Starting with polynomial:
P : -t+1
Extension levels are: 1 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^32 + 1778915425493405355440676172074738689/1776683398289895606164919649702140*t^31 - 835352638071788631685952056281580531649/1776683398289895606164919649702140*t^30 + 8159364141939959900826592118812491232335/59222779942996520205497321656738*t^29 - 1674683700139817540177867787628629495404845/59222779942996520205497321656738*t^28 + 128094709411841867278624455250511524402162490/29611389971498260102748660828369*t^27 - 15174647333025727787987445228039027308297093538/29611389971498260102748660828369*t^26 + 1427884618774080577470926420109035910795779501388/29611389971498260102748660828369*t^25 - 108619677072675626115105545841206699673349082452500/29611389971498260102748660828369*t^24 + 6763895571432077255378877767129278004209785046980000/29611389971498260102748660828369*t^23 - 347877372760263173843783931762288210431304604419300000/29611389971498260102748660828369*t^22 + 14869565470837856278633110104311255035356109513547752000/29611389971498260102748660828369*t^21 - 530395350353236884374134975007257208831254503899751672000/29611389971498260102748660828369*t^20 + 15825666758559463092569327805571562926559137943896106400000/29611389971498260102748660828369*t^19 - 395333074751822607050717694461795322381598452627937984800000/29611389971498260102748660828369*t^18 + 8263944606668503095261105079554927992875229294146615281600000/29611389971498260102748660828369*t^17 - 144295799801476084175469912504652328715437021958256472278080000/29611389971498260102748660828369*t^16 + 2098057037477682163844308547912941486073452646264315573191680000/29611389971498260102748660828369*t^15 - 25289863621370085310136906638124275275989347317406671018624000000/29611389971498260102748660828369*t^14 + 251230884092460638955532182092526803542519219214517993946368000000/29611389971498260102748660828369*t^13 - 2041324460651367151472244152413101679232071803299621016585984000000/29611389971498260102748660828369*t^12 + 13438271662089887340138797939275555669919013971907874178229657600000/29611389971498260102748660828369*t^11 - 70833894338422913886002140726736991895213874252258051906426265600000/29611389971498260102748660828369*t^10 + 294596932762397597396699533858514902634231181126186068837345280000000/29611389971498260102748660828369*t^9 - 949118890093238850404864353750465385623030796074056289938216960000000/29611389971498260102748660828369*t^8 + 2314171218210267672565421518664814015630160270968920569729007616000000/29611389971498260102748660828369*t^7 - 4143511761973475019870197088257438290738566288285561339368954265600000/29611389971498260102748660828369*t^6 + 5234267791298337696284338162810815607821927882737029832331499929600000/29611389971498260102748660828369*t^5 - 4414154672588132767328940661855696572612292304547599296581304320000000/29611389971498260102748660828369*t^4 + 2292334322807428424892851684603913652625422108103247582271242240000000/29611389971498260102748660828369*t^3 - 644781889256076458964024280524163931280804883419587286480322560000000/29611389971498260102748660828369*t^2 + 77659804086441856833573297505439195712772017342993586874744832000000/29611389971498260102748660828369*t - 2253810782595856136920813833911869363980489457245214959992832000000/29611389971498260102748660828369
-------------------------------------------------
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:   32 out of 32
Indefinite weights: 0 out of 32
Negative weights:   0 out of 32
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (110.18111500220769043 - 3.3654367799145280097e-625j)  +/-  (1.6e-243, 1.6e-243j)
| (71.382132446238687123 + 2.3730284510168726422e-619j)  +/-  (4.93e-240, 4.93e-240j)
| (97.337595770758330118 - 3.7584157745182114883e-625j)  +/-  (3.11e-242, 3.11e-242j)
| (58.697467860376837669 - 1.5395570042905321436e-627j)  +/-  (2.57e-239, 2.57e-239j)
| (64.725843630004587071 - 1.9682575721442409536e-654j)  +/-  (1.32e-239, 1.32e-239j)
| (8.5755621433593719098 - 3.5174076527501050507e-672j)  +/-  (8.71e-244, 8.71e-244j)
| (43.472719979540070557 + 1.3540678605951509206e-692j)  +/-  (5.28e-239, 5.28e-239j)
| (28.033273681373039431 + 3.3277411752421468084e-722j)  +/-  (1.26e-239, 1.26e-239j)
| (4.3653117691583378631 - 2.6099185212688035704e-744j)  +/-  (2.53e-246, 2.53e-246j)
| (87.310321782112554873 + 4.4133628174644307413e-737j)  +/-  (2.63e-241, 2.63e-241j)
| (35.167908539876567971 - 1.4108081209959994782e-748j)  +/-  (3.54e-239, 3.54e-239j)
| (3.2906395535138387451 + 1.1364700319868314258e-766j)  +/-  (2.96e-247, 2.96e-247j)
| (2.373856705131960875 + 6.2143586771013242058e-768j)  +/-  (2.92e-248, 2.92e-248j)
| (16.672975936806184584 + 2.7986468683838787663e-758j)  +/-  (3.04e-241, 3.04e-241j)
| (0.5363441316215313973 - 1.0420979354449282857e-770j)  +/-  (8.39e-252, 8.39e-252j)
| (14.364532197901223061 + 7.3495226408557346671e-763j)  +/-  (8.6e-242, 8.6e-242j)
| (24.851846364817006952 - 3.0240772099348860051e-758j)  +/-  (6.64e-240, 6.64e-240j)
| (12.25012937394442338 + 1.3904821759985403339e-766j)  +/-  (2.02e-242, 2.02e-242j)
| (78.823836636020316609 - 1.603761745233201332e-762j)  +/-  (1.41e-240, 1.41e-240j)
| (7.0035491704559071466 - 8.7371554883117872819e-770j)  +/-  (1.43e-244, 1.43e-244j)
| (1.6114353896694797083 - 2.8552718100862129887e-775j)  +/-  (2.01e-249, 2.01e-249j)
| (0.21755491959182036417 - 5.7205832836097489411e-778j)  +/-  (3.47e-253, 3.47e-253j)
| (19.183723985517332058 + 1.3803410518338289063e-764j)  +/-  (9.81e-241, 9.81e-241j)
| (48.13559976485462673 - 4.7842036786331173464e-778j)  +/-  (5.46e-239, 5.46e-239j)
| (31.465892133314354476 - 2.5883578499598810961e-805j)  +/-  (2.3e-239, 2.3e-239j)
| (10.322572441511264904 + 5.0665057618235198677e-822j)  +/-  (4.96e-243, 4.96e-243j)
| (0.041214530322809354351 + 3.5417598019125861703e-836j)  +/-  (1.01e-254, 1.01e-254j)
| (1 - 5.1450115971064648198e-839j)  +/-  (1.84e-250, 1.84e-250j)
| (53.192153505017595116 + 1.4159804654617340773e-836j)  +/-  (4.02e-239, 4.02e-239j)
| (39.16125412929121997 + 1.838679888912678247e-855j)  +/-  (5.18e-239, 5.18e-239j)
| (21.906318880358647675 - 4.4921478216121029352e-862j)  +/-  (2.65e-240, 2.65e-240j)
| (5.6016063041098174217 - 1.6227524582686014436e-868j)  +/-  (2.05e-245, 2.05e-245j)
-------------------------------------------------
The weights are:
| (2.1561317774521667734e-47 + 2.3978261490503273879e-659j)  +/-  (2.5e-97, 1.57e-214j)
| (7.0026481450297890103e-31 - 8.302911136600326518e-650j)  +/-  (5.93e-92, 3.73e-209j)
| (5.9132797542866325105e-42 - 1.873012777018425024e-656j)  +/-  (5.69e-96, 3.58e-213j)
| (1.8529495771421672761e-25 - 6.702517864487715026e-648j)  +/-  (3e-90, 1.89e-207j)
| (4.9061617901603639915e-28 + 6.591100427287358595e-649j)  +/-  (4.11e-91, 2.59e-208j)
| (0.00031292013154504283304 + 4.7834106311092198036e-638j)  +/-  (3.73e-71, 2.35e-188j)
| (5.9075890947759384141e-19 + 5.3827920179561165095e-645j)  +/-  (4.12e-88, 2.59e-205j)
| (2.2099241595204712621e-12 + 6.5604130808572724846e-642j)  +/-  (1.83e-84, 1.15e-201j)
| (0.014678816092472531462 - 2.6987233660755997549e-637j)  +/-  (6.09e-67, 3.83e-184j)
| (1.1031168348639703513e-37 + 4.1598014569008340076e-654j)  +/-  (5.93e-96, 3.73e-213j)
| (2.048882078828774837e-15 + 2.4203695482954675896e-643j)  +/-  (1.51e-86, 9.53e-204j)
| (0.03704853524886617041 + 3.9327700161161005216e-637j)  +/-  (3.21e-66, 2.02e-183j)
| (0.078131007669690413733 - 5.1311901076688987268e-637j)  +/-  (5.11e-64, 3.22e-181j)
| (1.3826003175305045655e-07 + 1.2506995039413979646e-639j)  +/-  (5.5e-81, 3.46e-198j)
| (0.22855559532442857518 + 4.8539268505668275589e-637j)  +/-  (1.22e-65, 7.69e-183j)
| (1.2763888057126612989e-06 - 3.5934298714158935005e-639j)  +/-  (6.89e-80, 4.34e-197j)
| (4.9301866528029225071e-11 - 2.8651532890382476362e-641j)  +/-  (1.44e-84, 9.05e-202j)
| (9.6640196906326715175e-06 + 9.3676837535519673234e-639j)  +/-  (3.07e-79, 1.93e-196j)
| (4.6272102814233286609e-34 - 5.7537487203720765207e-652j)  +/-  (5.88e-96, 3.7e-213j)
| (0.0013504398818546797619 - 9.3784996982107914251e-638j)  +/-  (8.03e-77, 5.06e-194j)
| (0.13700161292869457313 + 5.9164653069800320254e-637j)  +/-  (1.41e-70, 8.9e-188j)
| (0.19887643324408682992 - 2.9834196888329143592e-637j)  +/-  (4.19e-70, 2.64e-187j)
| (1.2192140669099267008e-08 - 3.940482698694669101e-640j)  +/-  (5.25e-83, 3.31e-200j)
| (6.0377390629549568671e-21 - 6.5586665424411435885e-646j)  +/-  (3.58e-91, 2.26e-208j)
| (7.6997187967630975056e-14 - 1.338543200118542677e-642j)  +/-  (1.87e-87, 1.18e-204j)
| (6.0382009057298158303e-05 - 2.2194370384799975346e-638j)  +/-  (2.18e-81, 1.37e-198j)
| (0.10154354436279499917 + 9.467680499197424972e-638j)  +/-  (6.91e-76, 4.35e-193j)
| (0.19756211518823295015 - 5.8933218237004277875e-637j)  +/-  (2.03e-76, 1.28e-193j)
| (4.1762521696313644701e-23 + 6.9951907146951929608e-647j)  +/-  (2.06e-92, 1.3e-209j)
| (4.0762993895530644137e-17 - 3.8561236321467927141e-644j)  +/-  (1.59e-89, 1e-206j)
| (8.675819407743245448e-10 + 1.1204811499048951422e-640j)  +/-  (9.17e-86, 5.78e-203j)
| (0.0048675061384343497113 + 1.6709800549067187268e-637j)  +/-  (6.37e-82, 4e-199j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^32 + 1778915425493405355440676172074738689/1776683398289895606164919649702140*t^31 - 835352638071788631685952056281580531649/1776683398289895606164919649702140*t^30 + 8159364141939959900826592118812491232335/59222779942996520205497321656738*t^29 - 1674683700139817540177867787628629495404845/59222779942996520205497321656738*t^28 + 128094709411841867278624455250511524402162490/29611389971498260102748660828369*t^27 - 15174647333025727787987445228039027308297093538/29611389971498260102748660828369*t^26 + 1427884618774080577470926420109035910795779501388/29611389971498260102748660828369*t^25 - 108619677072675626115105545841206699673349082452500/29611389971498260102748660828369*t^24 + 6763895571432077255378877767129278004209785046980000/29611389971498260102748660828369*t^23 - 347877372760263173843783931762288210431304604419300000/29611389971498260102748660828369*t^22 + 14869565470837856278633110104311255035356109513547752000/29611389971498260102748660828369*t^21 - 530395350353236884374134975007257208831254503899751672000/29611389971498260102748660828369*t^20 + 15825666758559463092569327805571562926559137943896106400000/29611389971498260102748660828369*t^19 - 395333074751822607050717694461795322381598452627937984800000/29611389971498260102748660828369*t^18 + 8263944606668503095261105079554927992875229294146615281600000/29611389971498260102748660828369*t^17 - 144295799801476084175469912504652328715437021958256472278080000/29611389971498260102748660828369*t^16 + 2098057037477682163844308547912941486073452646264315573191680000/29611389971498260102748660828369*t^15 - 25289863621370085310136906638124275275989347317406671018624000000/29611389971498260102748660828369*t^14 + 251230884092460638955532182092526803542519219214517993946368000000/29611389971498260102748660828369*t^13 - 2041324460651367151472244152413101679232071803299621016585984000000/29611389971498260102748660828369*t^12 + 13438271662089887340138797939275555669919013971907874178229657600000/29611389971498260102748660828369*t^11 - 70833894338422913886002140726736991895213874252258051906426265600000/29611389971498260102748660828369*t^10 + 294596932762397597396699533858514902634231181126186068837345280000000/29611389971498260102748660828369*t^9 - 949118890093238850404864353750465385623030796074056289938216960000000/29611389971498260102748660828369*t^8 + 2314171218210267672565421518664814015630160270968920569729007616000000/29611389971498260102748660828369*t^7 - 4143511761973475019870197088257438290738566288285561339368954265600000/29611389971498260102748660828369*t^6 + 5234267791298337696284338162810815607821927882737029832331499929600000/29611389971498260102748660828369*t^5 - 4414154672588132767328940661855696572612292304547599296581304320000000/29611389971498260102748660828369*t^4 + 2292334322807428424892851684603913652625422108103247582271242240000000/29611389971498260102748660828369*t^3 - 644781889256076458964024280524163931280804883419587286480322560000000/29611389971498260102748660828369*t^2 + 77659804086441856833573297505439195712772017342993586874744832000000/29611389971498260102748660828369*t - 2253810782595856136920813833911869363980489457245214959992832000000/29611389971498260102748660828369
-------------------------------------------------
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:   32 out of 32
Indefinite weights: 0 out of 32
Negative weights:   0 out of 32
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (110.18111500220769043 - 3.3654367799145280097e-625j)  +/-  (1.6e-243, 1.6e-243j)
| (71.382132446238687123 + 2.3730284510168726422e-619j)  +/-  (4.93e-240, 4.93e-240j)
| (97.337595770758330118 - 3.7584157745182114883e-625j)  +/-  (3.11e-242, 3.11e-242j)
| (58.697467860376837669 - 1.5395570042905321436e-627j)  +/-  (2.57e-239, 2.57e-239j)
| (64.725843630004587071 - 1.9682575721442409536e-654j)  +/-  (1.32e-239, 1.32e-239j)
| (8.5755621433593719098 - 3.5174076527501050507e-672j)  +/-  (8.71e-244, 8.71e-244j)
| (43.472719979540070557 + 1.3540678605951509206e-692j)  +/-  (5.28e-239, 5.28e-239j)
| (28.033273681373039431 + 3.3277411752421468084e-722j)  +/-  (1.26e-239, 1.26e-239j)
| (4.3653117691583378631 - 2.6099185212688035704e-744j)  +/-  (2.53e-246, 2.53e-246j)
| (87.310321782112554873 + 4.4133628174644307413e-737j)  +/-  (2.63e-241, 2.63e-241j)
| (35.167908539876567971 - 1.4108081209959994782e-748j)  +/-  (3.54e-239, 3.54e-239j)
| (3.2906395535138387451 + 1.1364700319868314258e-766j)  +/-  (2.96e-247, 2.96e-247j)
| (2.373856705131960875 + 6.2143586771013242058e-768j)  +/-  (2.92e-248, 2.92e-248j)
| (16.672975936806184584 + 2.7986468683838787663e-758j)  +/-  (3.04e-241, 3.04e-241j)
| (0.5363441316215313973 - 1.0420979354449282857e-770j)  +/-  (8.39e-252, 8.39e-252j)
| (14.364532197901223061 + 7.3495226408557346671e-763j)  +/-  (8.6e-242, 8.6e-242j)
| (24.851846364817006952 - 3.0240772099348860051e-758j)  +/-  (6.64e-240, 6.64e-240j)
| (12.25012937394442338 + 1.3904821759985403339e-766j)  +/-  (2.02e-242, 2.02e-242j)
| (78.823836636020316609 - 1.603761745233201332e-762j)  +/-  (1.41e-240, 1.41e-240j)
| (7.0035491704559071466 - 8.7371554883117872819e-770j)  +/-  (1.43e-244, 1.43e-244j)
| (1.6114353896694797083 - 2.8552718100862129887e-775j)  +/-  (2.01e-249, 2.01e-249j)
| (0.21755491959182036417 - 5.7205832836097489411e-778j)  +/-  (3.47e-253, 3.47e-253j)
| (19.183723985517332058 + 1.3803410518338289063e-764j)  +/-  (9.81e-241, 9.81e-241j)
| (48.13559976485462673 - 4.7842036786331173464e-778j)  +/-  (5.46e-239, 5.46e-239j)
| (31.465892133314354476 - 2.5883578499598810961e-805j)  +/-  (2.3e-239, 2.3e-239j)
| (10.322572441511264904 + 5.0665057618235198677e-822j)  +/-  (4.96e-243, 4.96e-243j)
| (0.041214530322809354351 + 3.5417598019125861703e-836j)  +/-  (1.01e-254, 1.01e-254j)
| (1 - 5.1450115971064648198e-839j)  +/-  (1.84e-250, 1.84e-250j)
| (53.192153505017595116 + 1.4159804654617340773e-836j)  +/-  (4.02e-239, 4.02e-239j)
| (39.16125412929121997 + 1.838679888912678247e-855j)  +/-  (5.18e-239, 5.18e-239j)
| (21.906318880358647675 - 4.4921478216121029352e-862j)  +/-  (2.65e-240, 2.65e-240j)
| (5.6016063041098174217 - 1.6227524582686014436e-868j)  +/-  (2.05e-245, 2.05e-245j)
-------------------------------------------------
The weights are:
| (2.1561317774521667734e-47 + 2.3978261490503273879e-659j)  +/-  (2.5e-97, 1.57e-214j)
| (7.0026481450297890103e-31 - 8.302911136600326518e-650j)  +/-  (5.93e-92, 3.73e-209j)
| (5.9132797542866325105e-42 - 1.873012777018425024e-656j)  +/-  (5.69e-96, 3.58e-213j)
| (1.8529495771421672761e-25 - 6.702517864487715026e-648j)  +/-  (3e-90, 1.89e-207j)
| (4.9061617901603639915e-28 + 6.591100427287358595e-649j)  +/-  (4.11e-91, 2.59e-208j)
| (0.00031292013154504283304 + 4.7834106311092198036e-638j)  +/-  (3.73e-71, 2.35e-188j)
| (5.9075890947759384141e-19 + 5.3827920179561165095e-645j)  +/-  (4.12e-88, 2.59e-205j)
| (2.2099241595204712621e-12 + 6.5604130808572724846e-642j)  +/-  (1.83e-84, 1.15e-201j)
| (0.014678816092472531462 - 2.6987233660755997549e-637j)  +/-  (6.09e-67, 3.83e-184j)
| (1.1031168348639703513e-37 + 4.1598014569008340076e-654j)  +/-  (5.93e-96, 3.73e-213j)
| (2.048882078828774837e-15 + 2.4203695482954675896e-643j)  +/-  (1.51e-86, 9.53e-204j)
| (0.03704853524886617041 + 3.9327700161161005216e-637j)  +/-  (3.21e-66, 2.02e-183j)
| (0.078131007669690413733 - 5.1311901076688987268e-637j)  +/-  (5.11e-64, 3.22e-181j)
| (1.3826003175305045655e-07 + 1.2506995039413979646e-639j)  +/-  (5.5e-81, 3.46e-198j)
| (0.22855559532442857518 + 4.8539268505668275589e-637j)  +/-  (1.22e-65, 7.69e-183j)
| (1.2763888057126612989e-06 - 3.5934298714158935005e-639j)  +/-  (6.89e-80, 4.34e-197j)
| (4.9301866528029225071e-11 - 2.8651532890382476362e-641j)  +/-  (1.44e-84, 9.05e-202j)
| (9.6640196906326715175e-06 + 9.3676837535519673234e-639j)  +/-  (3.07e-79, 1.93e-196j)
| (4.6272102814233286609e-34 - 5.7537487203720765207e-652j)  +/-  (5.88e-96, 3.7e-213j)
| (0.0013504398818546797619 - 9.3784996982107914251e-638j)  +/-  (8.03e-77, 5.06e-194j)
| (0.13700161292869457313 + 5.9164653069800320254e-637j)  +/-  (1.41e-70, 8.9e-188j)
| (0.19887643324408682992 - 2.9834196888329143592e-637j)  +/-  (4.19e-70, 2.64e-187j)
| (1.2192140669099267008e-08 - 3.940482698694669101e-640j)  +/-  (5.25e-83, 3.31e-200j)
| (6.0377390629549568671e-21 - 6.5586665424411435885e-646j)  +/-  (3.58e-91, 2.26e-208j)
| (7.6997187967630975056e-14 - 1.338543200118542677e-642j)  +/-  (1.87e-87, 1.18e-204j)
| (6.0382009057298158303e-05 - 2.2194370384799975346e-638j)  +/-  (2.18e-81, 1.37e-198j)
| (0.10154354436279499917 + 9.467680499197424972e-638j)  +/-  (6.91e-76, 4.35e-193j)
| (0.19756211518823295015 - 5.8933218237004277875e-637j)  +/-  (2.03e-76, 1.28e-193j)
| (4.1762521696313644701e-23 + 6.9951907146951929608e-647j)  +/-  (2.06e-92, 1.3e-209j)
| (4.0762993895530644137e-17 - 3.8561236321467927141e-644j)  +/-  (1.59e-89, 1e-206j)
| (8.675819407743245448e-10 + 1.1204811499048951422e-640j)  +/-  (9.17e-86, 5.78e-203j)
| (0.0048675061384343497113 + 1.6709800549067187268e-637j)  +/-  (6.37e-82, 4e-199j)
