Starting with polynomial:
P : -t+1
Extension levels are: 1 4 22
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : -t^5 + 319/15*t^4 - 2104/15*t^3 + 1656/5*t^2 - 1208/5*t + 152/5
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 18856521758959103379249183738232694199773136290461341249371584286591184870598629445015985796207408067/30691200855129668875975703080086204094093050679665059795078564116501726571420410396927533984625815*t^26 - 1523001897544375505143302468920368857060394332462286964855323206967465903471060219987916313972565439002078/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^25 + 264597237960621776783083729467640217379193439907093932702998030418501405369991398304878709775025658111867602/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^24 - 6318889129877025987683000613080340681071252376414781697192220280235964133386801794063670536015585789844513172/1749398448742391125930615075564913633363303888740908408319478154640598414570963392624869437123671455*t^23 + 2755379887690240584780040810863193710283686941036555317848539503361519360821958961605559164722789274708545501156/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^22 - 60693952763132032443610178020465351694547142761520918745152356334861338438307210792201870016337615631704116439512/2915664081237318543217691792608189388938839814568180680532463591067664024284938987708115728539452425*t^21 + 3112199234224545218106186180781832664148793273879805242266568032615768334098352682169156061315568393705308313186952/2915664081237318543217691792608189388938839814568180680532463591067664024284938987708115728539452425*t^20 - 1324259106314333959831056244884032048181141090598550268907402670006904967353565494934773492861962620271855794667104/30691200855129668875975703080086204094093050679665059795078564116501726571420410396927533984625815*t^19 + 2843003636713742750630851336590061514326672104533562629041049047101878059365216964053530320333248727998516264427040/2046080057008644591731713538672413606272870045311003986338570941100115104761360693128502265641721*t^18 - 122371288285911794655057798755366934945268151881050137969227359652579811455104372460940338964112435229444983770150208/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^17 + 2543862144073983823904866227668469291799559841768986332211648962418620202147911310965308317108456714027232105997219008/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^16 - 42619716465945323072592235750001855177150567234658524482731090087791253565434181939756499518708603674699058211273177088/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^15 + 114993116404744871970578058758580243008854745713603851215102365288633705046550191766019547925775197976647068622328977408/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^14 - 1245540479998403286841146314938650230147624629008307489181765977446459561422791788449728293101473602534694179562972508160/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^13 + 10778785493755298813871611840889168204736978342554905461047466362702058921136390437992000250748119156467374643591759089664/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^12 - 74003783455908627759528338256725700962238742338762914418869586245828134598456029946187822046100801819531332057822324998144/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^11 + 399306375895556567652369091480084038473027676579455106920308324865247290095108171419731028667419661404594470176251948908544/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^10 - 1672450266045827269167705550832951148128760875283122415271578477556348303333376757293932280099699539813595544718748402810880/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^9 + 5350417177661217639838661025813848506645366174993058300222702517221407598730199754027039831637935561675267281248734642995200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^8 - 12798822463849229400240997331838727221637878586554308103682048209511510526353298513969145974206306771180013504979242293002240/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^7 + 22244692076196821974007565118011303775705475268526930967248857825308118282851271836622598743412588940606367059864976699555840/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^6 - 26984535585423624679332028779720657206004136687226213459408498276310663224027261078021442588596982428323896824968048446013440/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^5 + 21540930240557791031196048037006982800298918396498992730817206882589250791756438271393005618503642152286076928526915528294400/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^4 - 10320364404366734539824120673043930585516371302196022274569275872396068912204341572454709835457952637521053872330075930624000/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^3 + 2532895016571774495392249509390951662059175277365553013130606643121339066153134877723076517528347856698896085196923548467200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^2 - 230541468506931457427585408822524489277394556721736038038980026793720230425971652323297438149319492829903845408351662899200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t + 2836885361100743145554145032222133127288397942879393355853592480170515164317378733936938119932660108719727191152603955200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   26 out of 27
Indefinite weights: 0 out of 27
Negative weights:   1 out of 27
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
Starting with polynomial:
P : -t+1
Extension levels are: 1 4 22
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : -t^5 + 319/15*t^4 - 2104/15*t^3 + 1656/5*t^2 - 1208/5*t + 152/5
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 18856521758959103379249183738232694199773136290461341249371584286591184870598629445015985796207408067/30691200855129668875975703080086204094093050679665059795078564116501726571420410396927533984625815*t^26 - 1523001897544375505143302468920368857060394332462286964855323206967465903471060219987916313972565439002078/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^25 + 264597237960621776783083729467640217379193439907093932702998030418501405369991398304878709775025658111867602/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^24 - 6318889129877025987683000613080340681071252376414781697192220280235964133386801794063670536015585789844513172/1749398448742391125930615075564913633363303888740908408319478154640598414570963392624869437123671455*t^23 + 2755379887690240584780040810863193710283686941036555317848539503361519360821958961605559164722789274708545501156/8746992243711955629653075377824568166816519443704542041597390773202992072854816963124347185618357275*t^22 - 60693952763132032443610178020465351694547142761520918745152356334861338438307210792201870016337615631704116439512/2915664081237318543217691792608189388938839814568180680532463591067664024284938987708115728539452425*t^21 + 3112199234224545218106186180781832664148793273879805242266568032615768334098352682169156061315568393705308313186952/2915664081237318543217691792608189388938839814568180680532463591067664024284938987708115728539452425*t^20 - 1324259106314333959831056244884032048181141090598550268907402670006904967353565494934773492861962620271855794667104/30691200855129668875975703080086204094093050679665059795078564116501726571420410396927533984625815*t^19 + 2843003636713742750630851336590061514326672104533562629041049047101878059365216964053530320333248727998516264427040/2046080057008644591731713538672413606272870045311003986338570941100115104761360693128502265641721*t^18 - 122371288285911794655057798755366934945268151881050137969227359652579811455104372460940338964112435229444983770150208/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^17 + 2543862144073983823904866227668469291799559841768986332211648962418620202147911310965308317108456714027232105997219008/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^16 - 42619716465945323072592235750001855177150567234658524482731090087791253565434181939756499518708603674699058211273177088/3410133428347740986219522564454022677121450075518339977230951568500191841268934488547503776069535*t^15 + 114993116404744871970578058758580243008854745713603851215102365288633705046550191766019547925775197976647068622328977408/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^14 - 1245540479998403286841146314938650230147624629008307489181765977446459561422791788449728293101473602534694179562972508160/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^13 + 10778785493755298813871611840889168204736978342554905461047466362702058921136390437992000250748119156467374643591759089664/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^12 - 74003783455908627759528338256725700962238742338762914418869586245828134598456029946187822046100801819531332057822324998144/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^11 + 399306375895556567652369091480084038473027676579455106920308324865247290095108171419731028667419661404594470176251948908544/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^10 - 1672450266045827269167705550832951148128760875283122415271578477556348303333376757293932280099699539813595544718748402810880/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^9 + 5350417177661217639838661025813848506645366174993058300222702517221407598730199754027039831637935561675267281248734642995200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^8 - 12798822463849229400240997331838727221637878586554308103682048209511510526353298513969145974206306771180013504979242293002240/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^7 + 22244692076196821974007565118011303775705475268526930967248857825308118282851271836622598743412588940606367059864976699555840/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^6 - 26984535585423624679332028779720657206004136687226213459408498276310663224027261078021442588596982428323896824968048446013440/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^5 + 21540930240557791031196048037006982800298918396498992730817206882589250791756438271393005618503642152286076928526915528294400/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^4 - 10320364404366734539824120673043930585516371302196022274569275872396068912204341572454709835457952637521053872330075930624000/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^3 + 2532895016571774495392249509390951662059175277365553013130606643121339066153134877723076517528347856698896085196923548467200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t^2 - 230541468506931457427585408822524489277394556721736038038980026793720230425971652323297438149319492829903845408351662899200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907*t + 2836885361100743145554145032222133127288397942879393355853592480170515164317378733936938119932660108719727191152603955200/682026685669548197243904512890804535424290015103667995446190313700038368253786897709500755213907
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   26 out of 27
Indefinite weights: 0 out of 27
Negative weights:   1 out of 27
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
