Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

Please answer the commented questions in the uploaded worksheet.

Binary_search.mw

Hi

I'm trying to automate this production of doubles combinations with a set scoreline in between. The minimum is 4 players, but we could have many more players, producing many combinations. 

example: 4 players, set score 2-0 for each match

with(combinat):
DBL:=choose([Novice,Weak_Intermediate,Strong_Intermediate,Advanced], 2);
DBL[1],2,DBL[6],0;DBL[2],2,DBL[5],0;DBL[3],2,DBL[4],0

#and the reverse
DBL[6],2,DBL[1],0;DBL[5],2,DBL[2],0;DBL[4],2,DBL[3],0
 

#the output contains square brackets. How do I remove them?

"Warning, unable to evaluate 2 of the 6 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct" How to fix it?

mww.mw

I inadvertently discovered that the save command (and probably read, write, export and import commands too?) returns an error (something like "can't write ...") when the file length is too large (265 in my case).

Is this documented somewhere?
Is there a way to exceed this limit?
Assuming D=".../" and F="xxx.m", can we set the path of the directory D to some value and then use save something, F instead of save something cat(D, F) ?

Thanks in advance

How to draw a phase portrait of (2) same as in the attached figure? I tried it by using dsolve, but couldn't redraw it.  

restart

with(DEtools); with(plots)

alias(phi = phi(xi))

phi

(1)

eq := (1/2)*m*(diff(phi, xi))^2+`Φ__∓` = h

(1/2)*m*(diff(phi, xi))^2+`Φ__∓` = h

(2)

NULL

`Φ__∓` = `&-+`(1-cos(phi))

`Φ__∓` = `&-+`(1-cos(phi))

(3)

``

Download PP.mw

Hi,

everyone! I want to get a system of equations (Fig. 1). But my result is a table (Fig. 2), so I wonder how to convert a table into a sequence or a system. And I am very sorry that my code is not concise, since I am a beginner. Thank you very much!

Download Equations.mw

I solved the differential equation using 'dsolve' and Maple returns it with fiver possible solutions. How can we get the single possible solution for w(x) if we assume c, g (constants) are positive? Also, can we convert JacobiSN() to a simple trigonometric or algebraic function?

restart

with(DEtools)

``

q := (1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

(1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

(1)

dsolve((1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0, {w(x)})

w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = (-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = 2*JacobiSN((1/2)*(-2*c+2*(c^2+2*g)^(1/2))^(1/2)*x+_C1, ((c*(c^2+2*g)^(1/2)-c^2-g)*g)^(1/2)/(c*(c^2+2*g)^(1/2)-c^2-g))*g/(g*(-c+(c^2+2*g)^(1/2)))^(1/2)

(2)

``

``

Download solve.mw

Is it possible to integrate eq (1) in such a way that the final result will be of 1st order differential equation? 

 


 

restart

with(PDEtools)

eq := (diff(U(z), z))^3*(diff(U(z), z, z))+(diff(U(z), z))*(diff(U(z), z, z, z, z))-(diff(U(z), z, z))*(diff(U(z), z, z, z)) = 0

(diff(U(z), z))^3*(diff(diff(U(z), z), z))+(diff(U(z), z))*(diff(diff(diff(diff(U(z), z), z), z), z))-(diff(diff(U(z), z), z))*(diff(diff(diff(U(z), z), z), z)) = 0

(1)

eq1 := map(convert, eq, diff); eq2 := map(int, lhs(eq1), z)-C1 = 0

(diff(U(z), z))^3*(diff(diff(U(z), z), z))+(diff(U(z), z))*(diff(diff(diff(diff(U(z), z), z), z), z))-(diff(diff(U(z), z), z))*(diff(diff(diff(U(z), z), z), z)) = 0

 

(1/4)*(diff(U(z), z))^4-(diff(diff(U(z), z), z))^2+(diff(diff(diff(U(z), z), z), z))*(diff(U(z), z))-C1 = 0

(2)

``


 

Download inttegration.mw

The wikipedia website below contains a general description of Doyle spirals but not the full mathematics of their construction.  

https://en.wikipedia.org/wiki/Doyle_spiral

The website below apparently contains the html coding for an animated display of Doyle spirals, but I am not familiar with this coding language.

https://bl.ocks.org/robinhouston/6096950

Can anyone direct me to 1) the complete mathematics describing the construction of a Doyle spiral and/or

                                        2) a Maple worksheet which codes for the display of a Doyle spiral?

``

In a physics problem, I came across the following triple integral:

exp := -sin(alpha)*i*r*(-sin(alpha)*cos(phi)*cos(theta)+sin(theta)*cos(alpha))/(4*sqrt(-2*sin(theta)*sin(alpha)*cos(phi)*p*r-2*cos(alpha)*cos(theta)*p*r+p^2+r^2)*Pi(-2*sin(theta)*sin(alpha)*cos(phi)*p*r-2*cos(alpha)*cos(theta)*p*r+p^2+r^2)*(-2+sqrt(2))*Pi)

`assuming`([int(int(int(exp*p^2*sin(alpha), p = 0 .. 1), alpha = 0 .. (1/4)*Pi), phi = 0 .. 2*Pi)], [alpha > 0, alpha < (1/4)*Pi, r > 0, r < 1, phi > 0, phi < 2*Pi, theta > 0, theta < (1/4)*Pi])

``

I tried to perform each integration separately, but got no result. Is there any transformation or procedure, that I am not aware of, to accomplish this task?
Grateful,
Oliveira

Download Triple_integral.mw

After substitution of (10) into (4), how to collect the terms of like powers of eta (i.e., eta^-3, eta^-2,eta^-1, eta^0, eta^1,eta^2 ), and equate the coefficients to
zero, get a system of algebraic equations for A[m]?

 

PA.mw 

 

Download text_program.mw

Dear all,

      The program is as follows (The "mw" files are also attached). The integraion "evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))" can not be worked out in several hours, but if the upper limit of x is changed to 0.5 (for example), the integration can be worked out quickly. I have tried to change the program to math model, however, the question still exists. How to solve this problem?

afa:=0.3:
vh:=3.5:
u:=3.12:
mu:=5.5:
gama:=-4*10^(-29)*(1-cos(6*afa))*(1-1*10^(-8)*I):
d1:=1.78*10^(-9):
d2:=48.22*10^(-9):
HBAR:=1.05457266*10^(-34):
ME:=9.1093897*10^(-31):
ELEC:=1.60217733*10^(-19):
Kh:=2.95*10^10:
kc:=sqrt(2*ME*ELEC/HBAR^2):
k:=kc*sqrt(mu):
k0:=sqrt(k^2-k^2*sin(x)^2):
kh:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2 - k^2 * sin(x)^2 * sin(y)^2):
khg:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2):
kg1:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2):
kg2:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2):
k0pl:=sqrt(k^2-k^2*sin(x)^2+kc^2*vh-kc^2*u):
k0mi:=sqrt(k^2-k^2*sin(x)^2-kc^2*vh-kc^2*u):
khpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+kc^2*vh-kc^2*u):
khmi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-kc^2*vh-kc^2*u):
k0plpl:=sqrt(k^2-k^2*sin(x)^2+2*kc^2*vh):
k0mimi:=sqrt(k^2-k^2*sin(x)^2-2*kc^2*vh):
khplpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+2*kc^2*vh):
khmimi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-2*kc^2*vh):
khgplpl:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2+2*kc^2*vh):
khgmimi:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg1plpl:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2+2*kc^2*vh):
kg1mimi:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg2plpl:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2+2*kc^2*vh):
kg2mimi:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2-2*kc^2*vh):
A1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
B1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
A2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
B2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
A3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
B3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
A4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
B4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
T1:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg1plpl*exp(I*(kg1plpl-conjugate(kg1plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg1mimi*exp(I*(kg1mimi-conjugate(kg1mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg1*exp(I*(kg1-conjugate(kg1))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg1mimi*exp(I*(kg1mimi-conjugate(kg1plpl))*d2)-A1*conjugate(B3)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1mimi))*d2)+conjugate(A1)*(A3-B1)*kg1*exp(I*(kg1-conjugate(kg1plpl))*d2)+A1*conjugate(A3-B1)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1))*d2)+conjugate(B3)*(B1-A3)*kg1*exp(I*(kg1-conjugate(kg1mimi))*d2)+B3*conjugate(B1-A3)*kg1mimi*exp(I*(kg1mimi-conjugate(kg1))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
T2:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg2plpl*exp(I*(kg2plpl-conjugate(kg2plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg2mimi*exp(I*(kg2mimi-conjugate(kg2mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg2*exp(I*(kg2-conjugate(kg2))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg2mimi*exp(I*(kg2mimi-conjugate(kg2plpl))*d2)-A1*conjugate(B3)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2mimi))*d2)+conjugate(A1)*(A3-B1)*kg2*exp(I*(kg2-conjugate(kg2plpl))*d2)+A1*conjugate(A3-B1)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2))*d2)+conjugate(B3)*(B1-A3)*kg2*exp(I*(kg2-conjugate(kg2mimi))*d2)+B3*conjugate(B1-A3)*kg2mimi*exp(I*(kg2mimi-conjugate(kg2))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))

 


 

afa:=0.3:
vh:=3.5:
u:=3.12:
mu:=5.5:
gama:=-4*10^(-29)*(1-cos(6*afa))*(1-1*10^(-8)*I):
d1:=1.78*10^(-9):
d2:=48.22*10^(-9):
HBAR:=1.05457266*10^(-34):
ME:=9.1093897*10^(-31):
ELEC:=1.60217733*10^(-19):
Kh:=2.95*10^10:
kc:=sqrt(2*ME*ELEC/HBAR^2):
k:=kc*sqrt(mu):
k0:=sqrt(k^2-k^2*sin(x)^2):
kh:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2 - k^2 * sin(x)^2 * sin(y)^2):
khg:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2):
kg1:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2):
kg2:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2):
k0pl:=sqrt(k^2-k^2*sin(x)^2+kc^2*vh-kc^2*u):
k0mi:=sqrt(k^2-k^2*sin(x)^2-kc^2*vh-kc^2*u):
khpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+kc^2*vh-kc^2*u):
khmi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-kc^2*vh-kc^2*u):
k0plpl:=sqrt(k^2-k^2*sin(x)^2+2*kc^2*vh):
k0mimi:=sqrt(k^2-k^2*sin(x)^2-2*kc^2*vh):
khplpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+2*kc^2*vh):
khmimi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-2*kc^2*vh):
khgplpl:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2+2*kc^2*vh):
khgmimi:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg1plpl:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2+2*kc^2*vh):
kg1mimi:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg2plpl:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2+2*kc^2*vh):
kg2mimi:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2-2*kc^2*vh):
A1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
B1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
A2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
B2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
A3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
B3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
A4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
B4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
T1:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg1plpl*exp(I*(kg1plpl-conjugate(kg1plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg1mimi*exp(I*(kg1mimi-conjugate(kg1mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg1*exp(I*(kg1-conjugate(kg1))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg1mimi*exp(I*(kg1mimi-conjugate(kg1plpl))*d2)-A1*conjugate(B3)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1mimi))*d2)+conjugate(A1)*(A3-B1)*kg1*exp(I*(kg1-conjugate(kg1plpl))*d2)+A1*conjugate(A3-B1)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1))*d2)+conjugate(B3)*(B1-A3)*kg1*exp(I*(kg1-conjugate(kg1mimi))*d2)+B3*conjugate(B1-A3)*kg1mimi*exp(I*(kg1mimi-conjugate(kg1))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
T2:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg2plpl*exp(I*(kg2plpl-conjugate(kg2plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg2mimi*exp(I*(kg2mimi-conjugate(kg2mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg2*exp(I*(kg2-conjugate(kg2))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg2mimi*exp(I*(kg2mimi-conjugate(kg2plpl))*d2)-A1*conjugate(B3)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2mimi))*d2)+conjugate(A1)*(A3-B1)*kg2*exp(I*(kg2-conjugate(kg2plpl))*d2)+A1*conjugate(A3-B1)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2))*d2)+conjugate(B3)*(B1-A3)*kg2*exp(I*(kg2-conjugate(kg2mimi))*d2)+B3*conjugate(B1-A3)*kg2mimi*exp(I*(kg2mimi-conjugate(kg2))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))

Warning,  computation interrupted

 

NULL


 

Download text_program.mw

In the website https://en.wikipedia.org/wiki/Geodesic there is an animation of an insect tracing a path on a torus while walking "forward". The caption to the animation says that the path is then by definition a geodesic.

I would like to duplicate this animation in Maple (and other "walking forward" geodesics on other surfaces) which seems to require an exact definition of walking forward but I cannot find such a definition on this or any other website.

Also, I thought that a geodesic is the shortest distance between two points in space, but no such end points are shown in the website's animation. Then how can the word geodesic apply to the insect's path?

The worksheet below displays a sphere with a surface patch defined by the arcs of three intersecting circles on the sphere's surface.

How can the patch be colored differently from the non-patch sphere's surface?

Patch_on_a_Sphere.mw

Is it possible to do machine learning using maplesoft I have 2020 for now

Say I have an excel sheet with one dependent variable and n number of independent variables. I can ask for the number of hidden layers we need.

Then i want to traing the data with 70% of the data for training ,  15% of the data for validation and 15% of the data for testing.

I want some charts may be on the performance of the neural networks.

and get the regression equation formed by this training would be looking to repeat the training until MSE has certain approximation.

 

If this is not possible in maplesoft kindly help me with some other code way to do this. Please help. I will surely acknowledge please advice me.

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