Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 25
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Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 25 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
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Ending with final polynomial:
P : t^39 - 17013651128611322459249057766501897729807477/31953937920019321059559451508016970375107*t^37 + 1241262770894434517458510704744418018388014107/9850462065569865890540883547584178837439*t^35 - 391206503039340529035806997814687924653868050514005/22271894730253466778512937701087828351449579*t^33 + 2110996793586087228755617176622671948871383453163530/1310111454720792163441937511828695785379387*t^31 - 2293360292421304682429663202012850311190344844882530030/22271894730253466778512937701087828351449579*t^29 + 80630677623169529255426595482312665004059492936971611070/17031448911370298124745187653773045209932031*t^27 - 46178284975498279919050144725335569867377858214963889245170/289534631493295068120668190114141768568844527*t^25 + 1150422018277957383364709158983357692122752048666848102982000/289534631493295068120668190114141768568844527*t^23 - 3034234681189706654888578674958012027070154504088229736087000/41362090213327866874381170016305966938406361*t^21 + 1008570900387246639814994230818786216794945216380289517199500/1008831468617752850594662683324535778985521*t^19 - 21675503416636886111450942983545687236228982212478527735020500/2176952116490940361809535264016103523074019*t^17 + 9125863598519827703036803619444211213632580332229412505715750/128056006852408256577031486118594324886707*t^15 - 45790696484004459767862184096418027934807339593920115672501250/128056006852408256577031486118594324886707*t^13 + 11960283409063160329211320465549670243638155183413800952711250/9850462065569865890540883547584178837439*t^11 - 26130908423522790268374546670106053385544781001955843243078750/9850462065569865890540883547584178837439*t^9 + 34085073498241368907951010743537937692511276969577753356900625/9850462065569865890540883547584178837439*t^7 - 23488796508238121512286769755164174390988520706906161175989375/9850462065569865890540883547584178837439*t^5 + 6699307328947459913648224063952737677502852871353954934990625/9850462065569865890540883547584178837439*t^3 - 372829467881574034182337011699076919358056582095430286496875/9850462065569865890540883547584178837439*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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