Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 8 26
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Trying to find an order 8 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
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Trying to find an order 26 Kronrod extension for:
P2 : t^13 - 170/3*t^11 + 3251/3*t^9 - 8652*t^7 + 29631*t^5 - 41790*t^3 + 19215*t
Solvable: 1
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Ending with final polynomial:
P : t^39 - 5202701469556038537182507144760312538011811/9207890989550589640350126401413210598967*t^37 + 19654481193003794350865218132958327758101386293/138118364843258844605251896021198158984505*t^35 - 55550904541184988271681382475546863360251560857719/2624248932021918047499786024402765020705595*t^33 + 1817802766725555229379582724133667519208151760409838/874749644007306015833262008134255006901865*t^31 - 373947461850434524809379263644639981933658818225726122/2624248932021918047499786024402765020705595*t^29 + 3698673677557692396122200407566970063998881828345156646/524849786404383609499957204880553004141119*t^27 - 24873622893940691137210408968271370713999018960793431922/97194404889700668425918000903806111877985*t^25 + 133826471553618499891427935449698573721669355066133183200/19438880977940133685183600180761222375597*t^23 - 2671577171734386415108428046274127749825861806698169332760/19438880977940133685183600180761222375597*t^21 + 691411254190403685217980046122371180880909008435410989620/341032999612984801494449125978267059221*t^19 - 7462598584126416825105478164772804250943279917370045434700/341032999612984801494449125978267059221*t^17 + 58008859481133274990470704474801901668979323070873519658890/341032999612984801494449125978267059221*t^15 - 317602106152966413532895946211294843675953342870229920100650/341032999612984801494449125978267059221*t^13 + 1188772725853902644261864502929956510018919502063416387220750/341032999612984801494449125978267059221*t^11 - 2923439501101634933910570427817666712592858731888463300123350/341032999612984801494449125978267059221*t^9 + 4469581812378790930408519025237549274822750886334910652864875/341032999612984801494449125978267059221*t^7 - 3895080142787386768870158242531170359092874858701290916806575/341032999612984801494449125978267059221*t^5 + 1638433588839839559652210405068126022097703781388273519218875/341032999612984801494449125978267059221*t^3 - 218056402088079953964415313268933592554539604993378811144875/341032999612984801494449125978267059221*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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   37 out of 39
Indefinite weights: 0 out of 39
Negative weights:   2 out of 39
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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