Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 51
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Trying to find an order 51 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
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Ending with final polynomial:
P : t^57 - 203586876292535540654266768920639615848732915705165690965/141049776424247813923944329821556430467928027552521411*t^55 + 3134687978340154952173007396499728343632914762768811785987685/3244144857757699720250719585895797900762344633707992453*t^53 - 1294045910180305324524661489377233599829465986825938290088028495/3244144857757699720250719585895797900762344633707992453*t^51 + 369455479212914295570555882674778122707047991204971215436788241750/3244144857757699720250719585895797900762344633707992453*t^49 - 77556907010291924541881052888170174811126869930513608322640449617050/3244144857757699720250719585895797900762344633707992453*t^47 + 11493956411216032368282012764831124869267160441834469449483229806750/3001059072856336466466900634501200648253787820266413*t^45 - 1439804255168529847472395730306155781681763165549988649988520053230250/3001059072856336466466900634501200648253787820266413*t^43 + 143353643781945117787937000243803224216658202573045199773572420983807375/3001059072856336466466900634501200648253787820266413*t^41 - 11471242786205005579627598437124392525793802518321441780352279351646025625/3001059072856336466466900634501200648253787820266413*t^39 + 743177651017558247715804334446564957498101614528989868374099845031600582375/3001059072856336466466900634501200648253787820266413*t^37 - 39154530207761771578621716735483812974780216441291272301623922394790058393125/3001059072856336466466900634501200648253787820266413*t^35 + 1681049393587204823783903929440793733476414226145018139593688202606463966232500/3001059072856336466466900634501200648253787820266413*t^33 - 58816813739828245871323564961635712721806750378175833498913682602937886959777500/3001059072856336466466900634501200648253787820266413*t^31 + 1673939212411802247984463180268382939463639071772766717126763745860309062779912500/3001059072856336466466900634501200648253787820266413*t^29 - 38608874329883649283023423027179569040307526873350603678567549964848199165776157500/3001059072856336466466900634501200648253787820266413*t^27 + 717630183337755386221706418854208834761992229985824814232015464663210122223781546875/3001059072856336466466900634501200648253787820266413*t^25 - 10666350011559551998563946657320205835898396395529465834486883506050530110732048328125/3001059072856336466466900634501200648253787820266413*t^23 + 125485611181715296298573002452157708819520445830743644735223860216845644148424615796875/3001059072856336466466900634501200648253787820266413*t^21 - 1153126681564151131472715832986689437943163563286093954334336732337994583566983165390625/3001059072856336466466900634501200648253787820266413*t^19 + 8135868151141290903170092673235325281246583842883080837220472377614833153969830932093750/3001059072856336466466900634501200648253787820266413*t^17 - 43092930625027237964673288030827093082944143799029104577292621665446173297562564455156250/3001059072856336466466900634501200648253787820266413*t^15 + 166277160807902128800544597295911233973377558878503113541691981297126111783425525065468750/3001059072856336466466900634501200648253787820266413*t^13 - 448442456011557295663309792539719764772613508541684354363088373906699283981204323392656250/3001059072856336466466900634501200648253787820266413*t^11 + 796448568064265826588256552731814562453830339243550428222656975558309740024448022578515625/3001059072856336466466900634501200648253787820266413*t^9 - 850091796715687575425240504927023261001213283360958977535183864016280053459031970975359375/3001059072856336466466900634501200648253787820266413*t^7 + 466550268245167084752698356648390805270226131180317092495794897012752493826861516680390625/3001059072856336466466900634501200648253787820266413*t^5 - 95028747902755215175904123448225393698345379376542457130770169160596273441813997034921875/3001059072856336466466900634501200648253787820266413*t^3 + 1870172146981008760171334686160876806834847998167345385345783276541945204045102448750000/3001059072856336466466900634501200648253787820266413*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: 0
  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:   56 out of 57
Indefinite weights: 0 out of 57
Negative weights:   1 out of 57
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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