Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 44
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Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
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Trying to find an order 44 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
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Ending with final polynomial:
P : t^51 - 502801104113177632431699760962800039726305523197440897060431638973/441205073237585111427986598071543479440417793326604661306488215*t^49 + 1578648344836693772765510286824389712465748760765073651756033524771339/2647230439425510668567919588429260876642506759959627967838929290*t^47 - 503867042966654807842557410376747824396673842085911962738813493936065801/2647230439425510668567919588429260876642506759959627967838929290*t^45 + 2442320492300985512437979835094949247982001421045204714070626175476797009/58827343098344681523731546409539130592055705776880621507531762*t^43 - 9429091354233355031527991495031583927646842827348282245342427198885465751/1434813246301089793261745034379003185172090384801966378232482*t^41 + 1122695456505320414296696019614199303262168053123764658509494574071168080233/1434813246301089793261745034379003185172090384801966378232482*t^39 - 102864654767907028028524881724921997713096609682385776580269122840769024019099/1434813246301089793261745034379003185172090384801966378232482*t^37 + 7358912885180672359380219917173250546849355472340251618576003897967460566361081/1434813246301089793261745034379003185172090384801966378232482*t^35 - 414777971664272962311676291438951672762847650279877540245713829824128710409224215/1434813246301089793261745034379003185172090384801966378232482*t^33 + 9254435879929143477638519776476018511091857215662559690204510782845868693610380955/717406623150544896630872517189501592586045192400983189116241*t^31 - 327436308925677321056070661482031501009178932193023187407841986871272754205504433065/717406623150544896630872517189501592586045192400983189116241*t^29 + 9172624170635292761088268343119128239022270991648846358983400634191291698626662741445/717406623150544896630872517189501592586045192400983189116241*t^27 - 202595193177776064810482061291945960611090434717381661527632653783114151947108185282155/717406623150544896630872517189501592586045192400983189116241*t^25 + 3503515113744404513682514953241690798866056186857441444231891709555390205693523507133625/717406623150544896630872517189501592586045192400983189116241*t^23 - 46967162539282914228537165325081273169099960985083571215453007008186421343621787408278875/717406623150544896630872517189501592586045192400983189116241*t^21 + 481634704474466940522161036216038796615078573836684115280559627769417733149372809060592250/717406623150544896630872517189501592586045192400983189116241*t^19 - 3713480797100681575184408829932408495297879590227556073709524867083501707511478311778039250/717406623150544896630872517189501592586045192400983189116241*t^17 + 42116610256241757962203702323850437178982826588543882906261416564058781201408511564071870875/1434813246301089793261745034379003185172090384801966378232482*t^15 - 170829067366143724909574776874798516776125015505559465161527695580501543283320396940118105625/1434813246301089793261745034379003185172090384801966378232482*t^13 + 478443700645597413324555951381348023304569186064074054638290237438917310499473830846786488125/1434813246301089793261745034379003185172090384801966378232482*t^11 - 884839217779094461151583205591670638725305015574576249854656083853450494439105826414928451875/1434813246301089793261745034379003185172090384801966378232482*t^9 + 1019735435000173567567120060098283728257090768966904321912110976940879198724858053717858543125/1434813246301089793261745034379003185172090384801966378232482*t^7 - 673858582897466298140717704369352787723460028257109961088543289073291498794044050963328269375/1434813246301089793261745034379003185172090384801966378232482*t^5 + 218723989830113167227044348670347886187337668236811373747945748063243474216680227475279090625/1434813246301089793261745034379003185172090384801966378232482*t^3 - 22941860727408634407145518307317406655924897303854607634057799027572598365988321418988909375/1434813246301089793261745034379003185172090384801966378232482*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:   49 out of 51
Indefinite weights: 0 out of 51
Negative weights:   2 out of 51
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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