Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 53
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Trying to find an order 53 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
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Ending with final polynomial:
P : t^59 - 205555454997603146883980831008756902906593676180306089029985/132673921194919697215055115424737796685927620643991976099*t^57 + 1777326364994255897795296631019082593947549087727753325721356885/1592087054339036366580661385096853560231131447727903713188*t^55 - 37224627196886482014538055931819498152121908515010358083042214937565/74828091553934709229291085099552117330863178043211474519836*t^53 + 1644114637476432882710895234222688513856393241500402827199264310592625/10689727364847815604184440728507445332980454006173067788548*t^51 - 875092312374712103952413057945755686293467687545391599585538758348777575/24942697184644903076430361699850705776954392681070491506612*t^49 + 1560367811123195124625010778297693348284440535087202397551962157640223375/254517318210662276290105731631129650785248904908882566394*t^47 - 4554949172537596561807301314739707458393132769254609046411404230356165375/5415262089588559070002249609172971293303168189550692902*t^45 + 498984515675288344700031285962222259665151075602238211907810178042285088875/5415262089588559070002249609172971293303168189550692902*t^43 - 44154444737267688213234914497420528703201556286310790765968105023959202805625/5415262089588559070002249609172971293303168189550692902*t^41 + 6362133319743129571162365018346516557507101947860640463779271045987989225912125/10830524179177118140004499218345942586606336379101385804*t^39 - 375078813454556641849392388769930844920660069000498392807025188729362531553666875/10830524179177118140004499218345942586606336379101385804*t^37 + 18146732720442866735398858105163732264141105938663898490031430120159591498969150625/10830524179177118140004499218345942586606336379101385804*t^35 - 721168827062875188321806728870531964851515348222639465197145478752225096361864891875/10830524179177118140004499218345942586606336379101385804*t^33 + 5880845378509273933865961874192785795526761859832353342746303772445507234177959996875/2707631044794279535001124804586485646651584094775346451*t^31 - 157064642256357322715804846414817759799902558849963517998328454389972274231720359393125/2707631044794279535001124804586485646651584094775346451*t^29 + 3420786110653513436959293880274942800526366982971795929873750227224940238334268492000000/2707631044794279535001124804586485646651584094775346451*t^27 - 60400983194118840455415364645266958210991580063787017761096073311190443287665609956250000/2707631044794279535001124804586485646651584094775346451*t^25 + 3431457909645396039132575065909516061104067393029140770887811584292516814069642961254890625/10830524179177118140004499218345942586606336379101385804*t^23 - 38801406986785180507445473313236612391569366694628403355281078690703161884580833043935234375/10830524179177118140004499218345942586606336379101385804*t^21 + 344691856757157634765926268168141132265690213380672046243318160605729639228519168786658703125/10830524179177118140004499218345942586606336379101385804*t^19 - 2364409103389564646557219884219531593832486673925076721793357281947524556678276967387790859375/10830524179177118140004499218345942586606336379101385804*t^17 + 6121061682853995741517331061532676533796367153829051093952690281616109925650488299163024765625/5415262089588559070002249609172971293303168189550692902*t^15 - 23205073605896841086743901186261945939767328316540385423998149339240769502406093569303545234375/5415262089588559070002249609172971293303168189550692902*t^13 + 61764730945655834205926395233275653792885466455244631642122791484667382522438471616466249609375/5415262089588559070002249609172971293303168189550692902*t^11 - 108681405463364877931730936138327601583208730292026741248918364626163405542344729995832848703125/5415262089588559070002249609172971293303168189550692902*t^9 + 230668175568733918641390634649229670502990146788436910545245406229052798030182942144993969296875/10830524179177118140004499218345942586606336379101385804*t^7 - 126457235627289748868856653701483607915443175041492575578772627945047164916971063680196281328125/10830524179177118140004499218345942586606336379101385804*t^5 + 26085629682060700133836439328208572475254833041841586110129529979524912615708701351635455234375/10830524179177118140004499218345942586606336379101385804*t^3 - 626857223464107267939842839050165807456308493211356266943681713189458130045065848652658203125/10830524179177118140004499218345942586606336379101385804*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:   56 out of 59
Indefinite weights: 0 out of 59
Negative weights:   3 out of 59
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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