Starting with polynomial:
P : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Extension levels are: 5 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/120*t^30 + 4627841573938565857578236410272540993226431763441132217004474944057802585/697720856087799750269627896997702750475636219152408701580464258114674208*t^29 - 5143944737655869229981172716040915041140522299828402047737318345841452196415/2093162568263399250808883690993108251426908657457226104741392774344022624*t^28 + 1032392900738969370191060698003519129669147565963349687240536407486358631719105/1831517247230474344457773229618969719998545075275072841648718677551019796*t^27 - 54823732262807085887649876644032213474117085266013724789553397875789784647891785/610505749076824781485924409872989906666181691758357613882906225850339932*t^26 + 6451582272125349229451081076724453509953556502051760756904824167239700689185130857/610505749076824781485924409872989906666181691758357613882906225850339932*t^25 - 582328625475566802844299605849465034696446858774038991833131418251622002629120485625/610505749076824781485924409872989906666181691758357613882906225850339932*t^24 + 10331498762887890093346880935257372730099968925202065688359338947483255148936930615000/152626437269206195371481102468247476666545422939589403470726556462584983*t^23 - 586300846610985611195514788973049873914081254023589503535347781805369665977707031995000/152626437269206195371481102468247476666545422939589403470726556462584983*t^22 + 2447288571473562337373523430937641845515196370753246902220531412885435619492038069857500/13875130660836926851952827497113406969685947539962673042793323314780453*t^21 - 13093217404525527535459570254761942976291376016922658893550834793953959570906856716508500/1982161522976703835993261071016200995669421077137524720399046187825779*t^20 + 402075251183987215490295317436829345071654015389781568406089904750280299098519344762900000/1982161522976703835993261071016200995669421077137524720399046187825779*t^19 - 10155805179582880278532087571250794509382838812102246778627579485715903649229353100468700000/1982161522976703835993261071016200995669421077137524720399046187825779*t^18 + 211257340236894316374487018791679548290542668170209178894512552643919799445786149507850100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^17 - 3617760475089774833059166415688683845970135195013551903971847525513748782933549428123750100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^16 + 50908159209599583842967671688931409456030742701014328442219884898256019731351646617521047040000/1982161522976703835993261071016200995669421077137524720399046187825779*t^15 - 586694975017069028896952066934715541633005045550093543848613475550794521342652149183549184000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^14 + 5511021615645875735092295110683602964279971496651208649486859063891091383812057623487893392000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^13 - 41926190845911628670756457359922079618837922833464085262674571274988337797086116228336889936000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^12 + 256248534743986176109121954447098428879553722623714710727862491949398073682488701337721220736000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^11 - 1245623180324424647032212852923514852052177332267439920063307865537807328219585233633024480332800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^10 + 4756128944067924178020114582288946035712877472471876672389613680868902027712907419793050218880000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^9 - 14046193450482049397280083403783477647447797453715854355006729939907188231950753955689903866240000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^8 + 31469686381760312793814800994018330461287326018129172883138985300368828204486565057793734840320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^7 - 52175453954838941982089202898227183686902291383387667779911561964635826719013747208486828216320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^6 + 61934650669086678303464673809230150681874871698039199927515556125786886006857799973694367855820800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^5 - 50254713052503168928001746692495759081712113446159798133809952275638815367792242623871179704320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^4 + 25990400709695870939493483513571371209416875612087402907308738818054795550934387408470523330560000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^3 - 7623405692180946858377564718332492222563033644087784838479592468936751640913651207844493639680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^2 + 1012979347134088540108235161337238911037152329438434593563467069216338217917983746962655559680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t - 34525359066166013663389327896199358418975949757454398692183575380452242358534211431524089856000000/1982161522976703835993261071016200995669421077137524720399046187825779
-------------------------------------------------
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:   29 out of 30
Indefinite weights: 0 out of 30
Negative weights:   1 out of 30
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
Starting with polynomial:
P : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Extension levels are: 5 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : -1/120*t^5 + 5/24*t^4 - 5/3*t^3 + 5*t^2 - 5*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/120*t^30 + 4627841573938565857578236410272540993226431763441132217004474944057802585/697720856087799750269627896997702750475636219152408701580464258114674208*t^29 - 5143944737655869229981172716040915041140522299828402047737318345841452196415/2093162568263399250808883690993108251426908657457226104741392774344022624*t^28 + 1032392900738969370191060698003519129669147565963349687240536407486358631719105/1831517247230474344457773229618969719998545075275072841648718677551019796*t^27 - 54823732262807085887649876644032213474117085266013724789553397875789784647891785/610505749076824781485924409872989906666181691758357613882906225850339932*t^26 + 6451582272125349229451081076724453509953556502051760756904824167239700689185130857/610505749076824781485924409872989906666181691758357613882906225850339932*t^25 - 582328625475566802844299605849465034696446858774038991833131418251622002629120485625/610505749076824781485924409872989906666181691758357613882906225850339932*t^24 + 10331498762887890093346880935257372730099968925202065688359338947483255148936930615000/152626437269206195371481102468247476666545422939589403470726556462584983*t^23 - 586300846610985611195514788973049873914081254023589503535347781805369665977707031995000/152626437269206195371481102468247476666545422939589403470726556462584983*t^22 + 2447288571473562337373523430937641845515196370753246902220531412885435619492038069857500/13875130660836926851952827497113406969685947539962673042793323314780453*t^21 - 13093217404525527535459570254761942976291376016922658893550834793953959570906856716508500/1982161522976703835993261071016200995669421077137524720399046187825779*t^20 + 402075251183987215490295317436829345071654015389781568406089904750280299098519344762900000/1982161522976703835993261071016200995669421077137524720399046187825779*t^19 - 10155805179582880278532087571250794509382838812102246778627579485715903649229353100468700000/1982161522976703835993261071016200995669421077137524720399046187825779*t^18 + 211257340236894316374487018791679548290542668170209178894512552643919799445786149507850100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^17 - 3617760475089774833059166415688683845970135195013551903971847525513748782933549428123750100000/1982161522976703835993261071016200995669421077137524720399046187825779*t^16 + 50908159209599583842967671688931409456030742701014328442219884898256019731351646617521047040000/1982161522976703835993261071016200995669421077137524720399046187825779*t^15 - 586694975017069028896952066934715541633005045550093543848613475550794521342652149183549184000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^14 + 5511021615645875735092295110683602964279971496651208649486859063891091383812057623487893392000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^13 - 41926190845911628670756457359922079618837922833464085262674571274988337797086116228336889936000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^12 + 256248534743986176109121954447098428879553722623714710727862491949398073682488701337721220736000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^11 - 1245623180324424647032212852923514852052177332267439920063307865537807328219585233633024480332800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^10 + 4756128944067924178020114582288946035712877472471876672389613680868902027712907419793050218880000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^9 - 14046193450482049397280083403783477647447797453715854355006729939907188231950753955689903866240000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^8 + 31469686381760312793814800994018330461287326018129172883138985300368828204486565057793734840320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^7 - 52175453954838941982089202898227183686902291383387667779911561964635826719013747208486828216320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^6 + 61934650669086678303464673809230150681874871698039199927515556125786886006857799973694367855820800000/1982161522976703835993261071016200995669421077137524720399046187825779*t^5 - 50254713052503168928001746692495759081712113446159798133809952275638815367792242623871179704320000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^4 + 25990400709695870939493483513571371209416875612087402907308738818054795550934387408470523330560000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^3 - 7623405692180946858377564718332492222563033644087784838479592468936751640913651207844493639680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t^2 + 1012979347134088540108235161337238911037152329438434593563467069216338217917983746962655559680000000/1982161522976703835993261071016200995669421077137524720399046187825779*t - 34525359066166013663389327896199358418975949757454398692183575380452242358534211431524089856000000/1982161522976703835993261071016200995669421077137524720399046187825779
-------------------------------------------------
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:   29 out of 30
Indefinite weights: 0 out of 30
Negative weights:   1 out of 30
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
