Starting with polynomial:
P : -t+1
Extension levels are: 1 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^31 + 67969312940235886703858549411577869/72576479020318191789826710781769*t^30 - 29786683293875695993962133392844078050/72576479020318191789826710781769*t^29 + 280209365724904015388149888987955112150/2502637207597179027235403820061*t^28 - 53406235416699222022261167748303157417400/2502637207597179027235403820061*t^27 + 7565771245062056074747274767774205054025720/2502637207597179027235403820061*t^26 - 827526905944281855194439497303961232576315920/2502637207597179027235403820061*t^25 + 71664605798652267199466015247502562118964350000/2502637207597179027235403820061*t^24 - 4999887411078400264758852284400618164283121200000/2502637207597179027235403820061*t^23 + 284479930584653325224622680905441825758269785200000/2502637207597179027235403820061*t^22 - 13313755356340338657434614361771250152173923878880000/2502637207597179027235403820061*t^21 + 515516253992827660084808501524011829863871568904480000/2502637207597179027235403820061*t^20 - 16575731744533694466476127575718602848171133591856000000/2502637207597179027235403820061*t^19 + 443407645885100094495530908307427351565459274936112000000/2502637207597179027235403820061*t^18 - 9870890775650792068425486735249545857439233311120672000000/2502637207597179027235403820061*t^17 + 182649189649852271283407173958881226605785387074622355200000/2502637207597179027235403820061*t^16 - 2801907472354655179442399522431272581731864731013116211200000/2502637207597179027235403820061*t^15 + 35489487048242744360518468167182367411677160911015400960000000/2502637207597179027235403820061*t^14 - 369077850191664558840147885381974429990331260370353617920000000/2502637207597179027235403820061*t^13 + 3128408981228346525689023377468373374025675760458354590720000000/2502637207597179027235403820061*t^12 - 21412566797413588117464465744345287827431042654882080722944000000/2502637207597179027235403820061*t^11 + 116970060025140611011720168746719655751768742855721191215104000000/2502637207597179027235403820061*t^10 - 502558861162091233826633491839057513951327064653584039731200000000/2502637207597179027235403820061*t^9 + 1667316788494178277002348612778600332279056998604806064742400000000/2502637207597179027235403820061*t^8 - 4172672987432209948075446185374139902003377356391973537382400000000/2502637207597179027235403820061*t^7 + 7642369029538024535323473630543810679141367991015416568152064000000/2502637207597179027235403820061*t^6 - 9839490928212347407964869944582886823570007272542013081124864000000/2502637207597179027235403820061*t^5 + 8423370484461295653223938262775389258424185558961171074252800000000/2502637207597179027235403820061*t^4 - 4420629268901614393121077620641245489220229383499532507545600000000/2502637207597179027235403820061*t^3 + 1250039164733974236537901491334398612504818828563245996441600000000/2502637207597179027235403820061*t^2 - 150421186825084947959119944421259356884126103931827472302080000000/2502637207597179027235403820061*t + 4328080161902365517629667419288136519385259055544800378880000000/2502637207597179027235403820061
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (106.28110321052240635 - 1.0432872016291719394e-261j)  +/-  (8.24e-244, 8.24e-244j)
| (55.570758194317364945 + 3.7894445480707800739e-247j)  +/-  (8.84e-240, 8.84e-240j)
| (40.676406324555125894 + 4.2682627698786013394e-248j)  +/-  (1.8e-239, 1.8e-239j)
| (83.708564349438438325 - 1.1003153435377908224e-260j)  +/-  (1.18e-241, 1.18e-241j)
| (93.598276690681730634 + 2.0775354362909992797e-265j)  +/-  (1.6e-242, 1.6e-242j)
| (12.576876531047589877 - 4.947806991066474333e-257j)  +/-  (1.39e-242, 1.39e-242j)
| (61.486189580634274366 + 5.0811055129929103524e-255j)  +/-  (4.41e-240, 4.41e-240j)
| (45.22996059131542469 + 6.892588412417039376e-250j)  +/-  (1.86e-239, 1.86e-239j)
| (50.176555219567277146 - 5.1712786044984756234e-252j)  +/-  (1.31e-239, 1.31e-239j)
| (7.1532118244979652167 - 8.1079080975194743123e-265j)  +/-  (1.06e-244, 1.06e-244j)
| (8.7759702800344133469 - 1.8642678690981412396e-262j)  +/-  (6.39e-244, 6.39e-244j)
| (19.772075212841682778 - 1.893342622001909842e-252j)  +/-  (5.38e-241, 5.38e-241j)
| (4.4364849239644242982 - 6.7311194984547770202e-273j)  +/-  (2.36e-246, 2.36e-246j)
| (22.605155060502080557 - 2.7855572575608891289e-265j)  +/-  (1.46e-240, 1.46e-240j)
| (2.395831024291543202 + 5.478238567302679611e-288j)  +/-  (2.43e-248, 2.43e-248j)
| (3.3336364854875441896 - 1.6042416990647043444e-287j)  +/-  (2.72e-247, 2.72e-247j)
| (1 - 1.2320284899697407027e-289j)  +/-  (1.31e-250, 1.31e-250j)
| (10.58184258235508954 - 1.2466587917732861878e-277j)  +/-  (3.11e-243, 3.11e-243j)
| (68.026754709117049028 + 7.1679735698427111374e-276j)  +/-  (1.85e-240, 1.85e-240j)
| (75.348539929964148165 + 1.1747511101534925001e-285j)  +/-  (5.75e-241, 5.75e-241j)
| (5.7082753048498150581 - 1.3547700563271736703e-298j)  +/-  (1.59e-245, 1.59e-245j)
| (1.6192689113666193986 + 3.1619717385961860895e-314j)  +/-  (1.95e-249, 1.95e-249j)
| (0.04070917969724578898 - 8.784427111366764097e-316j)  +/-  (9.37e-255, 9.37e-255j)
| (25.675301274107261646 - 2.9037855717100769363e-319j)  +/-  (3.13e-240, 3.13e-240j)
| (28.997573457616769094 + 3.2105039927894337258e-368j)  +/-  (6.3e-240, 6.3e-240j)
| (14.768025271865450238 + 8.6526363521729811022e-415j)  +/-  (5.25e-242, 5.25e-242j)
| (0.53368061725937067098 + 1.4228272510515845604e-446j)  +/-  (6.91e-252, 6.91e-252j)
| (0.21551919535491727473 - 4.6976319536224923366e-447j)  +/-  (3.32e-253, 3.32e-253j)
| (32.589933591063587061 + 8.3108899327537094752e-458j)  +/-  (1.08e-239, 1.08e-239j)
| (36.474046857404267242 + 4.7786626462565348659e-481j)  +/-  (1.49e-239, 1.49e-239j)
| (17.163319406295251714 + 4.9086044887412578089e-491j)  +/-  (1.74e-241, 1.74e-241j)
-------------------------------------------------
The weights are:
| (1.0525005357842345565e-45 - 3.4977610940285235316e-282j)  +/-  (1.42e-98, 3.87e-216j)
| (4.142334279654197886e-24 - 9.4931703375959235798e-270j)  +/-  (1.28e-90, 3.47e-208j)
| (9.4432996108599444125e-18 - 2.2485463995613422576e-265j)  +/-  (3.51e-87, 9.53e-205j)
| (3.9863834435543123556e-36 - 9.6699770579212514177e-277j)  +/-  (4.32e-96, 1.17e-213j)
| (2.4549650782756989144e-40 + 4.0836545201607162764e-279j)  +/-  (1.86e-97, 5.06e-215j)
| (7.2187539883317796261e-06 - 4.5873785708580494414e-260j)  +/-  (2.56e-77, 6.96e-195j)
| (1.2296798264655075912e-26 + 2.5378662048840691222e-271j)  +/-  (1.2e-92, 3.27e-210j)
| (1.07859254881011943e-19 - 7.4451051514288124661e-267j)  +/-  (8.27e-90, 2.25e-207j)
| (8.3415622654274767079e-22 + 2.48493897905634372e-268j)  +/-  (1.16e-90, 3.15e-208j)
| (0.0011993551778308769373 + 2.8363119349997854875e-259j)  +/-  (1.21e-75, 3.27e-193j)
| (0.00026454343745880328824 - 1.6130022588752597959e-259j)  +/-  (2.32e-77, 6.3e-195j)
| (7.0388254520668921947e-09 + 6.124943541497404577e-261j)  +/-  (5.21e-85, 1.41e-202j)
| (0.014046942607595543041 + 7.1450239945158184762e-259j)  +/-  (5.51e-74, 1.5e-191j)
| (4.4918654552222788267e-10 + 1.3447683896976511009e-261j)  +/-  (2.92e-86, 7.92e-204j)
| (0.078028802835410524862 + 1.2851239002782904365e-258j)  +/-  (4.71e-71, 1.28e-188j)
| (0.036365497619626297086 - 1.0046523673992922776e-258j)  +/-  (6.9e-73, 1.87e-190j)
| (0.19940122661916804226 + 1.4731561985447058704e-258j)  +/-  (1.76e-71, 4.77e-189j)
| (4.8191991251845414728e-05 + 8.7053787209195932301e-260j)  +/-  (5.52e-80, 1.5e-197j)
| (1.973095915463649081e-29 - 6.1108822431165358965e-273j)  +/-  (2.34e-96, 6.35e-214j)
| (1.4717406711890997138e-32 + 1.0036965158618164915e-274j)  +/-  (8.04e-98, 2.18e-215j)
| (0.0045051419571057782451 - 4.6730994555168166273e-259j)  +/-  (4.67e-79, 1.27e-196j)
| (0.13808207068587151387 - 1.472469478966475368e-258j)  +/-  (9.23e-76, 2.51e-193j)
| (0.10042295978256320974 - 2.4501516400828947142e-259j)  +/-  (3.58e-76, 9.73e-194j)
| (2.2574727830221556131e-11 - 1.6988412650441941349e-262j)  +/-  (4.99e-89, 1.36e-206j)
| (8.8072810086524807655e-13 + 2.6776766960428457814e-263j)  +/-  (2.5e-90, 6.79e-208j)
| (8.8410065617204811049e-07 + 2.4930934577841373927e-260j)  +/-  (1.65e-86, 4.49e-204j)
| (0.2295427359978974159 - 1.2272112783713579561e-258j)  +/-  (6.5e-80, 1.76e-197j)
| (0.19808433300638052997 + 7.6446292985721342922e-259j)  +/-  (7.3e-80, 1.98e-197j)
| (2.6216646100434101735e-14 - 4.6428717716433903728e-264j)  +/-  (1.28e-91, 3.47e-209j)
| (5.8307771301960371693e-16 + 9.841933698068530078e-265j)  +/-  (1.71e-92, 4.65e-210j)
| (8.7915700852766996489e-08 - 1.6351811358356852258e-260j)  +/-  (4.24e-88, 1.15e-205j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^31 + 67969312940235886703858549411577869/72576479020318191789826710781769*t^30 - 29786683293875695993962133392844078050/72576479020318191789826710781769*t^29 + 280209365724904015388149888987955112150/2502637207597179027235403820061*t^28 - 53406235416699222022261167748303157417400/2502637207597179027235403820061*t^27 + 7565771245062056074747274767774205054025720/2502637207597179027235403820061*t^26 - 827526905944281855194439497303961232576315920/2502637207597179027235403820061*t^25 + 71664605798652267199466015247502562118964350000/2502637207597179027235403820061*t^24 - 4999887411078400264758852284400618164283121200000/2502637207597179027235403820061*t^23 + 284479930584653325224622680905441825758269785200000/2502637207597179027235403820061*t^22 - 13313755356340338657434614361771250152173923878880000/2502637207597179027235403820061*t^21 + 515516253992827660084808501524011829863871568904480000/2502637207597179027235403820061*t^20 - 16575731744533694466476127575718602848171133591856000000/2502637207597179027235403820061*t^19 + 443407645885100094495530908307427351565459274936112000000/2502637207597179027235403820061*t^18 - 9870890775650792068425486735249545857439233311120672000000/2502637207597179027235403820061*t^17 + 182649189649852271283407173958881226605785387074622355200000/2502637207597179027235403820061*t^16 - 2801907472354655179442399522431272581731864731013116211200000/2502637207597179027235403820061*t^15 + 35489487048242744360518468167182367411677160911015400960000000/2502637207597179027235403820061*t^14 - 369077850191664558840147885381974429990331260370353617920000000/2502637207597179027235403820061*t^13 + 3128408981228346525689023377468373374025675760458354590720000000/2502637207597179027235403820061*t^12 - 21412566797413588117464465744345287827431042654882080722944000000/2502637207597179027235403820061*t^11 + 116970060025140611011720168746719655751768742855721191215104000000/2502637207597179027235403820061*t^10 - 502558861162091233826633491839057513951327064653584039731200000000/2502637207597179027235403820061*t^9 + 1667316788494178277002348612778600332279056998604806064742400000000/2502637207597179027235403820061*t^8 - 4172672987432209948075446185374139902003377356391973537382400000000/2502637207597179027235403820061*t^7 + 7642369029538024535323473630543810679141367991015416568152064000000/2502637207597179027235403820061*t^6 - 9839490928212347407964869944582886823570007272542013081124864000000/2502637207597179027235403820061*t^5 + 8423370484461295653223938262775389258424185558961171074252800000000/2502637207597179027235403820061*t^4 - 4420629268901614393121077620641245489220229383499532507545600000000/2502637207597179027235403820061*t^3 + 1250039164733974236537901491334398612504818828563245996441600000000/2502637207597179027235403820061*t^2 - 150421186825084947959119944421259356884126103931827472302080000000/2502637207597179027235403820061*t + 4328080161902365517629667419288136519385259055544800378880000000/2502637207597179027235403820061
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (106.28110321052240635 - 1.0432872016291719394e-261j)  +/-  (8.24e-244, 8.24e-244j)
| (55.570758194317364945 + 3.7894445480707800739e-247j)  +/-  (8.84e-240, 8.84e-240j)
| (40.676406324555125894 + 4.2682627698786013394e-248j)  +/-  (1.8e-239, 1.8e-239j)
| (83.708564349438438325 - 1.1003153435377908224e-260j)  +/-  (1.18e-241, 1.18e-241j)
| (93.598276690681730634 + 2.0775354362909992797e-265j)  +/-  (1.6e-242, 1.6e-242j)
| (12.576876531047589877 - 4.947806991066474333e-257j)  +/-  (1.39e-242, 1.39e-242j)
| (61.486189580634274366 + 5.0811055129929103524e-255j)  +/-  (4.41e-240, 4.41e-240j)
| (45.22996059131542469 + 6.892588412417039376e-250j)  +/-  (1.86e-239, 1.86e-239j)
| (50.176555219567277146 - 5.1712786044984756234e-252j)  +/-  (1.31e-239, 1.31e-239j)
| (7.1532118244979652167 - 8.1079080975194743123e-265j)  +/-  (1.06e-244, 1.06e-244j)
| (8.7759702800344133469 - 1.8642678690981412396e-262j)  +/-  (6.39e-244, 6.39e-244j)
| (19.772075212841682778 - 1.893342622001909842e-252j)  +/-  (5.38e-241, 5.38e-241j)
| (4.4364849239644242982 - 6.7311194984547770202e-273j)  +/-  (2.36e-246, 2.36e-246j)
| (22.605155060502080557 - 2.7855572575608891289e-265j)  +/-  (1.46e-240, 1.46e-240j)
| (2.395831024291543202 + 5.478238567302679611e-288j)  +/-  (2.43e-248, 2.43e-248j)
| (3.3336364854875441896 - 1.6042416990647043444e-287j)  +/-  (2.72e-247, 2.72e-247j)
| (1 - 1.2320284899697407027e-289j)  +/-  (1.31e-250, 1.31e-250j)
| (10.58184258235508954 - 1.2466587917732861878e-277j)  +/-  (3.11e-243, 3.11e-243j)
| (68.026754709117049028 + 7.1679735698427111374e-276j)  +/-  (1.85e-240, 1.85e-240j)
| (75.348539929964148165 + 1.1747511101534925001e-285j)  +/-  (5.75e-241, 5.75e-241j)
| (5.7082753048498150581 - 1.3547700563271736703e-298j)  +/-  (1.59e-245, 1.59e-245j)
| (1.6192689113666193986 + 3.1619717385961860895e-314j)  +/-  (1.95e-249, 1.95e-249j)
| (0.04070917969724578898 - 8.784427111366764097e-316j)  +/-  (9.37e-255, 9.37e-255j)
| (25.675301274107261646 - 2.9037855717100769363e-319j)  +/-  (3.13e-240, 3.13e-240j)
| (28.997573457616769094 + 3.2105039927894337258e-368j)  +/-  (6.3e-240, 6.3e-240j)
| (14.768025271865450238 + 8.6526363521729811022e-415j)  +/-  (5.25e-242, 5.25e-242j)
| (0.53368061725937067098 + 1.4228272510515845604e-446j)  +/-  (6.91e-252, 6.91e-252j)
| (0.21551919535491727473 - 4.6976319536224923366e-447j)  +/-  (3.32e-253, 3.32e-253j)
| (32.589933591063587061 + 8.3108899327537094752e-458j)  +/-  (1.08e-239, 1.08e-239j)
| (36.474046857404267242 + 4.7786626462565348659e-481j)  +/-  (1.49e-239, 1.49e-239j)
| (17.163319406295251714 + 4.9086044887412578089e-491j)  +/-  (1.74e-241, 1.74e-241j)
-------------------------------------------------
The weights are:
| (1.0525005357842345565e-45 - 3.4977610940285235316e-282j)  +/-  (1.42e-98, 3.87e-216j)
| (4.142334279654197886e-24 - 9.4931703375959235798e-270j)  +/-  (1.28e-90, 3.47e-208j)
| (9.4432996108599444125e-18 - 2.2485463995613422576e-265j)  +/-  (3.51e-87, 9.53e-205j)
| (3.9863834435543123556e-36 - 9.6699770579212514177e-277j)  +/-  (4.32e-96, 1.17e-213j)
| (2.4549650782756989144e-40 + 4.0836545201607162764e-279j)  +/-  (1.86e-97, 5.06e-215j)
| (7.2187539883317796261e-06 - 4.5873785708580494414e-260j)  +/-  (2.56e-77, 6.96e-195j)
| (1.2296798264655075912e-26 + 2.5378662048840691222e-271j)  +/-  (1.2e-92, 3.27e-210j)
| (1.07859254881011943e-19 - 7.4451051514288124661e-267j)  +/-  (8.27e-90, 2.25e-207j)
| (8.3415622654274767079e-22 + 2.48493897905634372e-268j)  +/-  (1.16e-90, 3.15e-208j)
| (0.0011993551778308769373 + 2.8363119349997854875e-259j)  +/-  (1.21e-75, 3.27e-193j)
| (0.00026454343745880328824 - 1.6130022588752597959e-259j)  +/-  (2.32e-77, 6.3e-195j)
| (7.0388254520668921947e-09 + 6.124943541497404577e-261j)  +/-  (5.21e-85, 1.41e-202j)
| (0.014046942607595543041 + 7.1450239945158184762e-259j)  +/-  (5.51e-74, 1.5e-191j)
| (4.4918654552222788267e-10 + 1.3447683896976511009e-261j)  +/-  (2.92e-86, 7.92e-204j)
| (0.078028802835410524862 + 1.2851239002782904365e-258j)  +/-  (4.71e-71, 1.28e-188j)
| (0.036365497619626297086 - 1.0046523673992922776e-258j)  +/-  (6.9e-73, 1.87e-190j)
| (0.19940122661916804226 + 1.4731561985447058704e-258j)  +/-  (1.76e-71, 4.77e-189j)
| (4.8191991251845414728e-05 + 8.7053787209195932301e-260j)  +/-  (5.52e-80, 1.5e-197j)
| (1.973095915463649081e-29 - 6.1108822431165358965e-273j)  +/-  (2.34e-96, 6.35e-214j)
| (1.4717406711890997138e-32 + 1.0036965158618164915e-274j)  +/-  (8.04e-98, 2.18e-215j)
| (0.0045051419571057782451 - 4.6730994555168166273e-259j)  +/-  (4.67e-79, 1.27e-196j)
| (0.13808207068587151387 - 1.472469478966475368e-258j)  +/-  (9.23e-76, 2.51e-193j)
| (0.10042295978256320974 - 2.4501516400828947142e-259j)  +/-  (3.58e-76, 9.73e-194j)
| (2.2574727830221556131e-11 - 1.6988412650441941349e-262j)  +/-  (4.99e-89, 1.36e-206j)
| (8.8072810086524807655e-13 + 2.6776766960428457814e-263j)  +/-  (2.5e-90, 6.79e-208j)
| (8.8410065617204811049e-07 + 2.4930934577841373927e-260j)  +/-  (1.65e-86, 4.49e-204j)
| (0.2295427359978974159 - 1.2272112783713579561e-258j)  +/-  (6.5e-80, 1.76e-197j)
| (0.19808433300638052997 + 7.6446292985721342922e-259j)  +/-  (7.3e-80, 1.98e-197j)
| (2.6216646100434101735e-14 - 4.6428717716433903728e-264j)  +/-  (1.28e-91, 3.47e-209j)
| (5.8307771301960371693e-16 + 9.841933698068530078e-265j)  +/-  (1.71e-92, 4.65e-210j)
| (8.7915700852766996489e-08 - 1.6351811358356852258e-260j)  +/-  (4.24e-88, 1.15e-205j)
