Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 30
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 506766691707880816268970589208086207397592012/845539399497391266332019985565096931719317*t^37 + 1755757989450075364289455547230919527050791894448/10992012193466086462316259812346260112351121*t^35 - 275514300962713215483345403545048150877515546057495/10992012193466086462316259812346260112351121*t^33 + 28417359252958387656608830349226950037051580644050790/10992012193466086462316259812346260112351121*t^31 - 2037275074188544674307919427033235083623814133121324370/10992012193466086462316259812346260112351121*t^29 + 104721705070709042843087347493113143656247187722812667270/10992012193466086462316259812346260112351121*t^27 - 302028365436169940597745755269953936163161976198728137970/845539399497391266332019985565096931719317*t^25 + 8326835132398548899323195658665584094385340539792123337000/845539399497391266332019985565096931719317*t^23 - 169043411393546331982836741185826809144749949139297220430250/845539399497391266332019985565096931719317*t^21 + 2516527423084774727073920413863534445623056827723517850477750/845539399497391266332019985565096931719317*t^19 - 27216422392423113812260493510666624023157189047093187518929000/845539399497391266332019985565096931719317*t^17 + 210673544122034545724743341982319018673924094570752648299093250/845539399497391266332019985565096931719317*t^15 - 1142036524988218086672079252639529924989458628521806229579588750/845539399497391266332019985565096931719317*t^13 + 4201444082399457888788016582244248267502792759307953038174596250/845539399497391266332019985565096931719317*t^11 - 10017978217672225491523404012366021328945762146439096723990848750/845539399497391266332019985565096931719317*t^9 + 14462380397535414513503124333658476281847856340206058957955751875/845539399497391266332019985565096931719317*t^7 - 11456879193245709282568598518086964939526280789650273290028321250/845539399497391266332019985565096931719317*t^5 + 4348999188232741762257787387362198593801874617635071710795081250/845539399497391266332019985565096931719317*t^3 - 598452682048084449352711595522475942733186027630331044574053125/845539399497391266332019985565096931719317*t
-------------------------------------------------
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:   35 out of 39
Indefinite weights: 0 out of 39
Negative weights:   4 out of 39
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
