Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 30
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Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
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Trying to find an order 30 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
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Ending with final polynomial:
P : 16*t^41 - 301619649563088778451063682584623628227711427092/57830037255501682299341379350291112494566129*t^39 + 44061305853941326460364601899747100471036453899078/57830037255501682299341379350291112494566129*t^37 - 7647591851050245487772550298960785271800510345290055/115660074511003364598682758700582224989132258*t^35 + 881464923656760669869764509446166657228558145369620315/231320149022006729197365517401164449978264516*t^33 - 35727243596735122112718429580841754905696535158630580585/231320149022006729197365517401164449978264516*t^31 + 2104823836693513233598697785245541707616262719986696418785/462640298044013458394731034802328899956529032*t^29 - 91855992354996593084129608758600633298412187385203353773605/925280596088026916789462069604657799913058064*t^27 + 230754895997319292233267389472872505500961880845022941006825/142350860936619525659917241477639661525085856*t^25 - 5659754491512560780947804267276082902768415864275852087678875/284701721873239051319834482955279323050171712*t^23 + 104058237383178305630928517588328108284510911168176570052636375/569403443746478102639668965910558646100343424*t^21 - 355991337644633448265667356636768853667201452526198016383192375/284701721873239051319834482955279323050171712*t^19 + 3580517635529124833097150854801221901273855431437012254858932125/569403443746478102639668965910558646100343424*t^17 - 103901980781688889994547379957039133772327885722338548928788939375/4555227549971824821117351727284469168802747392*t^15 + 529494610732702750468692707285708007136491436693248552928420404375/9110455099943649642234703454568938337605494784*t^13 - 44573745360403046508031797859857973624496269664322603978573699375/444412443899690226450473339247265284761243648*t^11 + 4058812807181001805489168367567995808065253357541727152644427718125/36441820399774598568938813818275753350421979136*t^9 - 335714989384443816763483715637146745412192634737560103898186998125/4555227549971824821117351727284469168802747392*t^7 + 1850274792794892752720147218629515661490573153795278481984996509375/72883640799549197137877627636551506700843958272*t^5 - 1931897254351260203101924567934088034292611995922782025371552553125/583069126396393577103021021092412053606751666176*t^3 + 25578653615964767992711550028943631712038314741116762820425140625/1166138252792787154206042042184824107213503332352*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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