Hello;

What trick if any is needed to obtain zero for this sum in Maple?

sum(sin(Pi*n/2)*sin(n*Pi*(x + 1)/2)*cos(n*Pi*t/2),n=1..infinity)

The above sum, according to Mathematica is zero. I am trying to see if same result can be obtained by Maple in order to verify this result. It is possible ofcourse that Mathematica result is not correct. I am also trying to verify the sum is zero by hand, but no success so far.

Here is Mathematica result

Using Maple 2019.2 on windows 10. 

Thanks

Download q2.mw

Hello,

a follow up question.

I am solving some overdetermined system of ODEs in cylindrical coordinates r,phi,Z. I obtain some equations of the following type:

(diff(_F1(phi, Z), phi)*r + diff(diff(s_r(phi, Z), phi), phi))/r = -s_r(phi, Z)/r

As can be seen, the differentiated functions do not depend on r, which is an independent variable. Thus, the correct solution is to separate the equation and have 

_F1(phi,Z)=_F1(Z), s_r(phi,Z)=s_r(Z).

By using dsolve, I always obtain a solution containing r.

A similar problem that does no contain derivatives is solved by solve/identity.

Is there something similar for dsolve?

EDIT: I again put here more info and file. I solve some overdetermined system of differential equations.

[diff(s_r(r, phi, Z), r) = 0, diff(s_r(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), r)*r^2,
diff(s_Z(r, phi, Z), r) = -diff(s_r(r, phi, Z), Z), diff(s_phi(r, phi, Z), phi) = -s_r(r, phi, Z)/r, 
diff(s_Z(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), Z)*r^2, diff(s_Z(r, phi, Z), Z) = 0, 
diff(m(r, phi, Z), r) = s_Z(r, phi, Z)*B_phi(r, phi, Z) - s_phi(r, phi, Z)*B_Z(r, phi, Z),
 diff(m(r, phi, Z), phi) = s_r(r, phi, Z)*B_Z(r, phi, Z) - s_Z(r, phi, Z)*B_r(r, phi, Z),
 diff(m(r, phi, Z), Z) = s_phi(r, phi, Z)*B_r(r, phi, Z) - s_r(r, phi, Z)*B_phi(r, phi, Z), 
s_r(r, phi, Z)*diff(W(r, phi, Z), r) + s_phi(r, phi, Z)*diff(W(r, phi, Z), phi) + 
s_Z(r, phi, Z)*diff(W(r, phi, Z), Z) = 0]

After some time, I arrive at the equation in the original question. So the independance of the other functions on r is the consequence of the other equations.

Here is the file (shortened): mwquestion2.mw

Hello everybody,

I am new to MaplePrimes, so I am sorry for possible bad formatting.

I am solving some physical problem in cylindrical coordinates, so the EDIT independent variables are r,phi,Z. The equations I obtain contain constants _C from dsolve and constant parameters aplha[i,j], for example

I would like to solve this type of equations for all values of the variables, namely phi in the example above.

If I do not choose the variables for which to solve, I get phi=phi as one of the equations in the solution. If i choose all the variables except phi, i get an the expression for the constants containing the variable phi.

Is there a way to solve these equations automatically or do I have to separate them manually using collect and coeffs?

Or could the solution be the comand Parameters from Physics package?

Thank you in advance for your help.

EDIT: I did not explain the problem properly. I am solving some complicated set of determining equations to obtain integrals of motion. They are rce in the attached file. I substitute some ansatz for the magnetic field and I solve them for 

The first set of equation, called third in the file are solved by HOconds_polar_solved. This is where the  konstants alpha[i,j] appear. I substitute HOconds_polar_solved into the equations rce and try to solve them for the remaining functions.

Because it is an overdetermined system, I get some equations of the type in the original question or (for example)

8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5])=0

Because r and phi are the independent veriables of the system, the solution to the equation above should be 

_C1=0 or (alpha[4,4]=alpha[5,5] and alpha[4,5]=0)

But I get the following.

solve(8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5]));
 {_C1 = 0, phi = phi, r = r, alpha[4, 4] = alpha[4, 4], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5,5]}, 
{_C1 = _C1, phi = phi, r = 0, alpha[4, 4] = alpha[4, 4],  alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]},
 {_C1 = _C1, phi = phi, r = r, alpha[4, 4] = -tan(2 phi) alpha[4, 5] + alpha[5, 5], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]}

The file (part of the original file, which is very long): question.mw

EDIT 2: I changed the title to contain independent variables, which makes the answer more clear. The second Answer from Carl Love works fine, at least in the presented case.

Hi everyone, I'm having a bit of trouble using the dsolve () command in maple, it keeps coming up with error messages.

My assignment is to find the first order differential equation of T_ovn(t), and then I know that you have to define it and then dsolve the definition.

The problem is, that what am I doing wrong?

This is another problem I just found in Maple 2019.2 on windows 10. professional.

I wanted to close Maple, so did  File->Exit 

But Maple did nothing. It did not close.  Also Alt-F4 did not close Maple. I had to click on the little X on top right corner of the open window to close Maple.  

In earlier version this used to work to close Maple.

Do others see this as well?  To reproduce, simply start Maple, and do File->Exit.

Here is a movie also

I want to separate  the derivative and non-derivative (the part other than  derivative) terms from the following (shown in figure) equations by using maple commands or code. Kindly help me. Thanks in advance. 

This may be a bug.  In Maple 2019.0

plot3d(x^2+y^2)

Now grab the graphing window and drag to adjust it's size.  It doesn't adjust it's size until you let go of the mouse button.

Maple 2019.2.

These two expressions are mathematically equivalent:

But simplify(expr1-expr2) does not give zero where simplify(convert(expr1,trig)-expr2) does.

Is this normal behavior or can be expected sometimes? As a user I would have expected Maple internally to figure all of this itself. Compare to Mathematica:

Is there a different command in Maple that will show mathematical equivalence of two expressions to try other than simplify?

Thanks
 

Download q.mw

How to change default directory for Maple 2019?

I'm only just hearing (haven't experienced) about some serious issues with the 2019.2 updates.  I would recommend waiting for Maplesoft to release an emergency 2019.3 fix update - Maplesoft can NOT leave the last update of 2019 in this state.

I have a .mapleinit file that amongst other things sets libname so my own packages are accessible and can be loaded using with(). Imagine my surprise when I found that a maple program that ran half an hour ago on Maple2019 bombed when it did not find its package. Closer investigation indicates that maybe .mapleinit is only searched for in currentdir()??

The updated Maple is `Maple 2019.2, APPLE UNIVERSAL OSX, Oct 30 2019, Build ID 1430966`

The old one is gone :-(. It was Maple2019.0. I should add that on this system, Maple is installed on an administrator account that is not my user account (luckily I have access to that). I am running macOS 10.14.6 Mojave.

I verified my older Maples still work as before.

Has anyone else seen this behaviour?

Mac Dude.

Edit: I need to be more specific here: When I double-click a worksheet (.mw file) then currentdir() will be set to the directory the .mw file is in. This has been long-standing Maple behaviour. But then currentdir() does not cover the home directory where .mapleinit sits. As a result, a blank sheet finds my .mapleinit whereas my files (that habitually I open with double-click or drag-drop) do no longer run the .mapleinit file.

I am interested in finding the lower Riemann sum for a partition of unequal width.

The points of the partition are P = { -1, -1/4, 1/4, 3/4, 1} , and the function is f(x) = x^2.

My attempt:

restart: with(Student[Calculus1]):
RiemannSum(x^2,x={[ -1,-1/4],[-1/4, 1/4],[1/4,3/4],[3/4,1]},method=lower)

It said error range must be specified. I looked at the help page but I didnt find a specific command for entering partition points manually.

I try to write a Maple Code. But I can' t finish it. 

This is very important for me. Could you help me? download_Maple Code.mw

I am using foslve to get the numerical solution of a very complex equition. When I rerun the code with different Digits settings, I got different solutions. I guess it is not surpprising since it is a numerical solution, but how can I trust/choose which one to use?? Is there anyway to unify the solutions regardless the Digits settings.

This attached are when Digits:=30 and Digits:=20 respectively.. Note, the K is a very large nubmer.. the X is a beta distribution..

We have just released updates to Maple and MapleSim.

Maple 2019.2 includes corrections and improvements to a variety of areas in the product, including a new “Go to page ____” option in print preview (that am personally quite pleased about), sections are expanded by default when printing or exporting, a fix to a problem using non-executable math with text in document mode that sometimes made it impossible to advance to a new line using Enter, improvements to VectorCalculus, select, abs and other math functions, support for macOS Catalina, and more.  We recommend that all Maple 2019 users install these updates.

This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2019.2 download page, where you can also find more details.

For MapleSim users, the MapleSim 2019.2 family of products includes enhancements in the areas of model development and toolchain connectivity, including substantial enhancements to the MapleSim CAD toolbox.   For more details and download instructions, visit the MapleSim 2019.2 download page.