Starting with polynomial:
P : -t+1
Extension levels are: 1 5 21
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 2178210190657888968032606354325612194224486704314262919444825619290036991465106609625663407543280877317743808349/3649874640193201785901397492262578430773141231849664098068171807573074184576812003754097107266001032496025080*t^26 - 2399318814465907203184766722124249106694462837418849889445565381317149911157153478557093630145858086600214509957371/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^25 + 1377970002347067519129460578657862056320764518832994213986228436644947003395701402144488575495623344911368598766037779/49638295106627544288259005894771066658514720753155431733727136582993808910244643251055720658817614041945941088*t^24 - 40027704506181496633387848371479919398721450707257584549979409750977498186345584282785669915881292518195420289746801079/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^23 + 3400877396383378683687840138766918059922471997164841509018417246003642013129948142699313484283721114110730503788773283383/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^22 - 257978638697711635991149297997887870163763652987769652793112970274155044662581810615249306295964381800492817716544281927637/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^21 + 31408153298737883128080027969345908234436930208248337956204408211055282134246603699680423248933834222336142286552032781639467/35455925076162531634470718496265047613224800537968165524090811844995577793031888036468371899155438601389957920*t^20 - 31108651920226059434206596143685904584229481990948526392195834623341576373810426674976053266843720225440849035660029941191915/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^19 + 984892004920230191288759431217908130074527377404649622794246649489966368328044119346025215836280914139187255464471943646137465/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^18 - 25100816179519702088416347275508680429259560202110764809194516622595424476143610870902964070933583262875809624870727665830730085/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^17 + 30426766050018701323590379069720660921352113383038022724663817846139245285683677226000459632497406125027530036981747824974291073/52141066288474311227162821318036834725330589026423772829545311536758202636811600053629958675228586178514644*t^16 - 127004518372453027409960426477464965205366137734841974113050439474560511740804337815264686670723991466046370644534913678590257952/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^15 + 1717980223524146166672631380480480833123805114890020466710119873432349875608709268573167253192234303765584657692380365490279452000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^14 - 18788082012686348916360546586531854995020497133397669735685776272565598982913244571328442204789394046053551651831413811023795662800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^13 + 165423062979395149280025282295207138173568040861715918572022190752674565192906739947626861705932142242814561038513465215967029128400/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^12 - 1165049325848380523072683413213874162336760509310407022880879443915515898187994726961624664072355206699474495708938241293267631473280/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^11 + 6503447173233608940969685132746028761205632055208055013874032679664531794577329107611586390814757601533568462214074502144327255287680/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^10 - 28416559411501982712907621526925490492441097529614917756353909019224836453799244762796553502104931470509872726931178773578585848528000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^9 + 95577512151735491221181768429735954141574330767227459114813120289580707823285064092536303332790663776785754568196889000082957047824000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^8 - 241963468300567426418555235033867842669565713064139031823889596302106776506204075575451765151853247653788672968046360896615106472960000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^7 + 447262994941184232064911781320080038014072146711467496885094071524014461226712638183607974106612235240422901292653926577438693260492800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^6 - 578884227369599812286816174306864481684736271540943236661021749681007611840781985763953777148696899241937193672637920665718593370444800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^5 + 494221834857096704327692771815708748704342425528190034262174021262361139543307425643644810876267319342144151150338613252239236196480000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^4 - 254594066881147203788504136414773353349324510057564266662008500006176046965883383488840661911264810594536171951999832980938789196800000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^3 + 68540601908648547607492270048404751367032373215496720092263568519665573079962358503130482126575700940294758300401441950390024903680000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^2 - 7399650104028392804493461920183108791804995906252665052938739325766838499893834363208452439021508171450506367689409206248957082624000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t + 168397152523344985552981175571817058735962772517332133926818458618569313685043912927272957029562498643606517043043414848143412224000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661
-------------------------------------------------
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:   25 out of 27
Indefinite weights: 0 out of 27
Negative weights:   2 out of 27
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
Starting with polynomial:
P : -t+1
Extension levels are: 1 5 21
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 2178210190657888968032606354325612194224486704314262919444825619290036991465106609625663407543280877317743808349/3649874640193201785901397492262578430773141231849664098068171807573074184576812003754097107266001032496025080*t^26 - 2399318814465907203184766722124249106694462837418849889445565381317149911157153478557093630145858086600214509957371/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^25 + 1377970002347067519129460578657862056320764518832994213986228436644947003395701402144488575495623344911368598766037779/49638295106627544288259005894771066658514720753155431733727136582993808910244643251055720658817614041945941088*t^24 - 40027704506181496633387848371479919398721450707257584549979409750977498186345584282785669915881292518195420289746801079/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^23 + 3400877396383378683687840138766918059922471997164841509018417246003642013129948142699313484283721114110730503788773283383/12409573776656886072064751473692766664628680188288857933431784145748452227561160812763930164704403510486485272*t^22 - 257978638697711635991149297997887870163763652987769652793112970274155044662581810615249306295964381800492817716544281927637/14599498560772807143605589969050313723092564927398656392272687230292296738307248015016388429064004129984100320*t^21 + 31408153298737883128080027969345908234436930208248337956204408211055282134246603699680423248933834222336142286552032781639467/35455925076162531634470718496265047613224800537968165524090811844995577793031888036468371899155438601389957920*t^20 - 31108651920226059434206596143685904584229481990948526392195834623341576373810426674976053266843720225440849035660029941191915/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^19 + 984892004920230191288759431217908130074527377404649622794246649489966368328044119346025215836280914139187255464471943646137465/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^18 - 25100816179519702088416347275508680429259560202110764809194516622595424476143610870902964070933583262875809624870727665830730085/886398126904063290861767962406626190330620013449204138102270296124889444825797200911709297478885965034748948*t^17 + 30426766050018701323590379069720660921352113383038022724663817846139245285683677226000459632497406125027530036981747824974291073/52141066288474311227162821318036834725330589026423772829545311536758202636811600053629958675228586178514644*t^16 - 127004518372453027409960426477464965205366137734841974113050439474560511740804337815264686670723991466046370644534913678590257952/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^15 + 1717980223524146166672631380480480833123805114890020466710119873432349875608709268573167253192234303765584657692380365490279452000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^14 - 18788082012686348916360546586531854995020497133397669735685776272565598982913244571328442204789394046053551651831413811023795662800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^13 + 165423062979395149280025282295207138173568040861715918572022190752674565192906739947626861705932142242814561038513465215967029128400/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^12 - 1165049325848380523072683413213874162336760509310407022880879443915515898187994726961624664072355206699474495708938241293267631473280/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^11 + 6503447173233608940969685132746028761205632055208055013874032679664531794577329107611586390814757601533568462214074502144327255287680/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^10 - 28416559411501982712907621526925490492441097529614917756353909019224836453799244762796553502104931470509872726931178773578585848528000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^9 + 95577512151735491221181768429735954141574330767227459114813120289580707823285064092536303332790663776785754568196889000082957047824000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^8 - 241963468300567426418555235033867842669565713064139031823889596302106776506204075575451765151853247653788672968046360896615106472960000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^7 + 447262994941184232064911781320080038014072146711467496885094071524014461226712638183607974106612235240422901292653926577438693260492800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^6 - 578884227369599812286816174306864481684736271540943236661021749681007611840781985763953777148696899241937193672637920665718593370444800/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^5 + 494221834857096704327692771815708748704342425528190034262174021262361139543307425643644810876267319342144151150338613252239236196480000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^4 - 254594066881147203788504136414773353349324510057564266662008500006176046965883383488840661911264810594536171951999832980938789196800000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^3 + 68540601908648547607492270048404751367032373215496720092263568519665573079962358503130482126575700940294758300401441950390024903680000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t^2 - 7399650104028392804493461920183108791804995906252665052938739325766838499893834363208452439021508171450506367689409206248957082624000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661*t + 168397152523344985552981175571817058735962772517332133926818458618569313685043912927272957029562498643606517043043414848143412224000/13035266572118577806790705329509208681332647256605943207386327884189550659202900013407489668807146544628661
-------------------------------------------------
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:   25 out of 27
Indefinite weights: 0 out of 27
Negative weights:   2 out of 27
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
