Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 38
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Trying to find an order 38 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Ending with final polynomial:
P : t^42 - 4045882219562673470908898221/5151895684408414257614025*t^40 + 24376810132734679059613141558852/87582226634943042379438425*t^38 - 5171049819931180062755435552502016/87582226634943042379438425*t^36 + 6993083893890325790949689527087983/834116444142314689327985*t^34 - 41434643274003584747363943829412943/49065673184842040548705*t^32 + 133108651611516588090384987301063008/2133290138471393067335*t^30 - 169285345822931147272588378160755918224/49065673184842040548705*t^28 + 7085649529991605108769941281571063313082/49065673184842040548705*t^26 - 3472265122413101989649699098094001359730/754856510536031393057*t^24 + 3661343774126288084285568102060089692920/32819848284175277959*t^22 - 67360507935408110415252716555874034241520/32819848284175277959*t^20 + 932867496083740574519879794738583700316770/32819848284175277959*t^18 - 9608107725469082448430251652865175961401810/32819848284175277959*t^16 + 72336824877615454460508589802200082636937600/32819848284175277959*t^14 - 388580315202673640832303510933087278607445200/32819848284175277959*t^12 + 1438933380059224246865362547936364112519732275/32819848284175277959*t^10 - 18270911670714842390722255008176392046555025/171831666409294649*t^8 + 5110564143810981789083466260932546938403262700/32819848284175277959*t^6 - 3924662865141826628081179641294639559636914000/32819848284175277959*t^4 + 1186701471380143445471422752077936261452171125/32819848284175277959*t^2 - 58966886019780348627966223500001232220043125/32819848284175277959
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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:   40 out of 42
Indefinite weights: 0 out of 42
Negative weights:   2 out of 42
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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