Kindly help me to obtain the first four numerical solution of given trancedental equation "luck 1"

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syms x
p = 0.47;
t = 0.2154;
r = 3.7037e-04;
s = 0.0013;
a = x*(r + s)/2;
b = x*(x*r*s - 1);
bt1 = sqrt((sqrt(a^2 - b) - a));
bt2 = sqrt((sqrt(a^2 - b) + a));
m1 = (x*s + bt1^2)/bt1;
m2 = (x*s - bt2^2)/bt2;
T1 = [1 0 1 0; m1*bt1 0 m2*bt2 0; 0 (bt1-m1) 0 (bt2+m2); -m1*bt1*t bt1 -m2*bt2*t bt2];
T2 = [cosh(bt1*p) sinh(bt1*p) cos(bt2*p) sin(bt2*p); m1*bt1*cosh(bt1*p) m1*bt1*sinh(bt1*p) m2*bt2*cos(bt2*p) m2*bt2*sin(bt2*p); (bt1-m1)*sinh(bt1*p) (bt1-m1)*cosh(bt1*p) -(bt2+m2)*sin(bt2*p) (bt2+m2)*cos(bt2*p); bt1*sinh(bt1*p) bt1*cosh(bt1*p) -bt2*sin(bt2*p) bt2*cos(bt2*p)];
Z = T2\T1;
N = [m1*bt1*cosh(bt1*0.53) m1*bt1*sinh(bt1*0.53) m2*bt2*cos(bt2*0.53) m2*bt2*sin(bt2*0.53); (bt1-m1)*sinh(bt1*0.53) (bt1-m1)*cosh(bt1*0.53) -(bt2+m2)*sin(bt2*0.53) (bt2+m2)*cos(bt2*0.53)];
B = N*Z;
d = [1 0 1 0; 0 m1 0 -m2];
luck = [d;B];
luck1 = det(luck);

回答 (2 件)

Sulaymon Eshkabilov
Sulaymon Eshkabilov 2020 年 8 月 9 日
Use the commands:
EQN = luck1==0
SOL = solve(EQN, x);
SOL = double(SOL);
  1 件のコメント
Kumar Arpit
Kumar Arpit 2020 年 8 月 9 日
Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.
I am getting this messaage while using this command.

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John D'Errico
John D'Errico 2020 年 8 月 9 日
Have you not tried plotting it? It is so easy to say that you want the "first" 4 roots.
>> vpa(subs(luck1,x,eps))
ans =
-1.7205356741102975599e-26
>> vpa(subs(luck1,x,0))
Error using symengine
Division by zero.
Error in sym/subs>mupadsubs (line 160)
G = mupadmex('symobj::fullsubs',F.s,X2,Y2);
Error in sym/subs (line 145)
G = mupadsubs(F,X,Y);
So at zero, the function is undefined. A singularity there ,with 0/0.
>> limit(luck1,x,0)
ans =
0
It does have a limit at 0 there, so one "solution" is 0.
Of course, this is an excessively nasty, complicated function. So it is VERY slow to evaluate. But the very first thing I would do is plot it. BEFORE asking to compute all the roots, or any fixed number of solutions.
fplot(luck1,[0,10])
And I do mean an excessively nasty mess of a function.
You have polynomial like terms in there, with coefficients on the order of 1e127. Any solution you do get out of this will have little real meaning. The numbers you put into it had all of 2 significant digits in them?
Regardless, if I do try to plot the function at lrager values o x, it does seem to rather smoothly drop down towards -inf, extending the same shape of that plot.
However, it is difficult to know what the function might do for numbers on the order of 1e100. But out there? You are just kidding yourself if you think the result has any meaning.
>> pretty(vpa(luck1,5))
2 2 3 2 2 3 2 2 3
(3.6223e-91 (1.4678e+127 #5 #7 #13 sqrt(#12) + 1.4678e+127 #10 #2 #13 sqrt(#12) - 1.4678e+127 #4 #8 #13
2 2 3 2 2 3 2 2 3
sqrt(#12) - 1.4678e+127 #9 #3 #13 sqrt(#12) + 1.4678e+127 #4 #7 #13 sqrt(#12) - 1.4678e+127 #9 #2 #13
2 2 3 2 2 3 5
sqrt(#12) - 1.4678e+127 #5 #8 #13 sqrt(#12) + 1.4678e+127 #10 #3 #13 sqrt(#12) + 1.0251e+117 x #5 #10 #3 #7
5 6 6 7
- 1.0251e+117 x #5 #9 #3 #8 + 2.2148e+110 x #5 #10 #3 #7 - 2.2148e+110 x #5 #9 #3 #8 - 1.5733e+87 x #5 #10 #3 #7
7 2 2 2 2 2 2
+ 1.5733e+87 x #5 #9 #3 #8 + 1.341e+121 x #5 #8 sqrt(#12) #1 - 1.341e+121 x #10 #3 sqrt(#12) #1
4 2 2 4 2 2 2 2 3/2 3/2
- 2.2121e+114 x #5 #8 #13 sqrt(#12) + 2.2121e+114 x #10 #3 #13 sqrt(#12) + 1.4678e+127 x #5 #8 #13 #12
2 2 2 2 2 2 2 2 2
- 1.341e+121 x #5 #7 sqrt(#12) #1 - 1.341e+121 x #10 #2 sqrt(#12) #1 + 1.341e+121 x #4 #8 sqrt(#12) #1
2 2 2 4 2 2 4 2 2
+ 1.341e+121 x #9 #3 sqrt(#12) #1 + 2.2121e+114 x #5 #7 #13 sqrt(#12) + 2.2121e+114 x #10 #2 #13
4 2 2 4 2 2 2 2 3/2
sqrt(#12) - 2.2121e+114 x #4 #8 #13 sqrt(#12) - 2.2121e+114 x #9 #3 #13 sqrt(#12) - 1.4678e+127 x #5 #7 #13
3/2 2 2 3/2 3/2 5 5
#12 + 1.4678e+127 x #4 #8 #13 #12 + 1.0251e+117 x #10 #4 #2 #7 - 1.0251e+117 x #4 #9 #8 #2
6 6 7 7
+ 2.2148e+110 x #10 #4 #2 #7 - 2.2148e+110 x #4 #9 #8 #2 - 1.5733e+87 x #10 #4 #2 #7 + 1.5733e+87 x #4 #9 #8 #2
2 2 2 2 2 2 4 2 2
- 1.341e+121 x #4 #7 sqrt(#12) #1 + 1.341e+121 x #9 #2 sqrt(#12) #1 + 2.2121e+114 x #4 #7 #13
4 2 2 2 2 3/2 3/2 2 2 2 3/2
sqrt(#12) - 2.2121e+114 x #9 #2 #13 sqrt(#12) - 1.4678e+127 x #4 #7 #13 #12 - 6.8227e+123 x #5 #8 #13
2 2 2 3/2 4 2 2 4 2
sqrt(#12) - 6.8227e+123 x #10 #3 #13 sqrt(#12) + 4.7591e+117 x #5 #8 sqrt(#13) sqrt(#12) + 4.7591e+117 x #10
2 3 2 2 3/2 3 2 2 3/2
#3 sqrt(#13) sqrt(#12) - 1.0239e+121 x #5 #8 sqrt(#13) #12 + 4.8467e+100 x #5 #8 #13
3 2 2 3/2 5 2 2 5 2
sqrt(#12) + 4.8467e+100 x #10 #3 #13 sqrt(#12) - 3.3807e+94 x #5 #8 sqrt(#13) sqrt(#12) - 3.3807e+94 x #10
2 2 2 2 3/2 3/2 4 2 2 3/2
#3 sqrt(#13) sqrt(#12) - 1.0427e+104 x #5 #8 #13 #12 + 7.2732e+97 x #5 #8 sqrt(#13) #12
2 2 2 3/2 2 2 2 3/2 2 2 2 3/2
+ 6.8227e+123 x #5 #7 #13 sqrt(#12) - 6.8227e+123 x #10 #2 #13 sqrt(#12) - 6.8227e+123 x #4 #8 #13
2 2 2 3/2 4 2 2 4 2
sqrt(#12) + 6.8227e+123 x #9 #3 #13 sqrt(#12) - 4.7591e+117 x #5 #7 sqrt(#13) sqrt(#12) + 4.7591e+117 x #10
2 4 2 2 4 2 2
#2 sqrt(#13) sqrt(#12) + 4.7591e+117 x #4 #8 sqrt(#13) sqrt(#12) - 4.7591e+117 x #9 #3
3 2 2 3/2 3 2 2 3/2 3
sqrt(#13) sqrt(#12) + 1.0239e+121 x #5 #7 sqrt(#13) #12 - 4.8467e+100 x #5 #7 #13 sqrt(#12) + 4.8467e+100 x
2 2 3/2 3 2 2 3/2 3 2 2 3/2
#10 #2 #13 sqrt(#12) - 1.0239e+121 x #4 #8 sqrt(#13) #12 + 4.8467e+100 x #4 #8 #13
3 2 2 3/2 5 2 2 5 2 2
sqrt(#12) - 4.8467e+100 x #9 #3 #13 sqrt(#12) + 3.3807e+94 x #5 #7 sqrt(#13) sqrt(#12) - 3.3807e+94 x #10 #2
5 2 2 5 2 2
sqrt(#13) sqrt(#12) - 3.3807e+94 x #4 #8 sqrt(#13) sqrt(#12) + 3.3807e+94 x #9 #3
2 2 2 3/2 3/2 2 2 2 3/2 3/2
sqrt(#13) sqrt(#12) + 1.0427e+104 x #5 #7 #13 #12 - 1.0427e+104 x #4 #8 #13 #12
4 2 2 3/2 4 2 2 3/2 2 2 2 3/2
- 7.2732e+97 x #5 #7 sqrt(#13) #12 + 7.2732e+97 x #4 #8 sqrt(#13) #12 + 6.8227e+123 x #4 #7 #13
2 2 2 3/2 4 2 2 4 2
sqrt(#12) + 6.8227e+123 x #9 #2 #13 sqrt(#12) - 4.7591e+117 x #4 #7 sqrt(#13) sqrt(#12) - 4.7591e+117 x #9
2 3 2 2 3/2 3 2 2 3/2
#2 sqrt(#13) sqrt(#12) + 1.0239e+121 x #4 #7 sqrt(#13) #12 - 4.8467e+100 x #4 #7 #13
3 2 2 3/2 5 2 2 5 2 2
sqrt(#12) - 4.8467e+100 x #9 #2 #13 sqrt(#12) + 3.3807e+94 x #4 #7 sqrt(#13) sqrt(#12) + 3.3807e+94 x #9 #2
2 2 2 3/2 3/2 4 2 2 3/2
sqrt(#13) sqrt(#12) + 1.0427e+104 x #4 #7 #13 #12 - 7.2732e+97 x #4 #7 sqrt(#13) #12
2 2 3/2 2 2 3/2 3
- 1.4678e+127 x #10 #2 #13 #11 sqrt(#12) + 1.4678e+127 x #9 #3 #13 #11 sqrt(#12) - 2.4124e+117 x #10 #4 #2 #7
3 3 3
#1 + 2.4124e+117 x #4 #9 #8 #2 #1 + 2.6406e+123 x #10 #4 #2 #7 #13 - 2.6406e+123 x #4 #9 #8 #2 #13
3 3 4
- 1.4696e+123 x #10 #4 #2 #7 #13 + 1.4696e+123 x #4 #9 #8 #2 #13 - 3.1752e+116 x #10 #4 #2 #7 #13
4 5 5
+ 3.1752e+116 x #4 #9 #8 #2 #13 + 3.9795e+110 x #10 #4 #2 #7 #13 - 3.9795e+110 x #4 #9 #8 #2 #13
5/2 5/2 4
- 3.1617e+126 x #10 #4 #2 #7 #13 + 3.1617e+126 x #4 #9 #8 #2 #13 - 2.2054e+120 x #10 #4 #2 #7 #11
4 5 5
+ 2.2054e+120 x #4 #9 #8 #2 #11 - 1.4295e+114 x #10 #4 #2 #7 #11 + 1.4295e+114 x #4 #9 #8 #2 #11
6 6 2 2 3/2
- 2.0589e+107 x #10 #4 #2 #7 #11 + 2.0589e+107 x #4 #9 #8 #2 #11 + 1.4678e+127 x #9 #2 #13 #11
3 3/2 3 3/2 5
sqrt(#12) + 4.1159e+120 x #5 #10 #3 #7 #13 - 4.1159e+120 x #5 #9 #3 #8 #13 - 1.3326e+114 x #5 #10 #3 #7
5 2 5/2 2 5/2
sqrt(#13) + 1.3326e+114 x #5 #9 #3 #8 sqrt(#13) - 6.831e+119 x #5 #10 #3 #7 #13 + 6.831e+119 x #5 #9 #3 #8 #13
4 3/2 4 3/2 6
+ 6.2407e+113 x #5 #10 #3 #7 #13 - 6.2407e+113 x #5 #9 #3 #8 #13 - 1.0295e+107 x #5 #10 #3 #7
6 3 2 2 2 2
sqrt(#13) + 1.0295e+107 x #5 #9 #3 #8 sqrt(#13) + 1.0239e+121 x #10 #3 sqrt(#13) #11 sqrt(#12) + 1.0427e+104 x #10
2 3/2 4 2 2 3 2 2
#3 #13 #11 sqrt(#12) - 7.2732e+97 x #10 #3 sqrt(#13) #11 sqrt(#12) + 1.0239e+121 x #10 #2 sqrt(#13) #11
3 2 2 2 2 2 3/2
sqrt(#12) - 1.0239e+121 x #9 #3 sqrt(#13) #11 sqrt(#12) + 1.0427e+104 x #10 #2 #13 #11 sqrt(#12) - 1.0427e+104
2 2 2 3/2 4 2 2 4 2 2
x #9 #3 #13 #11 sqrt(#12) - 7.2732e+97 x #10 #2 sqrt(#13) #11 sqrt(#12) + 7.2732e+97 x #9 #3 sqrt(#13) #11
3 3/2 3 3/2 5
sqrt(#12) + 4.1159e+120 x #10 #4 #2 #7 #13 - 4.1159e+120 x #4 #9 #8 #2 #13 - 1.3326e+114 x #10 #4 #2 #7
5 2 5/2 2 5/2
sqrt(#13) + 1.3326e+114 x #4 #9 #8 #2 sqrt(#13) - 6.831e+119 x #10 #4 #2 #7 #13 + 6.831e+119 x #4 #9 #8 #2 #13
4 3/2 4 3/2 6
+ 6.2407e+113 x #10 #4 #2 #7 #13 - 6.2407e+113 x #4 #9 #8 #2 #13 - 1.0295e+107 x #10 #4 #2 #7
6 3 2 2 2 2
sqrt(#13) + 1.0295e+107 x #4 #9 #8 #2 sqrt(#13) - 1.0239e+121 x #9 #2 sqrt(#13) #11 sqrt(#12) - 1.0427e+104 x #9
2 3/2 4 2 2 3
#2 #13 #11 sqrt(#12) + 7.2732e+97 x #9 #2 sqrt(#13) #11 sqrt(#12) - 2.4124e+117 x #5 #10 #3 #7 #1
3 3 3
+ 2.4124e+117 x #5 #9 #3 #8 #1 + 2.6406e+123 x #5 #10 #3 #7 #13 - 2.6406e+123 x #5 #9 #3 #8 #13
3 3 4
- 1.4696e+123 x #5 #10 #3 #7 #13 + 1.4696e+123 x #5 #9 #3 #8 #13 - 3.1752e+116 x #5 #10 #3 #7 #13
4 5 5
+ 3.1752e+116 x #5 #9 #3 #8 #13 + 3.9795e+110 x #5 #10 #3 #7 #13 - 3.9795e+110 x #5 #9 #3 #8 #13
5/2 5/2 4
- 3.1617e+126 x #5 #10 #3 #7 #13 + 3.1617e+126 x #5 #9 #3 #8 #13 - 2.2054e+120 x #5 #10 #3 #7 #11
4 5 5
+ 2.2054e+120 x #5 #9 #3 #8 #11 - 1.4295e+114 x #5 #10 #3 #7 #11 + 1.4295e+114 x #5 #9 #3 #8 #11
6 6 2 2 3/2
- 2.0589e+107 x #5 #10 #3 #7 #11 + 2.0589e+107 x #5 #9 #3 #8 #11 - 1.4678e+127 x #10 #3 #13 #11
5/2 5/2
sqrt(#12) + 3.1617e+126 #5 #10 #3 #7 #6 #13 #11 - 3.1617e+126 #5 #9 #3 #8 #6 #13 #11
2 3/2 4 3
+ 1.3645e+124 x #5 #10 #3 #8 #13 sqrt(#12) - 9.5182e+117 x #5 #10 #3 #8 sqrt(#13) sqrt(#12) - 1.0239e+121 x #5 #10
3/2 3 3/2 5
#3 #8 sqrt(#13) #12 - 9.6933e+100 x #5 #10 #3 #8 #13 sqrt(#12) + 6.7614e+94 x #5 #10 #3 #8
2 3/2 3/2 4 3/2
sqrt(#13) sqrt(#12) + 6.3426e+120 x #5 #10 #3 #8 #13 #12 - 4.4242e+114 x #5 #10 #3 #8 sqrt(#13) #12
4 4 5
- 3.4328e+120 x #5 #10 #8 #2 sqrt(#11) sqrt(#12) + 3.4328e+120 x #10 #4 #3 #8 sqrt(#11) sqrt(#12) - 7.4167e+113 x #5
5 6
#10 #8 #2 sqrt(#11) sqrt(#12) + 7.4167e+113 x #10 #4 #3 #8 sqrt(#11) sqrt(#12) + 5.2686e+90 x #5 #10 #8 #2
6 3
sqrt(#11) sqrt(#12) - 5.2686e+90 x #10 #4 #3 #8 sqrt(#11) sqrt(#12) - 3.1617e+126 #5 #10 #8 #2 #13
3 5/2
sqrt(#11) sqrt(#12) + 3.1617e+126 #10 #4 #3 #8 #13 sqrt(#11) sqrt(#12) + 3.1617e+126 #10 #4 #2 #7 #6 #13 #11
5/2 2 3/2 2
- 3.1617e+126 #4 #9 #8 #2 #6 #13 #11 - 1.3645e+124 x #5 #9 #3 #7 #13 sqrt(#12) + 1.3645e+124 x #10 #4 #8 #2
3/2 4 4
#13 sqrt(#12) + 9.5182e+117 x #5 #9 #3 #7 sqrt(#13) sqrt(#12) - 9.5182e+117 x #10 #4 #8 #2
3 3/2 3 3/2
sqrt(#13) sqrt(#12) + 1.0239e+121 x #5 #9 #3 #7 sqrt(#13) #12 + 9.6933e+100 x #5 #9 #3 #7 #13
3 3/2 3 3/2 5
sqrt(#12) - 1.0239e+121 x #10 #4 #8 #2 sqrt(#13) #12 - 9.6933e+100 x #10 #4 #8 #2 #13 sqrt(#12) - 6.7614e+94 x
5 2 3/2
#5 #9 #3 #7 sqrt(#13) sqrt(#12) + 6.7614e+94 x #10 #4 #8 #2 sqrt(#13) sqrt(#12) - 6.3426e+120 x #5 #9 #3 #7 #13
3/2 2 3/2 3/2 4 3/2
#12 + 6.3426e+120 x #10 #4 #8 #2 #13 #12 + 4.4242e+114 x #5 #9 #3 #7 sqrt(#13) #12
4 3/2 4 4
- 4.4242e+114 x #10 #4 #8 #2 sqrt(#13) #12 + 3.4328e+120 x #5 #9 #2 #7 sqrt(#11) sqrt(#12) - 3.4328e+120 x #4 #9
5 5
#3 #7 sqrt(#11) sqrt(#12) + 7.4167e+113 x #5 #9 #2 #7 sqrt(#11) sqrt(#12) - 7.4167e+113 x #4 #9 #3 #7
6 6
sqrt(#11) sqrt(#12) - 5.2686e+90 x #5 #9 #2 #7 sqrt(#11) sqrt(#12) + 5.2686e+90 x #4 #9 #3 #7
3 3
sqrt(#11) sqrt(#12) + 3.1617e+126 #5 #9 #2 #7 #13 sqrt(#11) sqrt(#12) - 3.1617e+126 #4 #9 #3 #7 #13
2 3/2 4
sqrt(#11) sqrt(#12) - 1.3645e+124 x #4 #9 #2 #7 #13 sqrt(#12) + 9.5182e+117 x #4 #9 #2 #7
3 3/2 3 3/2
sqrt(#13) sqrt(#12) + 1.0239e+121 x #4 #9 #2 #7 sqrt(#13) #12 + 9.6933e+100 x #4 #9 #2 #7 #13
5 2 3/2 3/2
sqrt(#12) - 6.7614e+94 x #4 #9 #2 #7 sqrt(#13) sqrt(#12) - 6.3426e+120 x #4 #9 #2 #7 #13 #12
4 3/2 3/2 2
+ 4.4242e+114 x #4 #9 #2 #7 sqrt(#13) #12 - 1.3645e+124 x #5 #10 #3 #8 #12 #1 - 2.4548e+120 x #5 #10 #3 #7 #11
2 2 2
#1 + 2.4548e+120 x #5 #9 #3 #8 #11 #1 + 3.1617e+126 x #5 #10 #3 #7 #13 #11 - 3.1617e+126 x #5 #9 #3 #8 #13 #11
3 3 4
+ 2.0493e+120 x #5 #10 #3 #7 #13 #11 - 2.0493e+120 x #5 #9 #3 #8 #13 #11 + 2.0075e+114 x #5 #10 #3 #7 #13 #11
4 3/2 3/2
- 2.0075e+114 x #5 #9 #3 #8 #13 #11 + 1.3645e+124 x #5 #9 #3 #7 #12 #1 - 1.3645e+124 x #10 #4 #8 #2 #12 #1
5/2 5/2
- 2.9357e+127 #5 #10 #2 #7 #6 #13 sqrt(#11) + 2.9357e+127 #5 #9 #8 #2 #6 #13 sqrt(#11) + 2.9357e+127 #10 #4 #3 #7
5/2 5/2 2
#6 #13 sqrt(#11) - 2.9357e+127 #4 #9 #3 #8 #6 #13 sqrt(#11) - 2.4548e+120 x #10 #4 #2 #7 #11 #1
2 2 2
+ 2.4548e+120 x #4 #9 #8 #2 #11 #1 + 3.1617e+126 x #10 #4 #2 #7 #13 #11 - 3.1617e+126 x #4 #9 #8 #2 #13 #11
3 3 4
+ 2.0493e+120 x #10 #4 #2 #7 #13 #11 - 2.0493e+120 x #4 #9 #8 #2 #13 #11 + 2.0075e+114 x #10 #4 #2 #7 #13 #11
4 3/2 3 3/2
- 2.0075e+114 x #4 #9 #8 #2 #13 #11 + 1.3645e+124 x #4 #9 #2 #7 #12 #1 + 9.5182e+117 x #5 #10 #3 #8 #13 #12
3/2 3/2 2 3/2 2 3/2
+ 1.4678e+127 x #5 #10 #3 #8 #13 #12 + 2.9861e+122 x #5 #10 #3 #7 #13 #11 - 2.9861e+122 x #5 #9 #3 #8 #13
4 4
#11 - 2.0829e+116 x #5 #10 #3 #7 sqrt(#13) #11 + 2.0829e+116 x #5 #9 #3 #8 sqrt(#13) #11
3 3/2 3 3/2 5
- 5.06e+116 x #5 #10 #3 #7 #13 #11 + 5.06e+116 x #5 #9 #3 #8 #13 #11 + 3.5295e+110 x #5 #10 #3 #7 sqrt(#13) #11
5 3 3/2 3
- 3.5295e+110 x #5 #9 #3 #8 sqrt(#13) #11 - 9.5182e+117 x #5 #9 #3 #7 #13 #12 + 9.5182e+117 x #10 #4 #8 #2 #13
3/2 3/2 3/2 3/2 3/2
#12 - 1.4678e+127 x #5 #9 #3 #7 #13 #12 + 1.4678e+127 x #10 #4 #8 #2 #13 #12
2 3/2 2 3/2 4
+ 2.9861e+122 x #10 #4 #2 #7 #13 #11 - 2.9861e+122 x #4 #9 #8 #2 #13 #11 - 2.0829e+116 x #10 #4 #2 #7
4 3 3/2
sqrt(#13) #11 + 2.0829e+116 x #4 #9 #8 #2 sqrt(#13) #11 - 5.06e+116 x #10 #4 #2 #7 #13 #11
3 3/2 5 5
+ 5.06e+116 x #4 #9 #8 #2 #13 #11 + 3.5295e+110 x #10 #4 #2 #7 sqrt(#13) #11 - 3.5295e+110 x #4 #9 #8 #2
3 3/2 3/2 3/2
sqrt(#13) #11 - 9.5182e+117 x #4 #9 #2 #7 #13 #12 - 1.4678e+127 x #4 #9 #2 #7 #13 #12
3 3
- 1.4696e+123 x #5 #10 #8 #2 sqrt(#13) sqrt(#11) sqrt(#12) + 1.4696e+123 x #10 #4 #3 #8
2 3/2 2
sqrt(#13) sqrt(#11) sqrt(#12) - 3.8116e+123 x #5 #10 #8 #2 #13 sqrt(#11) sqrt(#12) + 3.8116e+123 x #10 #4 #3 #8
3/2 4 4
#13 sqrt(#11) sqrt(#12) + 2.0949e+117 x #5 #10 #8 #2 sqrt(#13) sqrt(#11) sqrt(#12) - 2.0949e+117 x #10 #4 #3 #8
3 3/2 3
sqrt(#13) sqrt(#11) sqrt(#12) - 2.2054e+120 x #5 #10 #8 #2 sqrt(#13) sqrt(#11) #12 - 1.141e+117 x #5 #10 #8 #2
3/2 3 3/2 3 3/2
#13 sqrt(#11) sqrt(#12) + 2.2054e+120 x #10 #4 #3 #8 sqrt(#13) sqrt(#11) #12 + 1.141e+117 x #10 #4 #3 #8 #13
5 5
sqrt(#11) sqrt(#12) + 1.2326e+110 x #5 #10 #8 #2 sqrt(#13) sqrt(#11) sqrt(#12) - 1.2326e+110 x #10 #4 #3 #8
2 3/2 3/2 2 3/2
sqrt(#13) sqrt(#11) sqrt(#12) + 1.3662e+120 x #5 #10 #8 #2 #13 sqrt(#11) #12 - 1.3662e+120 x #10 #4 #3 #8 #13
3/2 4 3/2 4
sqrt(#11) #12 - 9.5297e+113 x #5 #10 #8 #2 sqrt(#13) sqrt(#11) #12 + 9.5297e+113 x #10 #4 #3 #8
3/2 3 3
sqrt(#13) sqrt(#11) #12 + 3.4328e+120 x #10 #4 #2 #7 #6 sqrt(#13) #11 - 3.4328e+120 x #4 #9 #8 #2 #6 sqrt(#13) #11
2 3/2 2 3/2 4
- 6.831e+119 x #10 #4 #2 #7 #6 #13 #11 + 6.831e+119 x #4 #9 #8 #2 #6 #13 #11 - 2.4386e+97 x #10 #4 #2 #7 #6
4
sqrt(#13) #11 + 2.4386e+97 x #4 #9 #8 #2 #6 sqrt(#13) #11 + 1.3645e+124 x #4 #9 #2 #7 #11 sqrt(#12) #1
3 3
+ 1.4696e+123 x #5 #9 #2 #7 sqrt(#13) sqrt(#11) sqrt(#12) - 1.4696e+123 x #4 #9 #3 #7
2 3/2 2
sqrt(#13) sqrt(#11) sqrt(#12) + 3.8116e+123 x #5 #9 #2 #7 #13 sqrt(#11) sqrt(#12) - 3.8116e+123 x #4 #9 #3 #7
3/2 4 4
#13 sqrt(#11) sqrt(#12) - 2.0949e+117 x #5 #9 #2 #7 sqrt(#13) sqrt(#11) sqrt(#12) + 2.0949e+117 x #4 #9 #3 #7
3 3/2 3 3/2
sqrt(#13) sqrt(#11) sqrt(#12) + 2.2054e+120 x #5 #9 #2 #7 sqrt(#13) sqrt(#11) #12 + 1.141e+117 x #5 #9 #2 #7 #13
3 3/2 3 3/2
sqrt(#11) sqrt(#12) - 2.2054e+120 x #4 #9 #3 #7 sqrt(#13) sqrt(#11) #12 - 1.141e+117 x #4 #9 #3 #7 #13
5 5
sqrt(#11) sqrt(#12) - 1.2326e+110 x #5 #9 #2 #7 sqrt(#13) sqrt(#11) sqrt(#12) + 1.2326e+110 x #4 #9 #3 #7
2 3/2 3/2 2 3/2
sqrt(#13) sqrt(#11) sqrt(#12) - 1.3662e+120 x #5 #9 #2 #7 #13 sqrt(#11) #12 + 1.3662e+120 x #4 #9 #3 #7 #13
3/2 4 3/2 4
sqrt(#11) #12 + 9.5297e+113 x #5 #9 #2 #7 sqrt(#13) sqrt(#11) #12 - 9.5297e+113 x #4 #9 #3 #7
3/2
sqrt(#13) sqrt(#11) #12 - 2.6406e+123 x #5 #10 #3 #7 #6 #11 #1 + 2.6406e+123 x #5 #9 #3 #8 #6 #11 #1
3 3/2
+ 9.5182e+117 x #5 #10 #3 #8 #13 #11 sqrt(#12) - 1.4678e+127 x #5 #10 #3 #8 #13 #11 sqrt(#12) - 3.1617e+126 x #5 #10
#8 #2 sqrt(#11) sqrt(#12) #1 + 3.1617e+126 x #10 #4 #3 #8 sqrt(#11) sqrt(#12) #1 - 2.9392e+123 x #5 #10 #8 #2
3/2 3/2
sqrt(#11) #12 #1 + 2.9392e+123 x #10 #4 #3 #8 sqrt(#11) #12 #1 - 2.6406e+123 x #10 #4 #2 #7 #6 #11 #1
3 3
+ 2.6406e+123 x #4 #9 #8 #2 #6 #11 #1 - 3.1874e+121 x #5 #10 #2 #7 #6 sqrt(#13) sqrt(#11) + 3.1874e+121 x #5 #9 #8 #2
3 3
#6 sqrt(#13) sqrt(#11) + 3.1874e+121 x #10 #4 #3 #7 #6 sqrt(#13) sqrt(#11) - 3.1874e+121 x #4 #9 #3 #8 #6
2 3/2 2 3/2
sqrt(#13) sqrt(#11) + 6.3426e+120 x #5 #10 #2 #7 #6 #13 sqrt(#11) - 6.3426e+120 x #5 #9 #8 #2 #6 #13
2 3/2 2 3/2
sqrt(#11) - 6.3426e+120 x #10 #4 #3 #7 #6 #13 sqrt(#11) + 6.3426e+120 x #4 #9 #3 #8 #6 #13
4 4
sqrt(#11) + 2.2642e+98 x #5 #10 #2 #7 #6 sqrt(#13) sqrt(#11) - 2.2642e+98 x #5 #9 #8 #2 #6
4 4
sqrt(#13) sqrt(#11) - 2.2642e+98 x #10 #4 #3 #7 #6 sqrt(#13) sqrt(#11) + 2.2642e+98 x #4 #9 #3 #8 #6
3 3
sqrt(#13) sqrt(#11) - 9.5182e+117 x #5 #9 #3 #7 #13 #11 sqrt(#12) + 9.5182e+117 x #10 #4 #8 #2 #13 #11
3/2 3/2
sqrt(#12) + 1.4678e+127 x #5 #9 #3 #7 #13 #11 sqrt(#12) - 1.4678e+127 x #10 #4 #8 #2 #13 #11
sqrt(#12) + 3.1617e+126 x #5 #9 #2 #7 sqrt(#11) sqrt(#12) #1 - 3.1617e+126 x #4 #9 #3 #7 sqrt(#11) sqrt(#12) #1
3/2 3/2
+ 2.9392e+123 x #5 #9 #2 #7 sqrt(#11) #12 #1 - 2.9392e+123 x #4 #9 #3 #7 sqrt(#11) #12 #1
3 3/2 2
- 9.5182e+117 x #4 #9 #2 #7 #13 #11 sqrt(#12) + 1.4678e+127 x #4 #9 #2 #7 #13 #11 sqrt(#12) - 1.4696e+123 x #5 #10
2 3
#3 #7 #6 #13 #11 + 1.4696e+123 x #5 #9 #3 #8 #6 #13 #11 + 5.7052e+116 x #5 #10 #3 #7 #6 #13 #11
3 3/2 3/2
- 5.7052e+116 x #5 #9 #3 #8 #6 #13 #11 - 3.1617e+126 x #5 #10 #3 #7 #6 #13 #11 + 3.1617e+126 x #5 #9 #3 #8 #6 #13
3 2 3/2
#11 + 1.0239e+121 x #5 #10 #3 #8 sqrt(#13) #11 sqrt(#12) - 6.3426e+120 x #5 #10 #3 #8 #13 #11
4 2
sqrt(#12) + 4.4242e+114 x #5 #10 #3 #8 sqrt(#13) #11 sqrt(#12) + 4.4108e+120 x #5 #10 #8 #2 sqrt(#11) sqrt(#12) #1
2 2
- 4.4108e+120 x #10 #4 #3 #8 sqrt(#11) sqrt(#12) #1 + 3.1617e+126 x #5 #10 #8 #2 #13 sqrt(#11) sqrt(#12) - 3.1617e+126
2 3 3
x #10 #4 #3 #8 #13 sqrt(#11) sqrt(#12) + 2.5936e+120 x #5 #10 #8 #2 #13 sqrt(#11) sqrt(#12) - 2.5936e+120 x #10 #4 #3
4 4
#8 #13 sqrt(#11) sqrt(#12) - 8.0539e+113 x #5 #10 #8 #2 #13 sqrt(#11) sqrt(#12) + 8.0539e+113 x #10 #4 #3 #8 #13
3 3/2 3
sqrt(#11) sqrt(#12) + 2.0502e+117 x #5 #10 #8 #2 #13 sqrt(#11) #12 - 2.0502e+117 x #10 #4 #3 #8 #13
3/2 3/2 3/2 5/2
sqrt(#11) #12 + 3.1617e+126 x #5 #10 #8 #2 #13 sqrt(#11) #12 + 2.6406e+123 x #5 #10 #8 #2 #13
3/2 3/2 5/2
sqrt(#11) sqrt(#12) - 3.1617e+126 x #10 #4 #3 #8 #13 sqrt(#11) #12 - 2.6406e+123 x #10 #4 #3 #8 #13
2 2
sqrt(#11) sqrt(#12) - 1.4696e+123 x #10 #4 #2 #7 #6 #13 #11 + 1.4696e+123 x #4 #9 #8 #2 #6 #13 #11
3 3 3/2
+ 5.7052e+116 x #10 #4 #2 #7 #6 #13 #11 - 5.7052e+116 x #4 #9 #8 #2 #6 #13 #11 - 3.1617e+126 x #10 #4 #2 #7 #6 #13
3/2 3 3
#11 + 3.1617e+126 x #4 #9 #8 #2 #6 #13 #11 - 1.0239e+121 x #5 #9 #3 #7 sqrt(#13) #11 sqrt(#12) + 1.0239e+121 x #10
2 3/2 2 3/2
#4 #8 #2 sqrt(#13) #11 sqrt(#12) + 6.3426e+120 x #5 #9 #3 #7 #13 #11 sqrt(#12) - 6.3426e+120 x #10 #4 #8 #2 #13
4 4
#11 sqrt(#12) - 4.4242e+114 x #5 #9 #3 #7 sqrt(#13) #11 sqrt(#12) + 4.4242e+114 x #10 #4 #8 #2 sqrt(#13) #11
2 2
sqrt(#12) - 4.4108e+120 x #5 #9 #2 #7 sqrt(#11) sqrt(#12) #1 + 4.4108e+120 x #4 #9 #3 #7 sqrt(#11) sqrt(#12) #1
2 2
- 3.1617e+126 x #5 #9 #2 #7 #13 sqrt(#11) sqrt(#12) + 3.1617e+126 x #4 #9 #3 #7 #13 sqrt(#11) sqrt(#12) - 2.5936e+120
3 3 4
x #5 #9 #2 #7 #13 sqrt(#11) sqrt(#12) + 2.5936e+120 x #4 #9 #3 #7 #13 sqrt(#11) sqrt(#12) + 8.0539e+113 x #5 #9 #2 #7
4 3
#13 sqrt(#11) sqrt(#12) - 8.0539e+113 x #4 #9 #3 #7 #13 sqrt(#11) sqrt(#12) - 2.0502e+117 x #5 #9 #2 #7 #13
3/2 3 3/2 3/2 3/2
sqrt(#11) #12 + 2.0502e+117 x #4 #9 #3 #7 #13 sqrt(#11) #12 - 3.1617e+126 x #5 #9 #2 #7 #13 sqrt(#11) #12
5/2 3/2 3/2
- 2.6406e+123 x #5 #9 #2 #7 #13 sqrt(#11) sqrt(#12) + 3.1617e+126 x #4 #9 #3 #7 #13 sqrt(#11) #12
5/2 3
+ 2.6406e+123 x #4 #9 #3 #7 #13 sqrt(#11) sqrt(#12) - 1.0239e+121 x #4 #9 #2 #7 sqrt(#13) #11
2 3/2 4
sqrt(#12) + 6.3426e+120 x #4 #9 #2 #7 #13 #11 sqrt(#12) - 4.4242e+114 x #4 #9 #2 #7 sqrt(#13) #11
3
sqrt(#12) - 1.3645e+124 x #5 #10 #3 #8 #11 sqrt(#12) #1 + 3.4328e+120 x #5 #10 #3 #7 #6 sqrt(#13) #11
3 2 3/2
- 3.4328e+120 x #5 #9 #3 #8 #6 sqrt(#13) #11 - 6.831e+119 x #5 #10 #3 #7 #6 #13 #11
2 3/2 4 4
+ 6.831e+119 x #5 #9 #3 #8 #6 #13 #11 - 2.4386e+97 x #5 #10 #3 #7 #6 sqrt(#13) #11 + 2.4386e+97 x #5 #9 #3 #8 #6
3/2 3/2
sqrt(#13) #11 + 2.9357e+127 x #5 #10 #2 #7 #6 #13 sqrt(#11) - 2.9357e+127 x #5 #9 #8 #2 #6 #13
3/2 3/2
sqrt(#11) - 2.9357e+127 x #10 #4 #3 #7 #6 #13 sqrt(#11) + 2.9357e+127 x #4 #9 #3 #8 #6 #13 sqrt(#11) + 1.3645e+124
2 2
x #5 #9 #3 #7 #11 sqrt(#12) #1 - 1.3645e+124 x #10 #4 #8 #2 #11 sqrt(#12) #1))/((#10 - 1.0 #9 )
2 2
#6 (1.9258e+15 x - 2.3058e+18 sqrt(#13)) (1.9258e+15 x + 2.3058e+18 sqrt(#13)) (#5 + #4 ) sqrt(#13) sqrt(#11))
where
4 3 2
#1 == 4.6679e-14 x + 4.3211e-7 x + x
#2 == sin(0.53 sqrt(#11))
#3 == cos(0.53 sqrt(#11))
#4 == sin(0.47 sqrt(#11))
#5 == cos(0.47 sqrt(#11))
#6 == 0.00083519 x - 1.0 sqrt(#13)
#7 == sinh(0.53 sqrt(#12))
#8 == cosh(0.53 sqrt(#12))
#9 == sinh(0.47 sqrt(#12))
#10 == cosh(0.47 sqrt(#12))
#11 == 0.00083519 x + sqrt(#13)
#12 == sqrt(#13) - 0.00083519 x
2
#13 == 2.1605e-7 x + x

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