pr

428 days ago by KylinRee

#####Project 3###### 
       
def f(x, c): return 3/x+x/2-c def g(x, c, n): z = x for i in range(n): z = f(z, c) return expand(z) 
       
f(2,2) var('x c') f(x,c) 
       
-c + 1/2*x + 3/x
-c + 1/2*x + 3/x
factor(f(x,c)-x,x) 
       
-1/2*(2*c*x + x^2 - 6)/x
-1/2*(2*c*x + x^2 - 6)/x
###solve for p(c)### solve(f(x,c)==x,x) 
       
[x == -c - sqrt(c^2 + 6), x == -c + sqrt(c^2 + 6)]
[x == -c - sqrt(c^2 + 6), x == -c + sqrt(c^2 + 6)]
diff(f(x,c),x)(sqrt(c^2+6)-c) 
       
__main__:3: DeprecationWarning: Substitution using function-call syntax
and unnamed arguments is deprecated and will be removed from a future
release of Sage; you can use named arguments instead, like EXPR(x=...,
y=...)
-3/(c - sqrt(c^2 + 6))^2 + 1/2
__main__:3: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
-3/(c - sqrt(c^2 + 6))^2 + 1/2
#for abs(-3/(c - sqrt(c^2 + 6))^2 + 1/2)<1. # 0< c < sqrt(2) 
       
###2 cycle### g(x,c,2) 
       
-3/2*c + 1/4*x - 6/(2*c - x - 6/x) + 3/2/x
-3/2*c + 1/4*x - 6/(2*c - x - 6/x) + 3/2/x
factor(g(x,c,2)-x,x) 
       
-3/4*(2*c*x - x^2 - 2)*(2*c*x + x^2 - 6)/((2*c*x - x^2 - 6)*x)
-3/4*(2*c*x - x^2 - 2)*(2*c*x + x^2 - 6)/((2*c*x - x^2 - 6)*x)
solve(g(x,c,2)==x,x) 
       
[x == c - sqrt(c^2 - 2), x == c + sqrt(c^2 - 2), x == -c - sqrt(c^2 +
6), x == -c + sqrt(c^2 + 6)]
[x == c - sqrt(c^2 - 2), x == c + sqrt(c^2 - 2), x == -c - sqrt(c^2 + 6), x == -c + sqrt(c^2 + 6)]
#except fixed point found above; #2 cycle: p1=c - sqrt(c^2 - 2), p2=c + sqrt(c^2 - 2), for sqrt(2)<c<2 
       
diff(f(x,c),x)(c - sqrt(c^2 - 2))*diff(f(x,c),x)(c + sqrt(c^2 - 2)) 
       
1/4*(6/(c + sqrt(c^2 - 2))^2 - 1)*(6/(c - sqrt(c^2 - 2))^2 - 1)
1/4*(6/(c + sqrt(c^2 - 2))^2 - 1)*(6/(c - sqrt(c^2 - 2))^2 - 1)
solve(-1<(1/4*(6/(c + sqrt(c^2 - 2))^2 - 1)*(6/(c - sqrt(c^2 - 2))^2 - 1))<1,c) 
       
[[c > -1/3*sqrt(3)*sqrt(10), c < 1/3*sqrt(3)*sqrt(10)]]
[[c > -1/3*sqrt(3)*sqrt(10), c < 1/3*sqrt(3)*sqrt(10)]]
##For c in range (sqrt(2),sqrt(30)/3), the 2-cycle is stable 
       
print " n p" P = vector (RDF,10000) P[0] = 1 for n in range(1,1001): P[n]=3/P[n-1]+P[n-1]/2-1; for n in range(0,1001): print "%3s %11s" %(n,P[n]) 
       
WARNING: Output truncated!  
full_output.txt



  n       p
  0               1.0
  1               2.5
  2              1.45
  3       1.79396551724
  4       1.56925570432
  5       1.69636218057
  6       1.61667135396
  7       1.66400039984
  8       1.63488438209
  9       1.65243433658
 10       1.64172047368
 11       1.64821151137
 12       1.64426049875
 13       1.64665866338
 14       1.6452005347
 15       1.64608618091
 16       1.64554791116
 17       1.64587492982
 18       1.64567620747
 19       1.6457969497
 20       1.64572358128
 21       1.6457681609
 22       1.64574107287
 23       1.64575753212
 24       1.64574753102
 25       1.64575360792
 26       1.64574991544
 27       1.64575215908
 28       1.64575079579
 29       1.64575162416
 30       1.64575112082
 31       1.64575142666
 32       1.64575124082
 33       1.64575135374
 34       1.64575128513
 35       1.64575132682
 36       1.64575130149
 37       1.64575131688
 38       1.64575130753
 39       1.64575131321
 40       1.64575130976
 41       1.64575131186
 42       1.64575131058
 43       1.64575131136
 44       1.64575131089
 45       1.64575131117
 46       1.645751311
 47       1.6457513111
 48       1.64575131104
 49       1.64575131108
 50       1.64575131106
 51       1.64575131107
 52       1.64575131106
 53       1.64575131107
 54       1.64575131106
 55       1.64575131107
 56       1.64575131106
 57       1.64575131106

...

941       1.64575131106
942       1.64575131106
943       1.64575131106
944       1.64575131106
945       1.64575131106
946       1.64575131106
947       1.64575131106
948       1.64575131106
949       1.64575131106
950       1.64575131106
951       1.64575131106
952       1.64575131106
953       1.64575131106
954       1.64575131106
955       1.64575131106
956       1.64575131106
957       1.64575131106
958       1.64575131106
959       1.64575131106
960       1.64575131106
961       1.64575131106
962       1.64575131106
963       1.64575131106
964       1.64575131106
965       1.64575131106
966       1.64575131106
967       1.64575131106
968       1.64575131106
969       1.64575131106
970       1.64575131106
971       1.64575131106
972       1.64575131106
973       1.64575131106
974       1.64575131106
975       1.64575131106
976       1.64575131106
977       1.64575131106
978       1.64575131106
979       1.64575131106
980       1.64575131106
981       1.64575131106
982       1.64575131106
983       1.64575131106
984       1.64575131106
985       1.64575131106
986       1.64575131106
987       1.64575131106
988       1.64575131106
989       1.64575131106
990       1.64575131106
991       1.64575131106
992       1.64575131106
993       1.64575131106
994       1.64575131106
995       1.64575131106
996       1.64575131106
997       1.64575131106
998       1.64575131106
999       1.64575131106
1000       1.64575131106
WARNING: Output truncated!  
full_output.txt



  n       p
  0               1.0
  1               2.5
  2              1.45
  3       1.79396551724
  4       1.56925570432
  5       1.69636218057
  6       1.61667135396
  7       1.66400039984
  8       1.63488438209
  9       1.65243433658
 10       1.64172047368
 11       1.64821151137
 12       1.64426049875
 13       1.64665866338
 14       1.6452005347
 15       1.64608618091
 16       1.64554791116
 17       1.64587492982
 18       1.64567620747
 19       1.6457969497
 20       1.64572358128
 21       1.6457681609
 22       1.64574107287
 23       1.64575753212
 24       1.64574753102
 25       1.64575360792
 26       1.64574991544
 27       1.64575215908
 28       1.64575079579
 29       1.64575162416
 30       1.64575112082
 31       1.64575142666
 32       1.64575124082
 33       1.64575135374
 34       1.64575128513
 35       1.64575132682
 36       1.64575130149
 37       1.64575131688
 38       1.64575130753
 39       1.64575131321
 40       1.64575130976
 41       1.64575131186
 42       1.64575131058
 43       1.64575131136
 44       1.64575131089
 45       1.64575131117
 46       1.645751311
 47       1.6457513111
 48       1.64575131104
 49       1.64575131108
 50       1.64575131106
 51       1.64575131107
 52       1.64575131106
 53       1.64575131107
 54       1.64575131106
 55       1.64575131107
 56       1.64575131106
 57       1.64575131106

...

941       1.64575131106
942       1.64575131106
943       1.64575131106
944       1.64575131106
945       1.64575131106
946       1.64575131106
947       1.64575131106
948       1.64575131106
949       1.64575131106
950       1.64575131106
951       1.64575131106
952       1.64575131106
953       1.64575131106
954       1.64575131106
955       1.64575131106
956       1.64575131106
957       1.64575131106
958       1.64575131106
959       1.64575131106
960       1.64575131106
961       1.64575131106
962       1.64575131106
963       1.64575131106
964       1.64575131106
965       1.64575131106
966       1.64575131106
967       1.64575131106
968       1.64575131106
969       1.64575131106
970       1.64575131106
971       1.64575131106
972       1.64575131106
973       1.64575131106
974       1.64575131106
975       1.64575131106
976       1.64575131106
977       1.64575131106
978       1.64575131106
979       1.64575131106
980       1.64575131106
981       1.64575131106
982       1.64575131106
983       1.64575131106
984       1.64575131106
985       1.64575131106
986       1.64575131106
987       1.64575131106
988       1.64575131106
989       1.64575131106
990       1.64575131106
991       1.64575131106
992       1.64575131106
993       1.64575131106
994       1.64575131106
995       1.64575131106
996       1.64575131106
997       1.64575131106
998       1.64575131106
999       1.64575131106
1000       1.64575131106
print " n p" P = vector (RDF,10000) P[0] = 2 for n in range(1,1001): P[n]=3/P[n-1]+P[n-1]/2-1; for n in range(0,1001): print "%3s %11s" %(n,P[n]) 
       
WARNING: Output truncated!  
full_output.txt



  n       p
  0               2.0
  1               1.5
  2              1.75
  3       1.58928571429
  4       1.68228330658
  5       1.62443224903
  6       1.65901521496
  7       1.63780928726
  8       1.65061974217
  9       1.64280903419
 10       1.64754494946
 11       1.64466361398
 12       1.64641302001
 13       1.64534953459
 14       1.64599554925
 15       1.64560294593
 16       1.64584147628
 17       1.64569652988
 18       1.64578459952
 19       1.64573108491
 20       1.64576360126
 21       1.64574384333
 22       1.64575584868
 23       1.64574855391
 24       1.64575298639
 25       1.6457502931
 26       1.64575192961
 27       1.64575093522
 28       1.64575153944
 29       1.6457511723
 30       1.64575139538
 31       1.64575125983
 32       1.64575134219
 33       1.64575129215
 34       1.64575132256
 35       1.64575130408
 36       1.64575131531
 37       1.64575130849
 38       1.64575131263
 39       1.64575131011
 40       1.64575131164
 41       1.64575131071
 42       1.64575131128
 43       1.64575131093
 44       1.64575131114
 45       1.64575131102
 46       1.64575131109
 47       1.64575131105
 48       1.64575131108
 49       1.64575131106
 50       1.64575131107
 51       1.64575131106
 52       1.64575131107
 53       1.64575131106
 54       1.64575131107
 55       1.64575131106
 56       1.64575131106
 57       1.64575131106

...

941       1.64575131106
942       1.64575131106
943       1.64575131106
944       1.64575131106
945       1.64575131106
946       1.64575131106
947       1.64575131106
948       1.64575131106
949       1.64575131106
950       1.64575131106
951       1.64575131106
952       1.64575131106
953       1.64575131106
954       1.64575131106
955       1.64575131106
956       1.64575131106
957       1.64575131106
958       1.64575131106
959       1.64575131106
960       1.64575131106
961       1.64575131106
962       1.64575131106
963       1.64575131106
964       1.64575131106
965       1.64575131106
966       1.64575131106
967       1.64575131106
968       1.64575131106
969       1.64575131106
970       1.64575131106
971       1.64575131106
972       1.64575131106
973       1.64575131106
974       1.64575131106
975       1.64575131106
976       1.64575131106
977       1.64575131106
978       1.64575131106
979       1.64575131106
980       1.64575131106
981       1.64575131106
982       1.64575131106
983       1.64575131106
984       1.64575131106
985       1.64575131106
986       1.64575131106
987       1.64575131106
988       1.64575131106
989       1.64575131106
990       1.64575131106
991       1.64575131106
992       1.64575131106
993       1.64575131106
994       1.64575131106
995       1.64575131106
996       1.64575131106
997       1.64575131106
998       1.64575131106
999       1.64575131106
1000       1.64575131106
WARNING: Output truncated!  
full_output.txt



  n       p
  0               2.0
  1               1.5
  2              1.75
  3       1.58928571429
  4       1.68228330658
  5       1.62443224903
  6       1.65901521496
  7       1.63780928726
  8       1.65061974217
  9       1.64280903419
 10       1.64754494946
 11       1.64466361398
 12       1.64641302001
 13       1.64534953459
 14       1.64599554925
 15       1.64560294593
 16       1.64584147628
 17       1.64569652988
 18       1.64578459952
 19       1.64573108491
 20       1.64576360126
 21       1.64574384333
 22       1.64575584868
 23       1.64574855391
 24       1.64575298639
 25       1.6457502931
 26       1.64575192961
 27       1.64575093522
 28       1.64575153944
 29       1.6457511723
 30       1.64575139538
 31       1.64575125983
 32       1.64575134219
 33       1.64575129215
 34       1.64575132256
 35       1.64575130408
 36       1.64575131531
 37       1.64575130849
 38       1.64575131263
 39       1.64575131011
 40       1.64575131164
 41       1.64575131071
 42       1.64575131128
 43       1.64575131093
 44       1.64575131114
 45       1.64575131102
 46       1.64575131109
 47       1.64575131105
 48       1.64575131108
 49       1.64575131106
 50       1.64575131107
 51       1.64575131106
 52       1.64575131107
 53       1.64575131106
 54       1.64575131107
 55       1.64575131106
 56       1.64575131106
 57       1.64575131106

...

941       1.64575131106
942       1.64575131106
943       1.64575131106
944       1.64575131106
945       1.64575131106
946       1.64575131106
947       1.64575131106
948       1.64575131106
949       1.64575131106
950       1.64575131106
951       1.64575131106
952       1.64575131106
953       1.64575131106
954       1.64575131106
955       1.64575131106
956       1.64575131106
957       1.64575131106
958       1.64575131106
959       1.64575131106
960       1.64575131106
961       1.64575131106
962       1.64575131106
963       1.64575131106
964       1.64575131106
965       1.64575131106
966       1.64575131106
967       1.64575131106
968       1.64575131106
969       1.64575131106
970       1.64575131106
971       1.64575131106
972       1.64575131106
973       1.64575131106
974       1.64575131106
975       1.64575131106
976       1.64575131106
977       1.64575131106
978       1.64575131106
979       1.64575131106
980       1.64575131106
981       1.64575131106
982       1.64575131106
983       1.64575131106
984       1.64575131106
985       1.64575131106
986       1.64575131106
987       1.64575131106
988       1.64575131106
989       1.64575131106
990       1.64575131106
991       1.64575131106
992       1.64575131106
993       1.64575131106
994       1.64575131106
995       1.64575131106
996       1.64575131106
997       1.64575131106
998       1.64575131106
999       1.64575131106
1000       1.64575131106
print " n p" P = vector (RDF,10000) P[0] = 1 for n in range(1,1001): P[n]=3/P[n-1]+P[n-1]/2-1.7; for n in range(0,1001): print "%3s %11s" %(n,P[n]) 
       
WARNING: Output truncated!  
full_output.txt



  n       p
  0               1.0
  1               1.8
  2       0.866666666667
  3       2.19487179487
  4       0.764258327342
  5       2.60750346797
  6       0.754277528812
  7       2.65445465333
  8       0.757402971683
  9       2.6396048783
 10       0.756336177462
 11       2.64465824139
 12       0.756691191774
 13       2.64297480343
 14       0.756572002638
 15       2.64353979017
 16       0.756611901684
 17       2.64335063666
 18       0.756598532222
 19       2.64341401619
 20       0.756603010623
 21       2.64339278552
 22       0.756601510317
 23       2.64339989796
 24       0.756602012915
 25       2.64339751531
 26       0.756601844544
 27       2.6433983135
 28       0.756601900948
 29       2.64339804611
 30       0.756601882053
 31       2.64339813568
 32       0.756601888383
 33       2.64339810568
 34       0.756601886262
 35       2.64339811573
 36       0.756601886973
 37       2.64339811236
 38       0.756601886735
 39       2.64339811349
 40       0.756601886814
 41       2.64339811311
 42       0.756601886788
 43       2.64339811324
 44       0.756601886797
 45       2.6433981132
 46       0.756601886794
 47       2.64339811321
 48       0.756601886795
 49       2.6433981132
 50       0.756601886794
 51       2.64339811321
 52       0.756601886794
 53       2.64339811321
 54       0.756601886794
 55       2.64339811321
 56       0.756601886794
 57       2.64339811321

...

941       2.64339811321
942       0.756601886794
943       2.64339811321
944       0.756601886794
945       2.64339811321
946       0.756601886794
947       2.64339811321
948       0.756601886794
949       2.64339811321
950       0.756601886794
951       2.64339811321
952       0.756601886794
953       2.64339811321
954       0.756601886794
955       2.64339811321
956       0.756601886794
957       2.64339811321
958       0.756601886794
959       2.64339811321
960       0.756601886794
961       2.64339811321
962       0.756601886794
963       2.64339811321
964       0.756601886794
965       2.64339811321
966       0.756601886794
967       2.64339811321
968       0.756601886794
969       2.64339811321
970       0.756601886794
971       2.64339811321
972       0.756601886794
973       2.64339811321
974       0.756601886794
975       2.64339811321
976       0.756601886794
977       2.64339811321
978       0.756601886794
979       2.64339811321
980       0.756601886794
981       2.64339811321
982       0.756601886794
983       2.64339811321
984       0.756601886794
985       2.64339811321
986       0.756601886794
987       2.64339811321
988       0.756601886794
989       2.64339811321
990       0.756601886794
991       2.64339811321
992       0.756601886794
993       2.64339811321
994       0.756601886794
995       2.64339811321
996       0.756601886794
997       2.64339811321
998       0.756601886794
999       2.64339811321
1000       0.756601886794
WARNING: Output truncated!  
full_output.txt



  n       p
  0               1.0
  1               1.8
  2       0.866666666667
  3       2.19487179487
  4       0.764258327342
  5       2.60750346797
  6       0.754277528812
  7       2.65445465333
  8       0.757402971683
  9       2.6396048783
 10       0.756336177462
 11       2.64465824139
 12       0.756691191774
 13       2.64297480343
 14       0.756572002638
 15       2.64353979017
 16       0.756611901684
 17       2.64335063666
 18       0.756598532222
 19       2.64341401619
 20       0.756603010623
 21       2.64339278552
 22       0.756601510317
 23       2.64339989796
 24       0.756602012915
 25       2.64339751531
 26       0.756601844544
 27       2.6433983135
 28       0.756601900948
 29       2.64339804611
 30       0.756601882053
 31       2.64339813568
 32       0.756601888383
 33       2.64339810568
 34       0.756601886262
 35       2.64339811573
 36       0.756601886973
 37       2.64339811236
 38       0.756601886735
 39       2.64339811349
 40       0.756601886814
 41       2.64339811311
 42       0.756601886788
 43       2.64339811324
 44       0.756601886797
 45       2.6433981132
 46       0.756601886794
 47       2.64339811321
 48       0.756601886795
 49       2.6433981132
 50       0.756601886794
 51       2.64339811321
 52       0.756601886794
 53       2.64339811321
 54       0.756601886794
 55       2.64339811321
 56       0.756601886794
 57       2.64339811321

...

941       2.64339811321
942       0.756601886794
943       2.64339811321
944       0.756601886794
945       2.64339811321
946       0.756601886794
947       2.64339811321
948       0.756601886794
949       2.64339811321
950       0.756601886794
951       2.64339811321
952       0.756601886794
953       2.64339811321
954       0.756601886794
955       2.64339811321
956       0.756601886794
957       2.64339811321
958       0.756601886794
959       2.64339811321
960       0.756601886794
961       2.64339811321
962       0.756601886794
963       2.64339811321
964       0.756601886794
965       2.64339811321
966       0.756601886794
967       2.64339811321
968       0.756601886794
969       2.64339811321
970       0.756601886794
971       2.64339811321
972       0.756601886794
973       2.64339811321
974       0.756601886794
975       2.64339811321
976       0.756601886794
977       2.64339811321
978       0.756601886794
979       2.64339811321
980       0.756601886794
981       2.64339811321
982       0.756601886794
983       2.64339811321
984       0.756601886794
985       2.64339811321
986       0.756601886794
987       2.64339811321
988       0.756601886794
989       2.64339811321
990       0.756601886794
991       2.64339811321
992       0.756601886794
993       2.64339811321
994       0.756601886794
995       2.64339811321
996       0.756601886794
997       2.64339811321
998       0.756601886794
999       2.64339811321
1000       0.756601886794
print " n p" P = vector (RDF,10000) P[0] = 4 for n in range(1,1001): P[n]=3/P[n-1]+P[n-1]/2-1.7; for n in range(0,1001): print "%3s %11s" %(n,P[n]) 
       
WARNING: Output truncated!  
full_output.txt



  n       p
  0               4.0
  1              1.05
  2       1.68214285714
  3       0.924510919017
  4       2.00721443002
  5       0.798215840343
  6       2.45748986197
  7       0.749502764588
  8       2.67740506383
  9       0.759190440348
 10       2.63117290156
 11       0.755762376969
 12       2.64738283533
 13       0.756886042924
 14       2.64205158321
 15       0.756507028635
 16       2.64384786631
 17       0.756633701531
 18       2.6432472972
 19       0.756591233048
 20       2.64344861984
 21       0.756605456269
 22       2.64338119161
 23       0.756600691073
 24       2.64340378173
 25       0.756602287367
 26       2.64339621423
 27       0.756601752603
 28       2.64339874936
 29       0.756601931748
 30       2.64339790009
 31       0.756601871735
 32       2.6433981846
 33       0.756601891839
 34       2.64339808929
 35       0.756601885104
 36       2.64339812122
 37       0.756601887361
 38       2.64339811052
 39       0.756601886605
 40       2.6433981141
 41       0.756601886858
 42       2.6433981129
 43       0.756601886773
 44       2.64339811331
 45       0.756601886801
 46       2.64339811317
 47       0.756601886792
 48       2.64339811322
 49       0.756601886795
 50       2.6433981132
 51       0.756601886794
 52       2.64339811321
 53       0.756601886794
 54       2.64339811321
 55       0.756601886794
 56       2.64339811321
 57       0.756601886794

...

941       0.756601886794
942       2.64339811321
943       0.756601886794
944       2.64339811321
945       0.756601886794
946       2.64339811321
947       0.756601886794
948       2.64339811321
949       0.756601886794
950       2.64339811321
951       0.756601886794
952       2.64339811321
953       0.756601886794
954       2.64339811321
955       0.756601886794
956       2.64339811321
957       0.756601886794
958       2.64339811321
959       0.756601886794
960       2.64339811321
961       0.756601886794
962       2.64339811321
963       0.756601886794
964       2.64339811321
965       0.756601886794
966       2.64339811321
967       0.756601886794
968       2.64339811321
969       0.756601886794
970       2.64339811321
971       0.756601886794
972       2.64339811321
973       0.756601886794
974       2.64339811321
975       0.756601886794
976       2.64339811321
977       0.756601886794
978       2.64339811321
979       0.756601886794
980       2.64339811321
981       0.756601886794
982       2.64339811321
983       0.756601886794
984       2.64339811321
985       0.756601886794
986       2.64339811321
987       0.756601886794
988       2.64339811321
989       0.756601886794
990       2.64339811321
991       0.756601886794
992       2.64339811321
993       0.756601886794
994       2.64339811321
995       0.756601886794
996       2.64339811321
997       0.756601886794
998       2.64339811321
999       0.756601886794
1000       2.64339811321
WARNING: Output truncated!  
full_output.txt



  n       p
  0               4.0
  1              1.05
  2       1.68214285714
  3       0.924510919017
  4       2.00721443002
  5       0.798215840343
  6       2.45748986197
  7       0.749502764588
  8       2.67740506383
  9       0.759190440348
 10       2.63117290156
 11       0.755762376969
 12       2.64738283533
 13       0.756886042924
 14       2.64205158321
 15       0.756507028635
 16       2.64384786631
 17       0.756633701531
 18       2.6432472972
 19       0.756591233048
 20       2.64344861984
 21       0.756605456269
 22       2.64338119161
 23       0.756600691073
 24       2.64340378173
 25       0.756602287367
 26       2.64339621423
 27       0.756601752603
 28       2.64339874936
 29       0.756601931748
 30       2.64339790009
 31       0.756601871735
 32       2.6433981846
 33       0.756601891839
 34       2.64339808929
 35       0.756601885104
 36       2.64339812122
 37       0.756601887361
 38       2.64339811052
 39       0.756601886605
 40       2.6433981141
 41       0.756601886858
 42       2.6433981129
 43       0.756601886773
 44       2.64339811331
 45       0.756601886801
 46       2.64339811317
 47       0.756601886792
 48       2.64339811322
 49       0.756601886795
 50       2.6433981132
 51       0.756601886794
 52       2.64339811321
 53       0.756601886794
 54       2.64339811321
 55       0.756601886794
 56       2.64339811321
 57       0.756601886794

...

941       0.756601886794
942       2.64339811321
943       0.756601886794
944       2.64339811321
945       0.756601886794
946       2.64339811321
947       0.756601886794
948       2.64339811321
949       0.756601886794
950       2.64339811321
951       0.756601886794
952       2.64339811321
953       0.756601886794
954       2.64339811321
955       0.756601886794
956       2.64339811321
957       0.756601886794
958       2.64339811321
959       0.756601886794
960       2.64339811321
961       0.756601886794
962       2.64339811321
963       0.756601886794
964       2.64339811321
965       0.756601886794
966       2.64339811321
967       0.756601886794
968       2.64339811321
969       0.756601886794
970       2.64339811321
971       0.756601886794
972       2.64339811321
973       0.756601886794
974       2.64339811321
975       0.756601886794
976       2.64339811321
977       0.756601886794
978       2.64339811321
979       0.756601886794
980       2.64339811321
981       0.756601886794
982       2.64339811321
983       0.756601886794
984       2.64339811321
985       0.756601886794
986       2.64339811321
987       0.756601886794
988       2.64339811321
989       0.756601886794
990       2.64339811321
991       0.756601886794
992       2.64339811321
993       0.756601886794
994       2.64339811321
995       0.756601886794
996       2.64339811321
997       0.756601886794
998       2.64339811321
999       0.756601886794
1000       2.64339811321
###4 cycle### g(x,c,4) 
       
-15/8*c + 1/16*x - 3/2/(2*c - x - 6/x) - 6/(6*c - x + 24/(2*c - x - 6/x)
- 6/x) - 24/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x -
6/x) - 6/x) - 6/x) + 3/8/x
-15/8*c + 1/16*x - 3/2/(2*c - x - 6/x) - 6/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 24/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 3/8/x
solve(g(x,c,4)==x,x) 
       
[x == -c - sqrt(c^2 + 6), x == -c + sqrt(c^2 + 6), x == c - sqrt(c^2 -
2), x == c + sqrt(c^2 - 2), 0 == -160*c*x^11 + 5*x^12 + 60*(31*c^2 +
15)*x^10 - 80*(128*c^3 + 201*c)*x^9 + 4*(7100*c^4 + 26232*c^2 +
8559)*x^8 - 1920*(20*c^5 + 161*c^3 + 183*c)*x^7 + 288*(70*c^6 + 1458*c^4
+ 4239*c^2 + 1371)*x^6 - 1152*(186*c^5 + 1508*c^3 + 1827*c)*x^5 +
144*(5932*c^4 + 23064*c^2 + 9531)*x^4 - 13824*(113*c^3 + 204*c)*x^3 +
15552*(83*c^2 + 51)*x^2 - 435456*c*x + 46656]
[x == -c - sqrt(c^2 + 6), x == -c + sqrt(c^2 + 6), x == c - sqrt(c^2 - 2), x == c + sqrt(c^2 - 2), 0 == -160*c*x^11 + 5*x^12 + 60*(31*c^2 + 15)*x^10 - 80*(128*c^3 + 201*c)*x^9 + 4*(7100*c^4 + 26232*c^2 + 8559)*x^8 - 1920*(20*c^5 + 161*c^3 + 183*c)*x^7 + 288*(70*c^6 + 1458*c^4 + 4239*c^2 + 1371)*x^6 - 1152*(186*c^5 + 1508*c^3 + 1827*c)*x^5 + 144*(5932*c^4 + 23064*c^2 + 9531)*x^4 - 13824*(113*c^3 + 204*c)*x^3 + 15552*(83*c^2 + 51)*x^2 - 435456*c*x + 46656]
solve(0 == -160*c*x^11 + 5*x^12 + 60*(31*c^2 +15)*x^10 - 80*(128*c^3 + 201*c)*x^9 + 4*(7100*c^4 + 26232*c^2 +8559)*x^8 - 1920*(20*c^5 + 161*c^3 + 183*c)*x^7 + 288*(70*c^6 + 1458*c^4+ 4239*c^2 + 1371)*x^6 - 1152*(186*c^5 + 1508*c^3 + 1827*c)*x^5 +144*(5932*c^4 + 23064*c^2 + 9531)*x^4 - 13824*(113*c^3 + 204*c)*x^3 +15552*(83*c^2 + 51)*x^2 - 435456*c*x + 46656,x,c) 
       
([0 == -160*c*x^11 + 5*x^12 + 60*(31*c^2 + 15)*x^10 - 80*(128*c^3 +
201*c)*x^9 + 4*(7100*c^4 + 26232*c^2 + 8559)*x^8 - 1920*(20*c^5 +
161*c^3 + 183*c)*x^7 + 288*(70*c^6 + 1458*c^4 + 4239*c^2 + 1371)*x^6 -
1152*(186*c^5 + 1508*c^3 + 1827*c)*x^5 + 144*(5932*c^4 + 23064*c^2 +
9531)*x^4 - 13824*(113*c^3 + 204*c)*x^3 + 15552*(83*c^2 + 51)*x^2 -
435456*c*x + 46656], [1])
([0 == -160*c*x^11 + 5*x^12 + 60*(31*c^2 + 15)*x^10 - 80*(128*c^3 + 201*c)*x^9 + 4*(7100*c^4 + 26232*c^2 + 8559)*x^8 - 1920*(20*c^5 + 161*c^3 + 183*c)*x^7 + 288*(70*c^6 + 1458*c^4 + 4239*c^2 + 1371)*x^6 - 1152*(186*c^5 + 1508*c^3 + 1827*c)*x^5 + 144*(5932*c^4 + 23064*c^2 + 9531)*x^4 - 13824*(113*c^3 + 204*c)*x^3 + 15552*(83*c^2 + 51)*x^2 - 435456*c*x + 46656], [1])
###8 cycle### g(x,c,8) 
       
-255/128*c + 1/256*x - 3/32/(2*c - x - 6/x) - 3/8/(6*c - x + 24/(2*c - x
- 6/x) - 6/x) - 3/2/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x +
24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/(30*c - x + 24/(2*c - x - 6/x) +
96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x -
6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 24/(62*c
- x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) +
384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) -
6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x +
24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c
- x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 96/(126*c - x +
24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c
- x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) -
6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x -
6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c
- x - 6/x) - 6/x) - 6/x) - 6/x) + 6144/(62*c - x + 24/(2*c - x - 6/x) +
96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x -
6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x +
24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c
- x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) -
6/x) - 6/x) - 6/x) - 6/x) - 384/(254*c - x + 24/(2*c - x - 6/x) +
96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x -
6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x +
24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c
- x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) -
6/x) - 6/x) + 6144/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x +
24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c
- x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x -
6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c
- x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) -
6/x) + 24576/(126*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x
- 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x +
24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) +
96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x -
6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) +
6144/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) -
6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x -
6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x +
24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c
- x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) +
3/128/x
-255/128*c + 1/256*x - 3/32/(2*c - x - 6/x) - 3/8/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 3/2/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 24/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 96/(126*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) + 6144/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 384/(254*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) + 6144/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) + 24576/(126*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) + 6144/(62*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) + 1536/(30*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) + 384/(14*c - x + 24/(2*c - x - 6/x) + 96/(6*c - x + 24/(2*c - x - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) - 6/x) + 3/128/x
solve(g(x,c,8)==x,x)