Mathematica 2.0 for SPARC Copyright 1988-91 Wolfram Research, Inc. -- X11 windows graphics initialized -- In[1]:= < 99243396983801910411100057579582194468 x + x , 1}} Factor-product of degree 1 is 99243396983801910411100057579582194468 + 3 > 99243396983801910411100057579582194468 x + x ddlist={{99243396983801910411100057579582194468 + 3 > 99243396983801910411100057579582194468 x + x , 1}} r=3 Random choice=-38907369926620726288954073468714639310 - > 16882564692716464556904485789459156004 x GCD=1 Random choice=19105898279092048609378978507555956875 - > 11683188592217947775753985679210574131 x GCD=11765735387981049030219416062950657434 + x f/GCD=25563089896395219813363000621276117802 + 2 > 87477661595820861380880641516631537035 x + x r=2 Random choice=2883104554886368994895344165770558516 + > 22149761584988417870910053726569641537 x GCD=96397959661466147602260729213939500339 + x f/GCD=90323098918156624189719969882274231165 + x czlist={11765735387981049030219416062950657434 + x, > 96397959661466147602260729213939500339 + x, > 90323098918156624189719969882274231165 + x} 15.6333 Second Out[6]= {{11765735387981049030219416062950657434 + x, 1}, > {96397959661466147602260729213939500339 + x, 1}, > {90323098918156624189719969882274231165 + x, 1}} In[7]:= (* testing integer factoring algorithm *) 0. Second In[8]:= f = Expand[(x^4+1) * (x^4+16)] 0. Second 4 8 Out[8]= 16 + 17 x + x In[9]:= FactorSqfPrimPoly[f, x] Modulus chosen = 83 4 8 sqflist={{16 + 17 x + x , 1}} 4 8 Factor-product of degree 2 is 16 + 17 x + x 4 8 ddlist={{16 + 17 x + x , 2}} r=4 2 3 Random choice=38 + 17 x + 30 x - 27 x 2 4 5 6 GCD=67 + 61 x + 16 x + 82 x + 9 x + x 2 f/GCD=82 + 74 x + x r=3 2 3 Random choice=7 + 10 x - 30 x - 39 x 2 GCD=79 + 18 x + x 2 3 4 f/GCD=4 + 65 x + 82 x + 74 x + x r=2 2 3 Random choice=-18 - 10 x + 11 x + 8 x 2 GCD=82 + 9 x + x 2 f/GCD=79 + 65 x + x 2 2 2 2 czlist={79 + 18 x + x , 82 + 9 x + x , 79 + 65 x + x , 82 + 74 x + x } 2 2 Modular factors = {{79 + 18 x + x , 1}, {82 + 9 x + x , 1}, 2 2 > {79 + 65 x + x , 1}, {82 + 74 x + x , 1}} 2 2 2 2 cominlist = {79 + 18 x + x , 82 + 9 x + x , 79 + 65 x + x , 82 + 74 x + x } Trying combinations of 1 factors 2 Test-division by -1 - 9 x + x 2 Combined factors list {82 + 74 x + x } Test polynomial division failed 2 Test-division by -4 - 18 x + x 2 Combined factors list {79 + 65 x + x } Test polynomial division failed 2 Test-division by -1 + 9 x + x 2 Combined factors list {82 + 9 x + x } Test polynomial division failed 2 Test-division by -4 + 18 x + x 2 Combined factors list {79 + 18 x + x } Test polynomial division failed Trying combinations of 2 factors 2 3 4 Test-division by 4 - 29 x - 9 x - 27 x + x 2 2 Combined factors list {79 + 65 x + x , 82 + 74 x + x } Test polynomial division failed 4 Test-division by 1 + x 2 2 Combined factors list {82 + 9 x + x , 82 + 74 x + x } 4 2 2 Factor 1 + x found, combinations = {82 + 9 x + x , 82 + 74 x + x } 2 2 Remaining combinations = {79 + 18 x + x , 79 + 65 x + x } 3.73333 Second 4 4 Out[9]= {1 + x , 16 + x } In[10]:= (* more difficult integer factoring problem *) 0. Second In[11]:= f = SwinnertonDyer[x, 2, {-1, 2, 3}] 0.133333 Second 2 4 6 8 Out[11]= 144 + 192 x + 88 x - 16 x + x In[12]:= g = SwinnertonDyer[x, 2, {-1, 2, 5}] 0.116667 Second 2 4 6 8 Out[12]= 576 + 64 x + 192 x - 24 x + x In[13]:= h = Expand[f*g] 0.0166667 Second 2 4 6 8 10 Out[13]= 82944 + 119808 x + 90624 x + 29824 x + 11984 x - 4928 x + 12 14 16 > 664 x - 40 x + x In[14]:= FactorSqfPrimPoly[h, x] Modulus chosen = 94837 2 4 6 8 10 sqflist={{82944 + 24971 x + 90624 x + 29824 x + 11984 x + 89909 x + 12 14 16 > 664 x + 94797 x + x , 1}} 2 4 6 Factor-product of degree 2 is 82944 + 24971 x + 90624 x + 29824 x + 8 10 12 14 16 > 11984 x + 89909 x + 664 x + 94797 x + x 2 4 6 8 10 ddlist={{82944 + 24971 x + 90624 x + 29824 x + 11984 x + 89909 x + 12 14 16 > 664 x + 94797 x + x , 2}} r=8 2 3 Random choice=46823 - 570 x + 5200 x - 31817 x 2 3 4 5 6 GCD=288 + 63256 x + 76533 x + 6836 x + 34803 x + 18873 x + 94809 x + 7 8 > 55689 x + x 2 3 4 5 6 f/GCD=288 + 31581 x + 76533 x + 88001 x + 34803 x + 75964 x + 94809 x + 7 8 > 39148 x + x r=4 2 3 Random choice=17725 - 35784 x + 12666 x + 3119 x 2 3 4 GCD=61527 + 32611 x + 2025 x + 63430 x + x 2 3 4 f/GCD=89325 + 26216 x + 38428 x + 87096 x + x r=2 2 3 Random choice=-30894 + 25174 x - 35056 x - 32967 x 2 GCD=15613 + 19574 x + x 2 f/GCD=13592 + 43856 x + x r=2 2 3 Random choice=-15286 - 2240 x + 22718 x + 4606 x 2 GCD=81245 + 11833 x + x 2 f/GCD=79208 + 75263 x + x r=4 2 3 Random choice=29830 - 32635 x + 30334 x + 19180 x 2 GCD=13592 + 50981 x + x 2 3 4 5 6 f/GCD=53140 + 68303 x + 20967 x + 69091 x + 81233 x + 83004 x + x r=3 2 3 Random choice=-7735 - 36097 x + 12456 x + 15720 x 2 4 GCD=24 + 21932 x + 94825 x + x 2 f/GCD=81245 + 83004 x + x r=2 2 3 Random choice=-32439 + 14811 x - 44598 x - 29434 x 2 4 GCD=24 + 21932 x + 94825 x + x 2 3 Random choice=-28880 - 24122 x - 6308 x - 16442 x 2 GCD=79208 + 19574 x + x 2 f/GCD=15613 + 75263 x + x 2 2 2 czlist={15613 + 19574 x + x , 13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 2 > 79208 + 75263 x + x , 13592 + 50981 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } 2 2 Modular factors = {{15613 + 19574 x + x , 1}, {13592 + 43856 x + x , 1}, 2 2 > {81245 + 11833 x + x , 1}, {79208 + 75263 x + x , 1}, 2 2 > {13592 + 50981 x + x , 1}, {79208 + 19574 x + x , 1}, 2 2 > {15613 + 75263 x + x , 1}, {81245 + 83004 x + x , 1}} 2 2 2 cominlist = {15613 + 19574 x + x , 13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 2 > 79208 + 75263 x + x , 13592 + 50981 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Trying combinations of 1 factors 2 Test-division by -13592 - 11833 x + x 2 Combined factors list {81245 + 83004 x + x } Test trailing coefficient division failed 2 Test-division by 15613 - 19574 x + x 2 Combined factors list {15613 + 75263 x + x } Test trailing coefficient division failed 2 Test-division by -15629 + 19574 x + x 2 Combined factors list {79208 + 19574 x + x } Test trailing coefficient division failed 2 Test-division by 13592 - 43856 x + x 2 Combined factors list {13592 + 50981 x + x } Test trailing coefficient division failed 2 Test-division by -15629 - 19574 x + x 2 Combined factors list {79208 + 75263 x + x } Test trailing coefficient division failed 2 Test-division by -13592 + 11833 x + x 2 Combined factors list {81245 + 11833 x + x } Test trailing coefficient division failed 2 Test-division by 13592 + 43856 x + x 2 Combined factors list {13592 + 43856 x + x } Test trailing coefficient division failed 2 Test-division by 15613 + 19574 x + x 2 Combined factors list {15613 + 19574 x + x } Test trailing coefficient division failed Trying combinations of 2 factors 2 3 4 Test-division by 33310 + 25870 x + 29209 x - 31407 x + x 2 2 Combined factors list {15613 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 Test-division by -5512 - 26216 x + 38428 x + 7741 x + x 2 2 Combined factors list {79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 4 Test-division by 24 + 21932 x - 12 x + x 2 2 Combined factors list {79208 + 19574 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 3 4 Test-division by 12 - 45214 x - 16 x + 39148 x + x 2 2 Combined factors list {13592 + 50981 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 Test-division by -33310 - 32611 x + 2025 x + 31407 x + x 2 2 Combined factors list {13592 + 50981 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 5512 - 24389 x + 25143 x - 24282 x + x 2 2 Combined factors list {13592 + 50981 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 Test-division by -5512 + 37830 x - 2033 x - 31407 x + x 2 2 Combined factors list {79208 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 24 + 28673 x - 20 x - 39148 x + x 2 2 Combined factors list {79208 + 75263 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 4 Test-division by -34471 - 31254 x + x 2 2 Combined factors list {79208 + 75263 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 5512 + 6402 x - 29217 x + 31407 x + x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x } Test trailing coefficient division failed 2 4 Test-division by -12 + 27176 x + x 2 2 Combined factors list {81245 + 11833 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 Test-division by 33310 + 38176 x - 25167 x - 7741 x + x 2 2 Combined factors list {81245 + 11833 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by -5512 - 37830 x - 2033 x + 31407 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 12 + 30791 x + 16 x - 32023 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x } Test polynomial division failed 2 3 4 Test-division by -5512 + 26216 x + 38428 x - 7741 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 12 - 30791 x + 16 x + 32023 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 Test-division by -33310 - 31435 x - 38452 x + 24282 x + x 2 2 Combined factors list {13592 + 43856 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 5512 - 6402 x - 29217 x - 31407 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 4 Test-division by -12 - 27192 x + x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x } Test polynomial division failed 2 3 4 Test-division by 5512 + 24389 x + 25143 x + 24282 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 12 + 45214 x - 16 x - 39148 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x } Test polynomial division failed 2 3 4 Test-division by 33310 - 38176 x - 25167 x + 7741 x + x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 4 Test-division by 34679 + 31230 x + x 2 2 Combined factors list {15613 + 19574 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 Test-division by 24 - 28673 x - 20 x + 39148 x + x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 19574 x + x } Test polynomial division failed 2 3 4 Test-division by -33310 + 31435 x - 38452 x - 24282 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 50981 x + x } Test trailing coefficient division failed 2 4 Test-division by 24 - 21932 x - 12 x + x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 75263 x + x } Test polynomial division failed 2 3 4 Test-division by 33310 - 25870 x + 29209 x + 31407 x + x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x } Test trailing coefficient division failed 2 3 4 Test-division by -33310 + 32611 x + 2025 x - 31407 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x } Test trailing coefficient division failed Trying combinations of 3 factors 2 3 4 5 Test-division by -41697 - 26534 x + 20967 x - 25746 x - 13604 x - 11833 x + 6 > x 2 2 Combined factors list {79208 + 19574 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 - 4768 x + 34667 x - 23282 x + 15605 x + 19574 x + x 2 2 Combined factors list {13592 + 50981 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 - 30504 x - 34387 x - 29655 x - 15653 x - 36115 x + x 2 2 Combined factors list {13592 + 50981 x + x , 79208 + 19574 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 + 17716 x + 13656 x - 20818 x + 13580 x - 43856 x + 6 > x 2 2 Combined factors list {13592 + 50981 x + x , 79208 + 19574 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 - 37664 x + 26530 x + 44868 x + 40764 x + 43856 x + 6 > x 2 2 Combined factors list {79208 + 75263 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 35052 + 1406 x - 5026 x - 35718 x - 44846 x - 11833 x + x 2 2 Combined factors list {79208 + 75263 x + x , 79208 + 19574 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 4252 - 29901 x + 28029 x - 27691 x - 15641 x - 19574 x + x 2 2 Combined factors list {79208 + 75263 x + x , 79208 + 19574 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 - 26095 x - 34483 x + 27691 x - 15637 x + 19574 x + x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 + 28846 x - 26610 x - 11786 x - 40788 x + 11833 x + 6 > x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -35052 - 36441 x + 30921 x - 3737 x - 17662 x - 43856 x + 6 > x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2318 + 45214 x - 1862 x - 2291 x + 42789 x - 19574 x + x 2 2 Combined factors list {81245 + 11833 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2126 - 45214 x + 41207 x + 2291 x + 11547 x + 19574 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 19574 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 - 27572 x + 20778 x - 25227 x - 13604 x + 11833 x + 6 > x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 19574 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 26570 - 42750 x - 13935 x - 14077 x + 40768 x - 43856 x + 6 > x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 - 34084 x + 46247 x + 7683 x - 38739 x + 43240 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 + 15613 x - 46479 x - 2755 x + 38755 x - 12449 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2126 + 45214 x + 41207 x - 2291 x + 11547 x - 19574 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 - 38702 x + 43013 x + 45733 x + 26849 x - 27315 x + 6 > x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 35052 - 1406 x - 5026 x + 35718 x - 44846 x + 11833 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 + 20022 x + 20560 x + 34736 x + 24856 x + 43240 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -2318 + 38493 x - 20792 x + 29808 x - 24840 x + 12449 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 - 20022 x + 20560 x - 34736 x + 24856 x - 43240 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 19574 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 + 36390 x + 39532 x - 30155 x + 13580 x + 43856 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 19574 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -26570 + 47159 x + 13863 x - 19005 x - 40784 x - 11833 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2318 + 45214 x + 36541 x + 30964 x - 11579 x - 19574 x + x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -2126 - 45214 x + 19159 x - 30964 x - 42821 x + 19574 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 - 15613 x - 46479 x + 2755 x + 38755 x + 12449 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 41697 - 47317 x - 42837 x + 35877 x - 26905 x + 4708 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -35052 + 36441 x + 30921 x + 3737 x - 17662 x + 43856 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -2126 + 45214 x + 19159 x + 30964 x - 42821 x - 19574 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 26570 + 42750 x - 13935 x + 14077 x + 40768 x + 43856 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 + 9177 x + 34763 x - 14209 x + 15589 x + 36115 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 + 26095 x - 34483 x - 27691 x - 15637 x - 19574 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -26570 - 47159 x + 13863 x + 19005 x - 40784 x + 11833 x + 6 > x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2126 + 30504 x - 34387 x + 29655 x - 15653 x + 36115 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 > 79208 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -17078 + 3092 x + 46931 x + 35199 x + 17638 x - 11833 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 15613 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 + 38702 x + 43013 x - 45733 x + 26849 x + 27315 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 19574 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -4636 - 36500 x - 27789 x - 23282 x + 15601 x + 19574 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 19574 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 - 9177 x + 34763 x + 14209 x + 15589 x - 36115 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 50981 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 17078 + 18745 x + 22427 x + 13074 x + 44822 x - 43856 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 50981 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 41697 + 47317 x - 42837 x - 35877 x - 26905 x - 4708 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 50981 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 + 27572 x + 20778 x + 25227 x - 13604 x - 11833 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 75263 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -4636 + 36500 x - 27789 x + 23282 x + 15601 x - 19574 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 75263 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 4252 + 29901 x + 28029 x + 27691 x - 15641 x + 19574 x + x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 75263 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 - 36390 x + 39532 x + 30155 x + 13580 x - 43856 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 79208 + 75263 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2318 - 45214 x - 1862 x + 2291 x + 42789 x + 19574 x + x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -17078 - 3092 x + 46931 x - 35199 x + 17638 x + 11833 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 + 37664 x + 26530 x - 44868 x + 40764 x - 43856 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -2318 - 38493 x - 20792 x - 29808 x - 24840 x - 12449 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -41697 + 26534 x + 20967 x + 25746 x - 13604 x + 11833 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 81245 + 11833 x + x , 2 > 79208 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 + 34084 x + 46247 x - 7683 x - 38739 x - 43240 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 17078 - 18745 x + 22427 x - 13074 x + 44822 x + 43856 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 - 28846 x - 26610 x + 11786 x - 40788 x - 11833 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by 2318 - 45214 x + 36541 x - 30964 x - 11579 x + 19574 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 13592 + 50981 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 41697 - 17716 x + 13656 x + 20818 x + 13580 x + 43856 x + 6 > x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 79208 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 6 Test-division by -2318 + 4768 x + 34667 x + 23282 x + 15605 x - 19574 x + x 2 2 Combined factors list {15613 + 19574 x + x , 13592 + 43856 x + x , 2 > 81245 + 11833 x + x } Test trailing coefficient division failed Trying combinations of 4 factors 2 3 4 5 Test-division by 288 + 31581 x - 18304 x - 6836 x + 34803 x - 18873 x - 6 7 8 > 28 x + 39148 x + x 2 2 Combined factors list {13592 + 50981 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 5 Test-division by -37451 - 12459 x - 24001 x + 10787 x + 1715 x - 37539 x - 6 7 8 > 2045 x - 31407 x + x 2 2 Combined factors list {79208 + 75263 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 288 + 17636 x + 144 x - 33082 x + 132 x + 16541 x - 6 8 > 20 x + x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 5 Test-division by -34304 + 20536 x - 13186 x + 12021 x - 8580 x + 10168 x - 6 7 8 > 31270 x + 39148 x + x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 37451 + 30820 x + 41248 x + 39450 x - 6015 x + 30798 x - 6 7 8 > 29229 x + 31407 x + x 2 2 Combined factors list {79208 + 75263 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -288 + 21327 x - 11491 x - 26513 x - 41589 x + 21932 x + 6 8 > 27164 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 5 Test-division by 20372 + 11984 x - 37695 x + 17693 x - 7382 x + 45858 x + 6 7 8 > 29201 x + 31407 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 28693 + 8157 x + 29284 x + 27202 x - 8917 x - 36175 x - 6 7 8 > 42518 x - 24282 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 288 - 41039 x - 25825 x - 28436 x + 34230 x - 37186 x + 6 7 8 > 4 x - 32023 x + x 2 2 Combined factors list {81245 + 11833 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 3 4 5 Test-division by -288 + 35272 x - 11395 x + 32247 x + 25514 x + 24091 x + 6 7 8 > 27156 x - 39148 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 4 6 8 Test-division by 34304 + 11690 x - 33015 x - 4078 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -37451 - 6684 x + 12627 x - 39714 x - 9821 x + 46203 x + 6 7 8 > 38416 x - 7741 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 28693 + 18013 x + 17745 x - 42679 x - 20328 x - 9966 x - 6 7 8 > 2041 x + 31407 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 288 + 39853 x + 32854 x + 27175 x - 11727 x - 21281 x - 6 7 8 > 13903 x + 23666 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 3 4 5 Test-division by -34304 + 19143 x + 21786 x + 26115 x + 34499 x - 32065 x - 6 7 8 > 31238 x - 32023 x + x 2 2 Combined factors list {81245 + 11833 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 288 - 1615 x + 26305 x - 28436 x - 34542 x - 13787 x + 6 7 8 > 4 x + 32023 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 19574 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 5 Test-division by -20372 - 25929 x - 43330 x + 41362 x + 42045 x + 37829 x + 6 7 8 > 2017 x - 31407 x + x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -28693 + 30081 x - 41944 x - 22312 x - 25634 x + 18652 x + 6 7 8 > 11236 x + 7741 x + x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -288 + 21327 x + 11395 x - 39888 x + 41805 x + 21932 x - 6 8 > 27204 x + x 2 2 Combined factors list {13592 + 43856 x + x , 13592 + 50981 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 3 4 5 Test-division by 288 - 15560 x - 32566 x + 45646 x + 11159 x - 36065 x + 6 7 8 > 13895 x - 7125 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test polynomial division failed 2 3 4 5 Test-division by -34304 - 19143 x + 21786 x - 26115 x + 34499 x + 32065 x - 6 7 8 > 31238 x + 32023 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 37451 - 11677 x - 12866 x - 35290 x + 31400 x + 39448 x + 6 7 8 > 25131 x + 24282 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -28693 + 20225 x - 30597 x + 21115 x - 14159 x - 45048 x - 6 7 8 > 29225 x - 31407 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by -288 + 35272 x + 11491 x - 25648 x - 25170 x - 4236 x - 6 7 8 > 27212 x - 39148 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 4 6 8 Test-division by 34304 - 37776 x - 10072 x + 36391 x + x 2 2 Combined factors list {13592 + 43856 x + x , 79208 + 75263 x + x , 2 2 > 13592 + 50981 x + x , 79208 + 19574 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 20372 - 2128 x - 26156 x + 7263 x + 4029 x - 19649 x - 6 7 8 > 11276 x + 24282 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 > 15613 + 75263 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 28693 - 18013 x + 17745 x + 42679 x - 20328 x + 9966 x - 6 7 8 > 2041 x - 31407 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 > 79208 + 19574 x + x , 81245 + 83004 x + x } Test trailing coefficient division failed 2 3 4 5 Test-division by 288 + 20602 x + 17248 x - 31129 x - 34347 x - 32100 x - 6 7 8 > 28 x - 39148 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } Test polynomial division failed 2 4 6 8 Test-division by 144 + 192 x + 88 x - 16 x + x 2 2 Combined factors list {13592 + 43856 x + x , 81245 + 11833 x + x , 2 2 > 13592 + 50981 x + x , 81245 + 83004 x + x } 2 4 6 8 Factor 144 + 192 x + 88 x - 16 x + x found, combinations = 2 2 2 > {13592 + 43856 x + x , 81245 + 11833 x + x , 13592 + 50981 x + x , 2 > 81245 + 83004 x + x } 2 2 Remaining combinations = {15613 + 19574 x + x , 79208 + 75263 x + x , 2 2 > 79208 + 19574 x + x , 15613 + 75263 x + x } 49.2333 Second 2 4 6 8 2 4 6 8 Out[14]= {144 + 192 x + 88 x - 16 x + x , 576 + 64 x + 192 x - 24 x + x } In[15]:= (* using Maeder's built-in factorizer *) 0. Second In[16]:= Factor[h] 0.566667 Second 2 4 6 8 2 4 6 8 Out[16]= (576 + 64 x + 192 x - 24 x + x ) (144 + 192 x + 88 x - 16 x + x ) In[17]:=