MaplePrimes Questions

If I make a single plot it will always be located in the centre of the worksheet. Is there an option to place it at the left border?

 

Dear friends,

I have to solve the BVP of the following type:

(x-1)*y''(x)+y'(x)=1+x, y(0)=1, y(1)=1

Expressing the highest derivative (y''(x)), we get a singularity at x=1.

So, as recommended, the method bvp[middefer] (or bvp[midrich]) is used:

dsolve({(x-1)*diff(y(x), x$2)+diff(y(x),x) = 1+x, y(0)=0, y(1)=1}, type = numeric, method = bvp[middefer], y(x), 'output' = Array([seq(k/10, k=0..10)]), 'abserr'=1.0e-3, 'maxmesh'=100)

Maple generates the following error:

Error, (in dsolve/numeric/bvp) unable to achieve requested accuracy of 0.10e-2 with maximum 100 point mesh (was able to get 0.82e3), consider increasing `maxmesh` or using larger `abserr`
But as I increase maxmesh, the achievable accuracy (reported in "(was able to get XXX)") decreases:

for

maxmesh = 200: 0.19e4

maxmesh = 500: 0.54e4

maxmesh = 1000: 0.12e5

maxmesh = 5000: 0.73e5

and so on.....

How to solve this equation with desirable accurancy and usage of Array as output?

i want to solve an ode , but maple return an integral in result, how can i have an answer?


 

restart:

eq:=1/(x*y^(2/3))*8.620689655172415*10^(-16)*(-3.11*10^23*x^2*y^(7/6)-3.92*10^19*y^(25/6)+2.14545039999999*10^29*(0.0108*exp(-45.07/y)+exp(-19.98/y^(1/3)-0.00935317203476387*y^2)))/(x+0.015*y^(1.2));

0.8620689655e-15*(-0.3110000000e24*x^2*y^(7/6)-0.3920000000e20*y^(25/6)+0.2317086432e28*exp(-45.07/y)+0.2145450400e30*exp(-19.98/y^(1/3)-0.935317203476387e-2*y^2))/(x*y^(2/3)*(x+0.15e-1*y^1.2))

(1)

eq:=subs(y=y(t),eq):

 

ans:=dsolve(diff(y(t),t)=eq);

t+Intat((12500/1724137931)*x*_a^(2/3)*(3*_a^(6/5)+200*x)/(49*_a^(25/6)+388750*x^2*_a^(7/6)-2896358040*exp(-(4507/100)/_a)-268181300000*exp(-(1/100000000000000000)*(935317203476387*_a^(7/3)+1998000000000000000)/_a^(1/3))), _a = y(t))+_C1 = 0

(2)

 

 

 


 

Download dsolve.mw

 Dear Maple users,

In Maple 18, I want to  label y axis as $\hat{\sigma}_y$.

labels = [x, sigma[y]] works fine but I have no idea how to put a hat on sigma[y] .

regards,

 

Using Tools -> Check for Updates, I have just tried to update my Maple installation from 2017.0 to 2017.1. The download itself went without a hitch, but then nothing happened. In view of the fact that I clicked a button titled 'Download and Install', I would certainly expect the installation to have started automatically after download. Are anyone else experiencing the same odd behaviour?

PS: Related question of mine is Automatic update of help pages?

Limit of function f(x)=[arcsin(x)]/tan(πx/2).  At point x=1

I can't take the inverse laplace transform of one kind of functions.

Would you like to help me?

Thanks.

hello,

i went to plot a complex numerical solution , i used odeplot but did not work

please help

Thank you very much 


 

restart; with(plots)

NULL

L := 1;

1

(1)

R := 0.57e-1;

0.57e-1

(2)

V := evalf(Pi*R^2*L);

0.1020703453e-1

(3)

pcy := m/V;

97.97164858*m

(4)

Am := 0.6e-1;

0.6e-1

(5)

``

k := evalf(2*Pi/(1.56*T*T));

4.027682890/T^2

(6)

h := 10; -1; zz := h+Am*cos(omega*t)

10+0.6e-1*cos(omega*t)

(7)

g := 9.81;

9.81

(8)

pe := 1025;

1025

(9)

T := 3.57;

3.57

(10)

omega := 2*Pi/T;

1.759995884

(11)

m := (1/2)*pe*evalf(Pi*R^2*L);

5.231105195

(12)

``

``

eq := m*(diff(z(t), `$`(t, 2)))-pe*g*L*R^2-pe*L*R^2*(diff(z(t), `$`(t, 2)))+I*R^3*pe*L*cosh(k*(zz+h))*cos(omega*t)*exp(-I*omega*t)/cosh(k*h)

1.900880195*(diff(diff(z(t), t), t))-32.66950725+(0.1607410765e-1*I)*cosh(6.320462130+0.1896138639e-1*cos(1.759995884*t))*cos(1.759995884*t)*exp(-(1.759995884*I)*t)

(13)

csi := z(0) = 0, (D(z))(0) = 0;

z(0) = 0, (D(z))(0) = 0

(14)

sol := dsolve({csi, eq}, numeric, maxfun = 0):

NULL

sol2 := simplify(evalf(expand(sol))):

fg1 := evalc(Re(sol)):

odeplot(rhs(sol), [t, z(t)], t = 0 .. 3, labels = ["t", "z(t)"], color = blue, thickness = 1, legend = ["z(t) "], axes = boxed)

Error, invalid input: rhs received sol, which is not valid for its 1st argument, expr

 

complexplot(sol, [t, z(t)], t = 0 .. 3, labels = ["t", "z(t)"], color = blue, thickness = 1, legend = ["z(t) "], axes = boxed)

Error, (in plots:-complexplot) invalid input: `plots/complexplot` expects its 2nd argument, r, to be of type {range, name = range}, but received [t, z(t)]

 

NULL

NULL

``


 

Download mapleprime.mwmapleprime.mw

I created a loop to calculate, using random numbers, the probability of a die roll. I got 0, which I originally attributed to the fact that the probability might have just been that low, but in comparing it to a binomial distribution, it shouldn't be 0.

I tried editing the loop to do a coin toss instead, where the probability is 0.5, and that worked fine. So I don't think my loop structure is necessarily wrong. But perhaps I wrongly input getting a 0.167 probability somehow.

Any advice would be appreciated!

dierollfail.mw

https://drive.google.com/file/d/0Bxs_ao6uuBDUNmd5ZVJtX29GT3c/view?usp=sharing
https://drive.google.com/file/d/0Bxs_ao6uuBDUSUdHSTcwSEQtS3M/view?usp=sharing

would like to return K map of P1

Summation expression for logic only consider 1 but how about wildcard x ?

if consider wildcard x as 1 too, then will use below

source = [[0,0,1,0],[0,0,1,1],[0,1,0,1],[0,1,1,0],[0,1,1,1],[1,0,0,0],[1,0,0,1],[1,0,1,0],[1,0,1,1],[1,1,0,0],[1,1,0,1],[1,1,1,0],[1,1,1,1]];
i use Quine Mccluskey algorithm

got result below

wildcard is 5 or x
[[0, 5, 1, 5], [5, 0, 1, 5], [5, 5, 1, 0], [1, 0, 5, 5], [1, 5, 0, 5], [1, 5, 5, 0], [5, 5, 1, 1], [5, 1, 5, 1], [5, 1, 1, 5], [1, 5, 5, 1], [1, 5, 1, 5], [1, 1, 5, 5]]
A'C + B'C + CD' + AB' + AC' + AD' + CD + BD + BC + AD + AC + AB
 
table1 = [[0,0,0,0],
[0,0,0,1],
[0,0,1,0],
[0,0,1,1],
[0,1,0,0],
[0,1,0,1],
[0,1,1,0],
[0,1,1,1],
[1,0,0,0],
[1,0,0,1],
[1,0,1,0],
[1,0,1,1],
[1,1,0,0],
[1,1,0,1],
[1,1,1,0],
[1,1,1,1]];
 
loand(lonot(tt[0]),tt[2])
loand(lonot(tt[1]),tt[2])
loand(lonot(tt[3]),tt[2])
loand(lonot(tt[1]),tt[0])
loand(lonot(tt[2]),tt[0])
loand(lonot(tt[3]),tt[0])
loand(tt[2],tt[3])
loand(tt[1],tt[3])
loand(tt[1],tt[2])
loand(tt[0],tt[3])
loand(tt[0],tt[2])
loand(tt[0],tt[1])
 
loor(loor(loor(loor(loor(loor(loor(loor(loor(loor(loor(loand(lonot(tt[0]),tt[2]),
loand(lonot(tt[1]),tt[2])),
loand(lonot(tt[3]),tt[2])),
loand(lonot(tt[1]),tt[0])),
loand(lonot(tt[2]),tt[0])),
loand(lonot(tt[3]),tt[0])),
loand(tt[2],tt[3])),
loand(tt[1],tt[3])),
loand(tt[1],tt[2])),
loand(tt[0],tt[3])),
loand(tt[0],tt[2])),
loand(tt[0],tt[1]));
def lonot(z):
    if z == 1:
        return 0
    else:
        return 1
def loand(a, b):
    if a == 1 and b == 1:
        return 1
    else:
        return 0
def loor(a, b):
    if a == 0 and b == 0:
        return 0
    else:
        return 1
#A'C + B'C + AB' + CD + A'BD
for tt in table1:
    print loor(loor(loor(loor(loor(loor(loor(loor(loor(loor(loor(loand(lonot(tt[0]),tt[2]),
loand(lonot(tt[1]),tt[2])),
loand(lonot(tt[3]),tt[2])),
loand(lonot(tt[1]),tt[0])),
loand(lonot(tt[2]),tt[0])),
loand(lonot(tt[3]),tt[0])),
loand(tt[2],tt[3])),
loand(tt[1],tt[3])),
loand(tt[1],tt[2])),
loand(tt[0],tt[3])),
loand(tt[0],tt[2])),
loand(tt[0],tt[1]));
 
finally i use python to verify
return
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
 
seems correct if wildcard is 1 too, but
can boolean simplify function simplify this
A'C + B'C + CD' + AB' + AC' + AD' + CD + BD + BC + AD + AC + AB
 
to
 
C + A + B.D   which is
P1 = D + Q0 + Q1.N in png file ?

Hi, friends

I need to calculate the double integral over a non-rectangular domain.

Say, the domain is the triangle (in red)

When I enter

int(int((x^2+y^2)*`if`((y-x-1/2 <= 0) and (y+2*x-2<=0) and (y+x/2-1/2>=0), 1, 0), x=0..1, numeric = true), y=0..1, numeric = true);

or 

int(int((x^2+y^2)*eval(`if`((y-x-1/2 <= 0) and (y+2*x-2<=0) and (y+x/2-1/2>=0), 1, 0)), x=0..1, numeric = true), y=0..1, numeric = true);

an error occur (Error, (in int) cannot determine if this expression is true or false: y-x <= 1/2 and y+2*x <= 2 and 0 <= y+(1/2)*x-1/2)

For me, it is desirable to write boundary conditions in the int operator itself, not as a separate expession.

 

Regarding my recent question http://www.mapleprimes.com/questions/221909-How-To-Extract-Data-From-Implicit-Function I would like to share an interesting observation. Here the code of the program:

restart;
R0 := ln(y)+Re(Psi(1/2+(2*(p^2+(1/2)*sqrt(2*I+4*ksi_fs^2*p^2)*tanh(sqrt(2*I+4*ksi_fs^2*p^2)*x)/(tau+0.5e-2*a)))/y))+gamma+2*ln(2)
tau:= 10.000:ksi_fs:=10:p:=0.037:
R0p:= unapply(R0, [a,x]):
R0f:= proc(a,x)
local r:= fsolve(R0p(a,x), y= 0..1);
   `if`(r::float, r, Float(undefined))
end proc:
M:= Matrix(
   (100,100),
   (i,j)-> R0f(i, 1 + (j-1)*(0.5-0)/(100-1)),
   datatype= float[8]
);

After approximately 2 hours of calculations I get a message window

But I repeat this calculations on another computer with the same Windows 7 64 bit and Maple 17 I don't get such error and I obtain desired data.

So can Maple be sensitive to the hardware? 

I don't like the font times new roman in Math 2D input. Can't find where to set a font anywhere except in the head at a new worksheet. But that alters immediately after executing a command. There should be a place in preferences at least to do a persistent change of font.

 

Hi,

I want to calculate the Jacobian of my function in terms of x,y,z. It is a Gerstner function and I need to caculate the normal of the displaced point. This can be achieved by getting the Jacobian Matrix. However when using Maple it isn't caculating it. The way I'm calling it is below. I have a vector function for tx,ty,tz:

 

with(VectorCalculus);
Jacobian([tx, ty, tz], [x, y]);

 

I'm not well versed in Maple I was wondering if anyone can help me out on how to get the Jacobian Matrix for tx,ty,tz

Best Regards

Paul

 

 

 

Hello everyone.

Please I am trying to obtain series expansion of the expression below in u and v up to order 30 but encounter difficulties cum maple is slow to display solution. Can I get help on the code and what to do to optimize the displayed time of maple?

Thank you in anticipation of your quick and positive responses and suggestions.

convert(series(convert(series((y[n]+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2+8 u^3 sin(u) h-4 sin(2 u) h u^3-4 sin(2 v) h v^3+8 v^3 h sin(v)-4 v^3 h sin(2 u+v)-4 u^3 h sin(u-2 v)-4 u^3 h sin(u+2 v)+4 v^3 h sin(2 u-v)+2 u^3 h sin(2 u+2 v)+2 v^3 h sin(2 u+2 v)+2 u^3 h sin(2 u-2 v)-2 v^3 h sin(2 u-2 v)+8 h u^3 v^2 sin(u)+8 h u^2 v^3 sin(v)-4 h u^3 v^2 sin(2 u+v)+4 h u^2 v^3 sin(2 u+v)+4 h u^3 v^2 sin(u-2 v)+4 h u^2 v^3 sin(u-2 v)+4 h u^3 v^2 sin(u+2 v)-4 h u^2 v^3 sin(u+2 v)-4 h u^3 v^2 sin(2 u-v)-4 h u^2 v^3 sin(2 u-v)+8 h u^2 v^2 cos(u)+8 h u^2 v^2 cos(v)+4 h u^3 v cos(2 u-v)-4 h u^2 v^2 cos(2 u-v)-8 h u v^3 cos(2 u-v)-4 h u^3 v cos(2 u+v)-4 h u^2 v^2 cos(2 u+v)+8 h u v^3 cos(2 u+v)-8 h u^3 v cos(u-2 v)-4 h u^2 v^2 cos(u-2 v)+4 h u v^3 cos(u-2 v)+8 h u^3 v cos(u+2 v)-4 h u^2 v^2 cos(u+2 v)-4 h u v^3 cos(u+2 v)-2 h u^3 v cos(2 u+2 v)+4 h u^2 v^2 cos(2 u+2 v)-2 h u v^3 cos(2 u+2 v)+2 h u^3 v cos(2 u-2 v)+4 h u^2 v^2 cos(2 u-2 v)+2 h u v^3 cos(2 u-2 v)-8 u sin(u) v^2 h+4 sin(2 u) h u v^2+4 sin(2 v) h u^2 v-8 v h sin(v) u^2+4 v u^2 h sin(2 u+v)+4 u v^2 h sin(u-2 v)+4 u v^2 h sin(u+2 v)-4 v u^2 h sin(2 u-v)-2 v u^2 h sin(2 u+2 v)-2 u v^2 h sin(2 u+2 v)+2 v u^2 h sin(2 u-2 v)-2 u v^2 h sin(2 u-2 v)) f[n+1])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-8 h u^2 v^2-4 u^3 sin(u) h+2 sin(2 u) h u^3+2 sin(2 v) h v^3-4 v^3 h sin(v)+2 v^3 h sin(2 u+v)+2 u^3 h sin(u-2 v)+2 u^3 h sin(u+2 v)-2 v^3 h sin(2 u-v)-u^3 h sin(2 u+2 v)-v^3 h sin(2 u+2 v)-u^3 h sin(2 u-2 v)+v^3 h sin(2 u-2 v)+4 h u^3 v^2 sin(2 u)+4 h u^2 v^3 sin(2 v)-4 h u^3 v^2 sin(u-v)+4 h u^2 v^3 sin(u-v)-4 h u^3 v^2 sin(u+v)-4 h u^2 v^3 sin(u+v)+4 h u^2 v^2 cos(u)+4 h u^2 v^2 cos(2 u)+4 h u^2 v^2 cos(2 v)+4 h u^2 v^2 cos(v)-4 h u^3 v cos(2 u-v)-2 h u^2 v^2 cos(2 u-v)+2 h u v^3 cos(2 u-v)+4 h u^3 v cos(2 u+v)-2 h u^2 v^2 cos(2 u+v)-2 h u v^3 cos(2 u+v)+2 h u^3 v cos(u-2 v)-2 h u^2 v^2 cos(u-2 v)-4 h u v^3 cos(u-2 v)-2 h u^3 v cos(u+2 v)-2 h u^2 v^2 cos(u+2 v)+4 h u v^3 cos(u+2 v)+4 h u^3 v cos(u-v)+4 h u v^3 cos(u-v)-4 h u^3 v cos(u+v)-4 h u v^3 cos(u+v)+4 u sin(u) v^2 h-2 sin(2 u) h u v^2-2 sin(2 v) h u^2 v+4 v h sin(v) u^2-2 v u^2 h sin(2 u+v)-2 u v^2 h sin(u-2 v)-2 u v^2 h sin(u+2 v)+2 v u^2 h sin(2 u-v)+v u^2 h sin(2 u+2 v)+u v^2 h sin(2 u+2 v)-v u^2 h sin(2 u-2 v)+u v^2 h sin(2 u-2 v)) f[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((-6 u^2 h^2-6 v^2 h^2-4 cos(2 u) h^2 u^2 v^2-4 cos(2 v) h^2 u^2 v^2+8 v^2 u^2 h^2 cos(u-v)+8 v^2 u^2 h^2 cos(u+v)+8 u sin(u) v^2 h^2+8 sin(2 u) h^2 u v^2+8 sin(2 v) h^2 u^2 v+8 v h^2 sin(v) u^2+4 v u^2 h^2 sin(2 u+v)-4 u v^2 h^2 sin(2 u+v)+8 v u^2 h^2 sin(u-v)-8 sin(u-v) h^2 u v^2-8 v u^2 h^2 sin(u+v)-8 sin(u+v) h^2 u v^2+4 v u^2 h^2 sin(u-2 v)+4 u v^2 h^2 sin(u-2 v)-4 v u^2 h^2 sin(u+2 v)+4 u v^2 h^2 sin(u+2 v)-4 v u^2 h^2 sin(2 u-v)-4 u v^2 h^2 sin(2 u-v)-4 u v h^2 cos(2 u-v)+4 u v h^2 cos(2 u+v)-4 u v h^2 cos(u-2 v)+4 u v h^2 cos(u+2 v)-2 u v h^2 cos(2 u+2 v)+2 u v h^2 cos(2 u-2 v)+8 cos(u-v) h^2 u v-8 cos(u+v) h^2 u v-8 v^2 u^2 h^2+8 h^2 cos(u) u^2-2 cos(2 u) h^2 u^2+6 cos(2 u) h^2 v^2+6 cos(2 v) h^2 u^2-2 cos(2 v) h^2 v^2+8 h^2 cos(v) v^2-4 v^2 h^2 cos(2 u-v)-4 v^2 h^2 cos(2 u+v)-4 u^2 h^2 cos(u-2 v)-4 u^2 h^2 cos(u+2 v)+u^2 h^2 cos(2 u+2 v)+v^2 h^2 cos(2 u+2 v)+u^2 h^2 cos(2 u-2 v)+v^2 h^2 cos(2 u-2 v)) g[n])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)+((6 u^2 h^2+6 v^2 h^2+4 cos(2 u) h^2 u^2 v^2+4 cos(2 v) h^2 u^2 v^2-8 v^2 u^2 h^2 cos(u-v)-8 v^2 u^2 h^2 cos(u+v)-8 u sin(u) v^2 h^2-8 sin(2 u) h^2 u v^2-8 sin(2 v) h^2 u^2 v-8 v h^2 sin(v) u^2-4 v u^2 h^2 sin(2 u+v)+4 u v^2 h^2 sin(2 u+v)-8 v u^2 h^2 sin(u-v)+8 sin(u-v) h^2 u v^2+8 v u^2 h^2 sin(u+v)+8 sin(u+v) h^2 u v^2-4 v u^2 h^2 sin(u-2 v)-4 u v^2 h^2 sin(u-2 v)+4 v u^2 h^2 sin(u+2 v)-4 u v^2 h^2 sin(u+2 v)+4 v u^2 h^2 sin(2 u-v)+4 u v^2 h^2 sin(2 u-v)+4 u v h^2 cos(2 u-v)-4 u v h^2 cos(2 u+v)+4 u v h^2 cos(u-2 v)-4 u v h^2 cos(u+2 v)+2 u v h^2 cos(2 u+2 v)-2 u v h^2 cos(2 u-2 v)-8 cos(u-v) h^2 u v+8 cos(u+v) h^2 u v+8 v^2 u^2 h^2-8 h^2 cos(u) u^2+2 cos(2 u) h^2 u^2-6 cos(2 u) h^2 v^2-6 cos(2 v) h^2 u^2+2 cos(2 v) h^2 v^2-8 h^2 cos(v) v^2+4 v^2 h^2 cos(2 u-v)+4 v^2 h^2 cos(2 u+v)+4 u^2 h^2 cos(u-2 v)+4 u^2 h^2 cos(u+2 v)-u^2 h^2 cos(2 u+2 v)-v^2 h^2 cos(2 u+2 v)-u^2 h^2 cos(2 u-2 v)-v^2 h^2 cos(2 u-2 v)) g[n+2])/(-12 u^2 v^2+4 sin(u) u^3 v^2+4 sin(2 u) u^3 v^2+4 sin(2 v) u^2 v^3+4 sin(v) u^2 v^3-2 sin(2 u+v) u^3 v^2+2 sin(2 u+v) u^2 v^3-4 sin(u-v) u^3 v^2+4 sin(u-v) u^2 v^3-4 sin(u+v) u^3 v^2-4 sin(u+v) u^2 v^3+2 sin(u-2 v) u^3 v^2+2 sin(u-2 v) u^2 v^3+2 sin(u+2 v) u^3 v^2-2 sin(u+2 v) u^2 v^3-2 sin(2 u-v) u^3 v^2-2 sin(2 u-v) u^2 v^3+8 cos(u) u^2 v^2+4 cos(2 u) u^2 v^2+4 cos(2 v) u^2 v^2+8 cos(v) u^2 v^2-2 cos(2 u-v) u^3 v-4 cos(2 u-v) u^2 v^2-2 cos(2 u-v) u v^3+2 cos(2 u+v) u^3 v-4 cos(2 u+v) u^2 v^2+2 cos(2 u+v) u v^3-2 cos(u-2 v) u^3 v-4 cos(u-2 v) u^2 v^2-2 cos(u-2 v) u v^3+2 cos(u+2 v) u^3 v-4 cos(u+2 v) u^2 v^2+2 cos(u+2 v) u v^3-cos(2 u+2 v) u^3 v+2 cos(2 u+2 v) u^2 v^2-cos(2 u+2 v) u v^3+cos(2 u-2 v) u^3 v+2 cos(2 u-2 v) u^2 v^2+cos(2 u-2 v) u v^3+4 cos(u-v) u^3 v+4 cos(u-v) u v^3-4 cos(u+v) u^3 v-4 cos(u+v) u v^3)),u=0,32),polynom),v=0,32),polynom);

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