Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 11 28
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Trying to find an order 11 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 28 Kronrod extension for:
P2 : t^15 - 641/6*t^13 + 29116/7*t^11 - 1045605/14*t^9 + 4515555/7*t^7 - 5082165/2*t^5 + 3863970*t^3 - 2916045/2*t
Solvable: 1
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Ending with final polynomial:
P : t^43 - 21689700740120204064175909610475898581468381110060875112070969083653/31036720677502311127603149011835624176656796705630125785511426728*t^41 + 31990365628308358527850625433428761581283013388075388558475729530731831/144838029828344118595481362055232912824398384626273920332386658064*t^39 - 379183361362781464997768308706121740890658232367292489992064741347709529/9052376864271507412217585128452057051524899039142120020774166129*t^37 + 14676554509044845804596983829975200280562082902230908813695062350451613102073/2751922566738538253314145879049425343663569307899204486315346503216*t^35 - 11873551593737651731357006245967751767126969210192042749198003978109348037445/24570737203022662976019159634369869139853297391957182913529879493*t^33 + 6335308036349144922858234857959136768997246168404240287549894141524401266197465/196565897624181303808153277074958953118826379135657463308239035944*t^31 - 79330580697103707718690203420408912735719696200064976233861321845413284304446205/49141474406045325952038319268739738279706594783914365827059758986*t^29 + 12072006704789286902575708876040078623164625704072721784508531532595027049938931405/196565897624181303808153277074958953118826379135657463308239035944*t^27 - 43821370660092640523506245672315740658421592775431514364982173577986974126553729530/24570737203022662976019159634369869139853297391957182913529879493*t^25 + 971355843046508637194993840207901148969849733293482066032621367546103858858012672125/24570737203022662976019159634369869139853297391957182913529879493*t^23 - 16360620845475494050401781288833812026588471087581647023668756814323392087727431083875/24570737203022662976019159634369869139853297391957182913529879493*t^21 + 10922596230310398671947922155746522398574929821521085409879554336833212858835371211000/1293196694895929630316797875493151007360699862734588574396309447*t^19 - 411723671840606523477413623750747216412481437793141194372288780758017069675219574050375/5172786779583718521267191501972604029442799450938354297585237788*t^17 + 5655548944046286494952532265566443606471830969345793758114349249131268288707329807219125/10345573559167437042534383003945208058885598901876708595170475576*t^15 - 6894339260222245258734201550013621543310460880974331707960147882717761607634144638734375/2586393389791859260633595750986302014721399725469177148792618894*t^13 + 92105253599976559057282763803302338662449801889340034846303367635234888097542251591600625/10345573559167437042534383003945208058885598901876708595170475576*t^11 - 200358846604990143497892619380591232239656237640034645430305291261545320999829746724350625/10345573559167437042534383003945208058885598901876708595170475576*t^9 + 527121529945982154111338651304890275751722155494685909974547290759073631637303028845439375/20691147118334874085068766007890416117771197803753417190340951152*t^7 - 23245829889147206192147203432818313240232752547443430725193749867983176285564775464668125/1293196694895929630316797875493151007360699862734588574396309447*t^5 + 112191711225739870573554388775019421953290737099974799427061635688580606464122896226596875/20691147118334874085068766007890416117771197803753417190340951152*t^3 - 2030705825440907966568944460560334442951858787285077552838731387587942504018136378415625/5172786779583718521267191501972604029442799450938354297585237788*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:   41 out of 43
Indefinite weights: 0 out of 43
Negative weights:   2 out of 43
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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