Maple 2020 Questions and Posts

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

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.

Kind help with Function given two graphs G1 and G2 then co-normal product be the graph G3 given by the function

conormal(G1,G2)

Defination is explained in youtube link  https://www.youtube.com/watch?v=qz1StIvzrAI

If any other explanation will surely give kind help please will surely acknowlege

Given a graph G say and a positive integer k

I am in look out how to remove

 edge-disjoint copies of G in G^k

That is edge disjoint copies of G into its power graph all possible ways 

Again it is the maximum number of copies I means 

Keeping this particular way can someone help kind help please

I will surely acknowledge it 

G into to GraphPower(G,k)

Why does an attempt to solve the ODEs in the uploaded worksheet fail and how can this error be removed so they can be solved?

Unable_to_convert.mw

Problem 1)   Give graph G1 and a graph G2  the problem is to extract maximum isomorphic copies of G1 from G2 such that it has no edge intersection maximum number is floor((number of edges of G2)/(number of edges of G1)) and display the Edge sets of those isomorphic graphs and the graph formed by the remaining edges sometimes their may be no remaing edges too.  Need all possible such copies.

Problem 2) Give graph G1 and a graph G2  the problem is to extract maximum isomorphic copies of G1 from G2 such that each copy has  exactly one edge intersection with each of the copies and that one edge intersection occurs only between those two copies and  display the Edge sets of those isomorphic graphs . Need all possible such copies.

If any more examples or explation will give kind help please I can give more examples or more kind please help.

I had written this c++ code years back for problem 2 which i have forgotten kind help if possible to make it better with maplesoft.

Please take your time. Kind help help plese it will be very helpful it is of real help.

orthogonal.txt

I had written this c++ code years back for problem 1 which i have forgotten kind help if possible to make it better with maplesoft.

Please take your time. Kind help help plese it will be very helpful it is of real help.

decom.txt

Need to maintain memory space as graph size is a little big may be 

would usage of database or any other be useful dont know I had done those code in c++ long back which i forgotten logic too.

Please please help based on latest technology please take your time and kind help I apologize disturb you kind help.

I would surely acknowledge for this great work as much as I can much more than I can acknowlege too

I am using Maple 2020

I am trying to solce eq (2) by integration. But maple integrate only 1st term in eq. Why not other two terms? 

 

Solve_integral.mw

The computer on which I have been executing Maple worksheets for the past six years (CPU: i7 - 5820K, 6 core, 3.3 GHz, 5th generation) is now significantly slower than new machines.

I don't know how to interpret public specifications of potential replacement machines into their actual future performance with Maple.

Please give me or direct me to any advice which would enable me to knowledgeably purchase a much faster processor of Maple code.

 

Why maple give empty solutions? See ref. (12) in the attached wokrsheet. Is there anything missing when deriving Sols?

sols_tw.mw

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