Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 24
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^26 - 32383677723060300373296059845926712039222/102932287663886812292693059653717801323*t^25 + 103350900197601675777053891001995098315335913/1132255164302754935219623656190895814553*t^24 - 18372571354219040594710810469765653911108765888/1132255164302754935219623656190895814553*t^23 + 2243068821391217420041803436563257640306866627376/1132255164302754935219623656190895814553*t^22 - 18164738567401796968442668173969601559378617366848/102932287663886812292693059653717801323*t^21 + 1224451005924526728835639374069377218190047183552992/102932287663886812292693059653717801323*t^20 - 63934004419275621842762757292397117284436443191759360/102932287663886812292693059653717801323*t^19 + 2625734786558673967915266081864594721494522383622788160/102932287663886812292693059653717801323*t^18 - 85661024075248112398058505644061924032834934375183909120/102932287663886812292693059653717801323*t^17 + 2232944207693451014309662012125720251043671903353876536960/102932287663886812292693059653717801323*t^16 - 46634735888104403647682476883989324514376796803591761264640/102932287663886812292693059653717801323*t^15 + 780340318154302118436643227300208457279693610041099274854400/102932287663886812292693059653717801323*t^14 - 10436136318812330517049272944614129953747543804654309848678400/102932287663886812292693059653717801323*t^13 + 111012444908611004505879349040654315555598444364083473622220800/102932287663886812292693059653717801323*t^12 - 932371682181238227345955350822204696640312644148451486525030400/102932287663886812292693059653717801323*t^11 + 6120752820536794647665436191199159559482760071393868921143705600/102932287663886812292693059653717801323*t^10 - 30991643661698238748304631130413017251515495064094552046280704000/102932287663886812292693059653717801323*t^9 + 118973134915182315342604605269278671304420234585039742126936064000/102932287663886812292693059653717801323*t^8 - 338701955082325177696370191523080436719726143158799884753829888000/102932287663886812292693059653717801323*t^7 + 694866796359959325733717823849943209419990045292043428064067584000/102932287663886812292693059653717801323*t^6 - 989112804809463838849102630328253438456791230597380727153360896000/102932287663886812292693059653717801323*t^5 + 927597680431909921053668378096417452602747211185089037609861120000/102932287663886812292693059653717801323*t^4 - 531794216793051003280096022193991059237270825935626344616427520000/102932287663886812292693059653717801323*t^3 + 165537741462109744480844619480209713455824519020093175597629440000/102932287663886812292693059653717801323*t^2 - 22452277453612780421758639571780565469940817102000915999621120000/102932287663886812292693059653717801323*t + 761783441023412465818317796018480673279343528172907861114880000/102932287663886812292693059653717801323
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (85.401577189983164748 - 1.7011603199580553235e-574j)  +/-  (1.55e-245, 1.55e-245j)
| (64.608514754727737737 + 7.1487698494949370952e-596j)  +/-  (1.56e-243, 1.56e-243j)
| (73.675865120532019802 - 5.6771098710693950111e-643j)  +/-  (2.34e-244, 2.34e-244j)
| (50.406910448866897866 - 1.7434063947424867418e-689j)  +/-  (1.33e-242, 1.33e-242j)
| (44.564979027605238213 - 1.3561048667516954067e-724j)  +/-  (2.31e-242, 2.31e-242j)
| (3.4142135623730950488 - 2.8777552271326863212e-743j)  +/-  (5.33e-248, 5.33e-248j)
| (26.453159231005081206 - 7.7788127865659091138e-743j)  +/-  (2.25e-242, 2.25e-242j)
| (57.007043523092413209 - 1.8736628397348022517e-765j)  +/-  (5.2e-243, 5.2e-243j)
| (39.333577295816291872 + 2.8102399749353500713e-783j)  +/-  (3.42e-242, 3.42e-242j)
| (7.7553940646718480007 - 1.0295773250002969386e-793j)  +/-  (1.28e-245, 1.28e-245j)
| (1.603222221379538507 + 4.1957387288454073356e-798j)  +/-  (8.53e-250, 8.53e-250j)
| (11.778993058596634255 + 3.4405258900147846477e-792j)  +/-  (2.37e-244, 2.37e-244j)
| (16.794054986070635276 - 4.1986767044739692808e-791j)  +/-  (2.34e-243, 2.34e-243j)
| (14.15621044418397301 - 4.5310442561607677306e-792j)  +/-  (8.27e-244, 8.27e-244j)
| (0.25224945758995138167 - 5.0528427106257289286e-801j)  +/-  (3.84e-253, 3.84e-253j)
| (1.0187327630842280678 - 1.6234928315206334576e-798j)  +/-  (1.08e-250, 1.08e-250j)
| (6.0892025623961924837 + 2.5196849992894006664e-795j)  +/-  (2.65e-246, 2.65e-246j)
| (4.6436427919793671815 + 6.1438149922074541306e-795j)  +/-  (3.5e-247, 3.5e-247j)
| (9.6490401427992341632 - 6.3498097317738165319e-794j)  +/-  (5.94e-245, 5.94e-245j)
| (19.708789658641669129 + 1.03263956701304081e-789j)  +/-  (5.96e-243, 5.96e-243j)
| (34.614461072528450456 - 1.8217174029840347684e-794j)  +/-  (3.67e-242, 3.67e-242j)
| (0.5857864376269049512 + 6.6395368956388974987e-810j)  +/-  (9.62e-252, 9.62e-252j)
| (22.920303753597539481 + 1.6248490216053742734e-799j)  +/-  (1.33e-242, 1.33e-242j)
| (0.049165064454264849297 + 3.4601196368754588137e-820j)  +/-  (8.99e-255, 8.99e-255j)
| (30.338120849653812452 - 2.0377515147545885307e-807j)  +/-  (2.92e-242, 2.92e-242j)
| (2.3997186771547161878 + 8.4302928496164857289e-825j)  +/-  (6.87e-249, 6.87e-249j)
-------------------------------------------------
The weights are:
| (1.1422863456574002927e-36 + 9.8317064832128655284e-611j)  +/-  (5.67e-101, 2.48e-221j)
| (7.1793219456794751572e-28 + 2.7008248046086366593e-607j)  +/-  (2.38e-98, 1.04e-218j)
| (1.0145006357610409416e-31 - 5.3242681339735019301e-609j)  +/-  (1.24e-99, 5.45e-220j)
| (7.948688861226766424e-22 + 1.917572214792547933e-604j)  +/-  (9.08e-97, 3.98e-217j)
| (2.4399881758427654402e-19 - 3.0675585557056199418e-603j)  +/-  (4.3e-96, 1.88e-216j)
| (0.03692023886574051145 - 2.5689871147773443156e-594j)  +/-  (2.1e-76, 9.19e-197j)
| (1.2025747106359308264e-11 - 1.9573946414056319243e-599j)  +/-  (2.62e-93, 1.15e-213j)
| (1.2309658530336789805e-24 - 8.7311799442474502999e-606j)  +/-  (3.22e-98, 1.41e-218j)
| (4.1046755209052266152e-17 + 3.7619689792874776258e-602j)  +/-  (1.03e-95, 4.52e-216j)
| (0.00076200183452865842214 + 2.3272136494713761574e-595j)  +/-  (3.52e-86, 1.54e-206j)
| (0.13816874912653635932 - 8.0333657058437457194e-594j)  +/-  (1.29e-76, 5.63e-197j)
| (1.7255759617961770198e-05 + 2.9074687603333246464e-596j)  +/-  (2.99e-89, 1.31e-209j)
| (1.4106923800837420551e-07 + 2.3211990728766556047e-597j)  +/-  (5.6e-92, 2.45e-212j)
| (1.7817955882437385738e-06 - 8.7198038650504161717e-597j)  +/-  (8.55e-91, 3.74e-211j)
| (0.2142667513656198628 + 5.2344047863491172816e-594j)  +/-  (3.44e-80, 1.51e-200j)
| (0.1781570037973346629 + 1.0443338509476537686e-593j)  +/-  (3e-80, 1.31e-200j)
| (0.0035253253267452177755 - 5.6638748425876972779e-595j)  +/-  (5.75e-87, 2.52e-207j)
| (0.012865116806237215623 + 1.2583823128943065927e-594j)  +/-  (4.82e-86, 2.11e-206j)
| (0.000129629769126240412 - 8.6687399170530514938e-596j)  +/-  (3.88e-89, 1.7e-209j)
| (8.4377451867052161627e-09 - 5.4392197436015536197e-598j)  +/-  (6.69e-94, 2.93e-214j)
| (4.1607764954855474061e-15 - 3.6712995637368895977e-601j)  +/-  (4.01e-98, 1.76e-218j)
| (0.21350218780162856972 - 9.2457339108414448791e-594j)  +/-  (2.14e-87, 9.35e-208j)
| (3.7425156797991302028e-10 + 1.1112964171524305289e-598j)  +/-  (1.28e-95, 5.6e-216j)
| (0.1194449683566959578 - 1.5108411099812374505e-594j)  +/-  (3.78e-89, 1.65e-209j)
| (2.7180788271204249487e-13 + 2.9317747953088053668e-600j)  +/-  (2.16e-97, 9.46e-218j)
| (0.082238839501064018147 + 4.8209294352936118441e-594j)  +/-  (4.82e-90, 2.11e-210j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 24
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^26 - 32383677723060300373296059845926712039222/102932287663886812292693059653717801323*t^25 + 103350900197601675777053891001995098315335913/1132255164302754935219623656190895814553*t^24 - 18372571354219040594710810469765653911108765888/1132255164302754935219623656190895814553*t^23 + 2243068821391217420041803436563257640306866627376/1132255164302754935219623656190895814553*t^22 - 18164738567401796968442668173969601559378617366848/102932287663886812292693059653717801323*t^21 + 1224451005924526728835639374069377218190047183552992/102932287663886812292693059653717801323*t^20 - 63934004419275621842762757292397117284436443191759360/102932287663886812292693059653717801323*t^19 + 2625734786558673967915266081864594721494522383622788160/102932287663886812292693059653717801323*t^18 - 85661024075248112398058505644061924032834934375183909120/102932287663886812292693059653717801323*t^17 + 2232944207693451014309662012125720251043671903353876536960/102932287663886812292693059653717801323*t^16 - 46634735888104403647682476883989324514376796803591761264640/102932287663886812292693059653717801323*t^15 + 780340318154302118436643227300208457279693610041099274854400/102932287663886812292693059653717801323*t^14 - 10436136318812330517049272944614129953747543804654309848678400/102932287663886812292693059653717801323*t^13 + 111012444908611004505879349040654315555598444364083473622220800/102932287663886812292693059653717801323*t^12 - 932371682181238227345955350822204696640312644148451486525030400/102932287663886812292693059653717801323*t^11 + 6120752820536794647665436191199159559482760071393868921143705600/102932287663886812292693059653717801323*t^10 - 30991643661698238748304631130413017251515495064094552046280704000/102932287663886812292693059653717801323*t^9 + 118973134915182315342604605269278671304420234585039742126936064000/102932287663886812292693059653717801323*t^8 - 338701955082325177696370191523080436719726143158799884753829888000/102932287663886812292693059653717801323*t^7 + 694866796359959325733717823849943209419990045292043428064067584000/102932287663886812292693059653717801323*t^6 - 989112804809463838849102630328253438456791230597380727153360896000/102932287663886812292693059653717801323*t^5 + 927597680431909921053668378096417452602747211185089037609861120000/102932287663886812292693059653717801323*t^4 - 531794216793051003280096022193991059237270825935626344616427520000/102932287663886812292693059653717801323*t^3 + 165537741462109744480844619480209713455824519020093175597629440000/102932287663886812292693059653717801323*t^2 - 22452277453612780421758639571780565469940817102000915999621120000/102932287663886812292693059653717801323*t + 761783441023412465818317796018480673279343528172907861114880000/102932287663886812292693059653717801323
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (85.401577189983164748 - 1.7011603199580553235e-574j)  +/-  (1.55e-245, 1.55e-245j)
| (64.608514754727737737 + 7.1487698494949370952e-596j)  +/-  (1.56e-243, 1.56e-243j)
| (73.675865120532019802 - 5.6771098710693950111e-643j)  +/-  (2.34e-244, 2.34e-244j)
| (50.406910448866897866 - 1.7434063947424867418e-689j)  +/-  (1.33e-242, 1.33e-242j)
| (44.564979027605238213 - 1.3561048667516954067e-724j)  +/-  (2.31e-242, 2.31e-242j)
| (3.4142135623730950488 - 2.8777552271326863212e-743j)  +/-  (5.33e-248, 5.33e-248j)
| (26.453159231005081206 - 7.7788127865659091138e-743j)  +/-  (2.25e-242, 2.25e-242j)
| (57.007043523092413209 - 1.8736628397348022517e-765j)  +/-  (5.2e-243, 5.2e-243j)
| (39.333577295816291872 + 2.8102399749353500713e-783j)  +/-  (3.42e-242, 3.42e-242j)
| (7.7553940646718480007 - 1.0295773250002969386e-793j)  +/-  (1.28e-245, 1.28e-245j)
| (1.603222221379538507 + 4.1957387288454073356e-798j)  +/-  (8.53e-250, 8.53e-250j)
| (11.778993058596634255 + 3.4405258900147846477e-792j)  +/-  (2.37e-244, 2.37e-244j)
| (16.794054986070635276 - 4.1986767044739692808e-791j)  +/-  (2.34e-243, 2.34e-243j)
| (14.15621044418397301 - 4.5310442561607677306e-792j)  +/-  (8.27e-244, 8.27e-244j)
| (0.25224945758995138167 - 5.0528427106257289286e-801j)  +/-  (3.84e-253, 3.84e-253j)
| (1.0187327630842280678 - 1.6234928315206334576e-798j)  +/-  (1.08e-250, 1.08e-250j)
| (6.0892025623961924837 + 2.5196849992894006664e-795j)  +/-  (2.65e-246, 2.65e-246j)
| (4.6436427919793671815 + 6.1438149922074541306e-795j)  +/-  (3.5e-247, 3.5e-247j)
| (9.6490401427992341632 - 6.3498097317738165319e-794j)  +/-  (5.94e-245, 5.94e-245j)
| (19.708789658641669129 + 1.03263956701304081e-789j)  +/-  (5.96e-243, 5.96e-243j)
| (34.614461072528450456 - 1.8217174029840347684e-794j)  +/-  (3.67e-242, 3.67e-242j)
| (0.5857864376269049512 + 6.6395368956388974987e-810j)  +/-  (9.62e-252, 9.62e-252j)
| (22.920303753597539481 + 1.6248490216053742734e-799j)  +/-  (1.33e-242, 1.33e-242j)
| (0.049165064454264849297 + 3.4601196368754588137e-820j)  +/-  (8.99e-255, 8.99e-255j)
| (30.338120849653812452 - 2.0377515147545885307e-807j)  +/-  (2.92e-242, 2.92e-242j)
| (2.3997186771547161878 + 8.4302928496164857289e-825j)  +/-  (6.87e-249, 6.87e-249j)
-------------------------------------------------
The weights are:
| (1.1422863456574002927e-36 + 9.8317064832128655284e-611j)  +/-  (5.67e-101, 2.48e-221j)
| (7.1793219456794751572e-28 + 2.7008248046086366593e-607j)  +/-  (2.38e-98, 1.04e-218j)
| (1.0145006357610409416e-31 - 5.3242681339735019301e-609j)  +/-  (1.24e-99, 5.45e-220j)
| (7.948688861226766424e-22 + 1.917572214792547933e-604j)  +/-  (9.08e-97, 3.98e-217j)
| (2.4399881758427654402e-19 - 3.0675585557056199418e-603j)  +/-  (4.3e-96, 1.88e-216j)
| (0.03692023886574051145 - 2.5689871147773443156e-594j)  +/-  (2.1e-76, 9.19e-197j)
| (1.2025747106359308264e-11 - 1.9573946414056319243e-599j)  +/-  (2.62e-93, 1.15e-213j)
| (1.2309658530336789805e-24 - 8.7311799442474502999e-606j)  +/-  (3.22e-98, 1.41e-218j)
| (4.1046755209052266152e-17 + 3.7619689792874776258e-602j)  +/-  (1.03e-95, 4.52e-216j)
| (0.00076200183452865842214 + 2.3272136494713761574e-595j)  +/-  (3.52e-86, 1.54e-206j)
| (0.13816874912653635932 - 8.0333657058437457194e-594j)  +/-  (1.29e-76, 5.63e-197j)
| (1.7255759617961770198e-05 + 2.9074687603333246464e-596j)  +/-  (2.99e-89, 1.31e-209j)
| (1.4106923800837420551e-07 + 2.3211990728766556047e-597j)  +/-  (5.6e-92, 2.45e-212j)
| (1.7817955882437385738e-06 - 8.7198038650504161717e-597j)  +/-  (8.55e-91, 3.74e-211j)
| (0.2142667513656198628 + 5.2344047863491172816e-594j)  +/-  (3.44e-80, 1.51e-200j)
| (0.1781570037973346629 + 1.0443338509476537686e-593j)  +/-  (3e-80, 1.31e-200j)
| (0.0035253253267452177755 - 5.6638748425876972779e-595j)  +/-  (5.75e-87, 2.52e-207j)
| (0.012865116806237215623 + 1.2583823128943065927e-594j)  +/-  (4.82e-86, 2.11e-206j)
| (0.000129629769126240412 - 8.6687399170530514938e-596j)  +/-  (3.88e-89, 1.7e-209j)
| (8.4377451867052161627e-09 - 5.4392197436015536197e-598j)  +/-  (6.69e-94, 2.93e-214j)
| (4.1607764954855474061e-15 - 3.6712995637368895977e-601j)  +/-  (4.01e-98, 1.76e-218j)
| (0.21350218780162856972 - 9.2457339108414448791e-594j)  +/-  (2.14e-87, 9.35e-208j)
| (3.7425156797991302028e-10 + 1.1112964171524305289e-598j)  +/-  (1.28e-95, 5.6e-216j)
| (0.1194449683566959578 - 1.5108411099812374505e-594j)  +/-  (3.78e-89, 1.65e-209j)
| (2.7180788271204249487e-13 + 2.9317747953088053668e-600j)  +/-  (2.16e-97, 9.46e-218j)
| (0.082238839501064018147 + 4.8209294352936118441e-594j)  +/-  (4.82e-90, 2.11e-210j)
