.4e-137j)
| (-0.74196378430272585765 + 2.382850363529691652e-148j)  +/-  (4.8e-62, 4.8e-62j)
| (1.6453397661043056661 + 2.0230749233380560791e-153j)  +/-  (6.55e-61, 6.55e-61j)
| (2.3344142183389772393 + 2.0714376015169324197e-154j)  +/-  (2.29e-60, 2.29e-60j)
| (0.74196378430272585765 - 9.0898527661502519684e-154j)  +/-  (4.72e-62, 4.72e-62j)
| (-1.6453397661043056661 - 5.7513882642926379884e-161j)  +/-  (5.81e-61, 5.81e-61j)
| (-2.948175424779571609 - 9.2787698614137285455e-175j)  +/-  (4.88e-60, 4.88e-60j)
| (-1.0379709584894152952 + 4.6833403628464251898e-182j)  +/-  (1.65e-61, 1.65e-61j)
| (-2.3344142183389772393 + 1.0970689636303947836e-186j)  +/-  (2.4e-60, 2.4e-60j)
| (5.8752140359939481631 + 2.2444127733846047127e-190j)  +/-  (1.29e-60, 1.29e-60j)
| (1.0379709584894152952 - 5.1200666392836295009e-190j)  +/-  (1.65e-61, 1.65e-61j)
-------------------------------------------------
The weights are:
| (0.0034720934657563079831 + 8.9205849535940357362e-135j)  +/-  (1.33e-20, 1.31e-49j)
| (6.7800054165279309254e-06 + 2.5368140589903188828e-136j)  +/-  (3.5e-24, 3.46e-53j)
| (0.00033409473641363794051 - 1.7294755748650563751e-135j)  +/-  (8.37e-23, 8.26e-52j)
| (6.7800054165279309254e-06 + 2.5239045801989937848e-138j)  +/-  (4.98e-25, 4.92e-54j)
| (1.7257211497250684825e-08 + 1.1366786399421620526e-138j)  +/-  (3e-26, 2.96e-55j)
| (0.00033409473641363794051 + 7.2468222378545338543e-137j)  +/-  (1.97e-23, 1.94e-52j)
| (0.31249158255138975188 - 2.0774053576956893734e-133j)  +/-  (1.62e-19, 1.6e-48j)
| (0.18173523646896890428 + 3.854872619395435499e-133j)  +/-  (1.03e-19, 1.02e-48j)
| (0.075790688286665234334 + 7.7486127481842806969e-134j)  +/-  (2.89e-20, 2.85e-49j)
| (0.01624012654383245988 - 2.6947120916804963764e-134j)  +/-  (1.56e-21, 1.54e-50j)
| (0.18173523646896890428 + 3.2414100919213756575e-133j)  +/-  (1.75e-20, 1.73e-49j)
| (0.075790688286665234334 + 1.0777366324661075987e-133j)  +/-  (2.28e-21, 2.25e-50j)
| (0.0034720934657563079831 + 1.0273416323412007322e-134j)  +/-  (1.76e-23, 1.73e-52j)
| (0.066175171960040554466 - 3.5955444333516147674e-133j)  +/-  (7.82e-21, 7.77e-50j)
| (0.01624012654383245988 - 3.4445811119151910779e-134j)  +/-  (7.75e-23, 7.63e-52j)
| (1.7257211497250684825e-08 - 6.9489140865122167564e-140j)  +/-  (2.68e-28, 2.67e-57j)
| (0.066175171960040554466 - 2.8399441714394523381e-133j)  +/-  (1.03e-21, 1.01e-50j)
