Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello everyone, my computer installed Maple 2016, 2020 and set Maple 2016 as default opening files .mw, .mws. How to change default to Maple 2020 . I tried searching on Google but not found.

Thank you very much.

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

Determine how many transitive relations there are on a set with n elements for all positive integers n with n<=7.

Custom Palettes and Palette Entries on windows Pro 7 
Read a tutorial from a user @les 185

https://www.mapleprimes.com/posts/207781-Custom-Palettes-And-Palette-Entries

Is this still valid this tutorial from 2015  in the current version of Maple ?
This seems to be userunfriendly.

 

Hi,

Thank you all for participating to my questions before.

I was wondering if we can change an equation into quartic form or quadratic form in maple.

I have succesfully got an equation like the following:

`S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*(gamma*H^2*sin(beta - varepsilon)*sin(alpha) - h^2*sin(beta)*sin(alpha - varepsilon)*gamma + h^2*sin(beta)*sin(alpha - varepsilon)*psi)/(2*sin(-beta - delta - phi + alpha)*sin(beta)^2*sin(alpha - varepsilon)*sin(alpha)) - S__1

From the paper I studied, they change it to form an equation like this

 

`S__2 ` = 1/2*gamma*H^2*sin(beta - alpha)*(M__3(X)^3 + M__2(X)^2 + M__1*X)/(sin(beta)^2*(D__3(X)^3 + D__2(X)^2 + D__1*X + D__0)) - S__1

 

Where value of M, D and X is sets of long equation. Can someone teach me how to assign maple to change this kind of equation to another form of equation. It's good enough if I can learn how to learn the basic.

 

Thank you.

 

Regards

Faiz Farhan

 

Dear All,

I want to apply the ‘simplify’ command, in parallel, for the simplification of some parameters. Both Grid:-Map and Grid:-Run commands are tested. There is no error in both, whereas no simplification is implemented. It seems that the ‘simplify’ command correctly works on only ‘Master’ node, namely anywhere we are typing.

Can anyone help me to simplify in parallel. I examined two following codes.

1)

with (Grid);

for i from 1 to nops(dummy_UU1) do

freenode:=WaitForFirst():

Run(freenode,simplify,[dummy_UU1[i]],assignto='dummy_UU2'[i]):

end do:

Wait();

2)

dummy_UU2:=Map[tasksize=1](simplify,[seq(dummy_UU1[i],i=1..nops(dummy_UU1))]):

 

 

The following code is correctly executed and resulted in the simplification of dummy_UU1 components in serial.

for i from 1 to nops(dummy_UU1) do

dummy_UU2[i]:=simplify(dummy_UU1[i]):

end do:

 

Could anyone help me out to convert the equation into differential transform method

 

Hello Everyone, can anyone explain how to import a mathematical equation from maple to word directly?

I want to to solve the system of partial differential equation using maple. I tried it but I am not able to solve it ... please help.

the equations are as follows

 


 

``

Finding transformation eqn between zero and harmonic with conformal1

``

 

restart

``

with(PDEtools)

sys := {(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}

{(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}

(1)

``

declare(Phi(r1, r2, r4), R(r1, r2, r4), T(r1, r2, r4), Theta(r1, r2, r4))

` Phi`(r1, r2, r4)*`will now be displayed as`*Phi

 

` R`(r1, r2, r4)*`will now be displayed as`*R

 

` T`(r1, r2, r4)*`will now be displayed as`*T

 

` Theta`(r1, r2, r4)*`will now be displayed as`*Theta

(2)

``

cases := [PDEtools:-casesplit({(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}, caseplot)]

`========= Pivots Legend =========`

 

p1 = diff(R(r1, r2, r4), r2)

 

p2 = diff(Phi(r1, r2, r4), r1)

 

p3 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2

 

p4 = diff(Phi(r1, r2, r4), r2)

 

p5 = diff(R(r1, r2, r4), r1)

 

 

[`casesplit/ans`([diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))^2-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*cos(T(r1, r2, r4))^2+(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/(cos(T(r1, r2, r4))^2*(diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^4), diff(Theta(r1, r2, r4), r2) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))+(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r1) = (diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1))/(diff(R(r1, r2, r4), r2)), (diff(R(r1, r2, r4), r2))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r4) = -(diff(Phi(r1, r2, r4), r2))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r2) = 0, (diff(Phi(r1, r2, r4), r1))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r2) <> 0, diff(Phi(r1, r2, r4), r1) <> 0]), `casesplit/ans`([diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r2) = 0, (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(Phi(r1, r2, r4), r1) = 0, (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r1) <> 0, diff(Phi(r1, r2, r4), r2) <> 0])]

(3)

``

map(length, cases)

[2101, 1405]

(4)

sys1 := op(1, cases[2])

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r2) = 0, (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(Phi(r1, r2, r4), r1) = 0, (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(5)

``

sys2 := op(1, cases[1])

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))^2-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*cos(T(r1, r2, r4))^2+(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/(cos(T(r1, r2, r4))^2*(diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^4), diff(Theta(r1, r2, r4), r2) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))+(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r1) = (diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1))/(diff(R(r1, r2, r4), r2)), (diff(R(r1, r2, r4), r2))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r4) = -(diff(Phi(r1, r2, r4), r2))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r2) = 0, (diff(Phi(r1, r2, r4), r1))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(6)

``

sys3 := op(2, cases[1])

[diff(R(r1, r2, r4), r2) <> 0, diff(Phi(r1, r2, r4), r1) <> 0]

(7)

``

sys4 := op(2, cases[2])

[diff(R(r1, r2, r4), r1) <> 0, diff(Phi(r1, r2, r4), r2) <> 0]

(8)

``

sol1 := dsolve(sys1, explicit)

(9)

``

constraint, subsystem := selectremove(has, sys1, T)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r2) = 0, diff(Phi(r1, r2, r4), r1) = 0]

(10)

``

sol__subsystem := dsolve(subsystem)

{Phi(r1, r2, r4) = _F1(r2, r4), R(r1, r2, r4) = _F2(r1, r4)}

(11)

``

eval(constraint, sol__subsystem)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(12)

map(simplify, [diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0])

[diff(Theta(r1, r2, r4), r4) = (1/2)*((_F1(r2, r4)^2-_F2(r1, r4)^2)*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -cos(T(r1, r2, r4))*(_F2(r1, r4)*cos(T(r1, r2, r4))^3+2*(diff(_F2(r1, r4), r4))*sin(T(r1, r2, r4))), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -cos(T(r1, r2, r4))*(_F1(r2, r4)*cos(T(r1, r2, r4))^3+2*(diff(_F1(r2, r4), r4))*sin(T(r1, r2, r4))), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = sin(T(r1, r2, r4))^2, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(13)

``

eval(constraint, sol__subsystem)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(14)

``

``


 

Download Finding_transformation_eqn_between_zero_and_harmonic_with_conformal1.mw

Hi,

I am trying to solve a differentiation but I think I am stuck since the solution is not what it should be.

So, I got the equation below

eq4 := `S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*H^2*M/(2*sin(-beta - delta - phi + alpha)*sin(beta)*sin(alpha)) - S__1

And according to the paper I read, to get the maximum value of alpha for maximum value of S_2, I need to make differentiation to first derivative where dS_2/d(alpha) = 0

Then I should substitute back value of alpha to equation above and the paper shows that i should get equation below.

`S__2 ` = 1/2*M*K__a*H^2 - `S__2 `

where K_a is

`K__a`= [(sin(beta+phi))/((sin(beta))/(sqrt(sin(beta+delta))+(sqrt(sin(phi+delta)*(sin(phi-varepsilon)))/(sin(beta-varepsilon))))]

 

I know its really hard but hope someone can give some idea how to do it.

 

Thank you very much.

 

Kind regards

Faiz Farhan

Got a lot of worksheets who are not complete anymore once opened in maple 2020

It can be only opened with a old version of Maple
Can it be imported in Maple 2020?

example 

Dynmod03.mws

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw

I am currently working on a project that generates a set of matrices and I want to find their eigenvalues, but using the inbuilt Maple engine takes too long. The problem is that whenever I try to use the Matlab[eig] command I get the error:

Error, (in Matlab:-setvar) unable to store '-3.*Re(X)' when datatype=float[8]
I found out that solving symbolic matrices in MATLAB requires first defining symbols with the "sym" command but I've been unable to do that in Maple.

Hi, 

Could anyone help me to numerically solve this ode?
I've tried almost all the methods Maple proposes, trying to adjust stepsizes, tolerances and so on;, always without success.

I give also the exact solution of this ode in order to compare the numerical solution to.

Thanks in advance
 

restart

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

with(plots):

# Source term

F := t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2);

plot(F, t=0..0.5);

t*(-600*t/(100*t^2+1)^2+80000*t^3/(100*t^2+1)^3)/(100*t^2+1)-(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)/(1+(1/(100*t^2+1)-200*t^2/(100*t^2+1)^2)^2)

 

 

# Ode

ode := X(t)*diff(X(t), t$2)-diff(X(t),t)/(1+diff(X(t),t)^2) - 'F'

X(t)*(diff(diff(X(t), t), t))-(diff(X(t), t))/(1+(diff(X(t), t))^2)-F

(2)

# Initial conditions

ics := X(0) = 0, D(X)(0) = 1

X(0) = 0, (D(X))(0) = 1

(3)

# I used alot methods with allways either failure or either a HFloat(undefined)

printf("rkf45\n");
sol := dsolve({ode, ics}, numeric):
sol(1e-8);

printf("\n\nrosenbrock\n");
sol := dsolve({ode, ics}, numeric, method=rosenbrock):
sol(1e-8);

printf("\n\ngear\n");
sol := dsolve({ode, ics}, numeric, method=gear):
sol(1e-8);

printf("\n\ngear\n");
sol := dsolve({ode, ics}, numeric, method=classical[heunform]):
sol(1e-8);

rkf45

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 



rosenbrock

Error, (in dsolve/numeric/SC/firststep) unable to evaluate the partial derivatives of f(x,y) for stiff solution

 

Error, (in sol) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

 



gear

 

[t = 0.1e-7, X(t) = HFloat(HFloat(undefined)), diff(X(t), t) = HFloat(HFloat(undefined))]

 



gear

 

[t = 0.1e-7, X(t) = HFloat(HFloat(undefined)), diff(X(t), t) = HFloat(HFloat(undefined))]

(4)

# The solution must be this one

U := t -> t/((t*10)^2+1)

proc (t) options operator, arrow; t/(100*t^2+1) end proc

(5)

# Check ode and ics

eval(ode, X(t)=U(t));
U(0);
D(U)(0);

0

 

0

 

1

(6)

# Plots when a solution is obtained

display(
  plot(U(t), t=0..1, color=blue),
  odeplot(sol, [t, x(t)], t=0..1, color=red, linestyle=3)
);


 

Download Unsuccessful_dsolve.mw

 

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