Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 30
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Trying to find an order 7 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 30 Kronrod extension for:
P2 : t^11 - 41*t^9 + 528*t^7 - 2520*t^5 + 4095*t^3 - 1575*t
Solvable: 1
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Ending with final polynomial:
P : t^41 - 75404912390772194612765920646155907056927856773/115660074511003364598682758700582224989132258*t^39 + 22030652926970663230182300949873550235518226949539/115660074511003364598682758700582224989132258*t^37 - 7647591851050245487772550298960785271800510345290055/231320149022006729197365517401164449978264516*t^35 + 881464923656760669869764509446166657228558145369620315/231320149022006729197365517401164449978264516*t^33 - 35727243596735122112718429580841754905696535158630580585/115660074511003364598682758700582224989132258*t^31 + 2104823836693513233598697785245541707616262719986696418785/115660074511003364598682758700582224989132258*t^29 - 91855992354996593084129608758600633298412187385203353773605/115660074511003364598682758700582224989132258*t^27 + 230754895997319292233267389472872505500961880845022941006825/8896928808538720353744827592352478845317866*t^25 - 5659754491512560780947804267276082902768415864275852087678875/8896928808538720353744827592352478845317866*t^23 + 104058237383178305630928517588328108284510911168176570052636375/8896928808538720353744827592352478845317866*t^21 - 711982675289266896531334713273537707334402905052396032766384750/4448464404269360176872413796176239422658933*t^19 + 7161035271058249666194301709602443802547710862874024509717864250/4448464404269360176872413796176239422658933*t^17 - 103901980781688889994547379957039133772327885722338548928788939375/8896928808538720353744827592352478845317866*t^15 + 529494610732702750468692707285708007136491436693248552928420404375/8896928808538720353744827592352478845317866*t^13 - 44573745360403046508031797859857973624496269664322603978573699375/216998263622895618384020185179328752324826*t^11 + 4058812807181001805489168367567995808065253357541727152644427718125/8896928808538720353744827592352478845317866*t^9 - 2685719915075550534107869725097173963297541077900480831185495985000/4448464404269360176872413796176239422658933*t^7 + 1850274792794892752720147218629515661490573153795278481984996509375/4448464404269360176872413796176239422658933*t^5 - 1931897254351260203101924567934088034292611995922782025371552553125/17793857617077440707489655184704957690635732*t^3 + 25578653615964767992711550028943631712038314741116762820425140625/17793857617077440707489655184704957690635732*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:   40 out of 41
Indefinite weights: 0 out of 41
Negative weights:   1 out of 41
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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