Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 22
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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 22 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^31 - 142636938339268560547702324976/394334649438902047439291999*t^29 + 22231957846082443519850935312714/394334649438902047439291999*t^27 - 1969527957204823179534275143880421/394334649438902047439291999*t^25 + 110202597553555404630830260160458875/394334649438902047439291999*t^23 - 4095632244137571713066290378071570000/394334649438902047439291999*t^21 + 5451168717552120426640719256208791050/20754455233626423549436421*t^19 - 94578798240134650855030604178268882575/20754455233626423549436421*t^17 + 1121582156113366272255712317195171533175/20754455233626423549436421*t^15 - 8953922135947127169238259697787867695000/20754455233626423549436421*t^13 + 46789063664233840164130063816460591048250/20754455233626423549436421*t^11 - 153086331990136240261409846974659930367125/20754455233626423549436421*t^9 + 293927126963706132256150583662299207652875/20754455233626423549436421*t^7 - 304209906509161227641175530571704603049000/20754455233626423549436421*t^5 + 153865265459165746367392531794125370768750/20754455233626423549436421*t^3 - 29620971981452253508004310914218154563125/20754455233626423549436421*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   29 out of 31
Indefinite weights: 0 out of 31
Negative weights:   2 out of 31
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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