Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 42
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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 42 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^53 - 15767333081375341737723581901043029147232858209489011672160283897003807298951/12172946534731404259994921631531913551723325534407284336727305941037734402*t^51 + 345792102701007820316307325774342704052706444046638954170893106972790542378858785/450399021785061957619812100366680801413763044773069520458910319818396172874*t^49 - 62374116066591860369371366533819933204872997053474302072525524589587910306385613657/225199510892530978809906050183340400706881522386534760229455159909198086437*t^47 + 15363094522379800363025724339352992881157304878289759464920368630977069822354959033235/225199510892530978809906050183340400706881522386534760229455159909198086437*t^45 - 2746539313221555841428329734499334148323949964868491524148216810669467630417413288825060/225199510892530978809906050183340400706881522386534760229455159909198086437*t^43 + 369838502195314343538092352487399461076816484582542098546852365127256043327031019037131470/225199510892530978809906050183340400706881522386534760229455159909198086437*t^41 - 38419260470448634277199514212340951805874203529857887322265027440125980776863115530599421875/225199510892530978809906050183340400706881522386534760229455159909198086437*t^39 + 4449762295430423971000791673712187865718096049942738396994014167385340032808240088962146930/320340698282405375263024253461366146097982250905454850966508051079940379*t^37 - 573929144964966403140732628991280119305534435707039647716409588853992675636997577320947449125/640681396564810750526048506922732292195964501810909701933016102159880758*t^35 + 29507184643949478593601088125910514219904822933918704413658527166418048622568738486289559177275/640681396564810750526048506922732292195964501810909701933016102159880758*t^33 - 606788295300064404767433429942068727738198279104274539863224201972653612166885983749240669068150/320340698282405375263024253461366146097982250905454850966508051079940379*t^31 + 19981019133143070139544415855555694914213816725302519397655957663683774629032121909479979180274250/320340698282405375263024253461366146097982250905454850966508051079940379*t^29 - 526019505941375089854350338659962138086041404059324268241475278762282884412605234739950466084660300/320340698282405375263024253461366146097982250905454850966508051079940379*t^27 + 11030028478135654339952922146587589609759312370109926185978777434145412777504057536320329414518886000/320340698282405375263024253461366146097982250905454850966508051079940379*t^25 - 183110211388146793955055342168573900921673063562361421509070774123991365836802173846846299604247586250/320340698282405375263024253461366146097982250905454850966508051079940379*t^23 + 2385863160057886703553802456629312463917108649839639423064829682212715313829651923772578683209402169375/320340698282405375263024253461366146097982250905454850966508051079940379*t^21 - 48227230054961722719503346358058833304230386585118466834553445495294945566136990076466750361234951284375/640681396564810750526048506922732292195964501810909701933016102159880758*t^19 + 372209852058176776776775450786136361523226364255206909916742824722562035559939855340148901447464700493125/640681396564810750526048506922732292195964501810909701933016102159880758*t^17 - 1074263969982152291758628224950542755917583329342234627127495841087224264317580559259049815560619510721875/320340698282405375263024253461366146097982250905454850966508051079940379*t^15 + 4511186473705371948525056930663075034737519006485668680390828153771449799361194357539995267765551303465625/320340698282405375263024253461366146097982250905454850966508051079940379*t^13 - 13275076637172849463472883334828507315562345083127328317657923416531368516568531926978432513028375739275000/320340698282405375263024253461366146097982250905454850966508051079940379*t^11 + 25996033695633918479486874574982081981962139287958172377649767370443395728677214733392152480333497490718750/320340698282405375263024253461366146097982250905454850966508051079940379*t^9 - 31469298621941054344308140001781725247221874412162703326519750530756819627235062541118762304502152432565625/320340698282405375263024253461366146097982250905454850966508051079940379*t^7 + 21068288220735252466816544507863729538874960959399226981218194631352567089607163353929164373208426984562500/320340698282405375263024253461366146097982250905454850966508051079940379*t^5 - 12918673252209893224754169300657155335519160085431261363622093361927833713060258528914584046427006499234375/640681396564810750526048506922732292195964501810909701933016102159880758*t^3 + 1188482173252745613881830180639479086036271425257587123484695822918877507087761617344111972337554040390625/640681396564810750526048506922732292195964501810909701933016102159880758*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:   51 out of 53
Indefinite weights: 0 out of 53
Negative weights:   2 out of 53
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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