I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day
EDIT: I added a Screenshot

Hi

My integrals are convolutions.and I know I can evaluate this using numerical integration, but I am seeking a numerical solution of this problem using FFT. I have many many integrals of this type to evaluate and I need FFT for speed reasons.

fft.mw

This might inspire you.

https://www.mathworks.com/matlabcentral/answers/228107-how-to-evaluate-a-convolution-integral-by-fast-fourier-transform

How can i get mapple code for solving Fractional Patfial Differential Equation with Laplace, Adomian and New Iteration Method

A system of differential equations

But solution I want to express in terms of other specified function

How to dsolve to get a solution that in terms of a list of specified function? For example in terms of sin , cos , Bessel etc ?

Sol := [a(t) = sin(t) + cos(t) , b(t)= sin(t) ....]

As a Maple user for 10+ years, I've had plenty of stack limit errors, pretty much all of them my fault. But I am currently experiencing a very unusual one after updating my Mac from Maple 2019 to Maple 2021.2.

I am running a long script to fetch json data from a url, parse it, and do a bunch of analysis. In most cases it works fine, but some cases give either an "Execution stopped: Stack limit reached." error, or the error "Error, (in type/polynom) result from type `algfun` must be true or false". Both are being caused by calling the gfun:-ratpolytocoeff command.

I kind of think some internal memory of Maple is being accidentally overwritten because I can cause the error to occur or not occur by adding / commenting out random lines of code that have nothing to do with the part of the code causing the problem. I've managed to find a fairly small script that causes the problem to occur:

with(PolynomialIdeals):
url := "https://api.combopal.ru.is/garpur_run/61e5f7acf2e929ff811caad3":

root_func := F[0, x]:

latex:-Settings(useimaginaryunit=i):

data := URL[Get](url):
json := JSON[ParseString](data):
json := JSON[ParseString](data):

debug_solved := (x^5-3*x^4+5*x^3-7*x^2+4*x-1)/(x^5-5*x^4+10*x^3-10*x^2+5*x-1):

debug_gfun := gfun[ratpolytocoeff](debug_solved, x, n);

If I remove ANY of these lines of code, there is no longer any problem, which is very strange because, for example, I'm not using the PolynomialIdeals package anywhere in the script. This particular script works fine on a Linux machine running 2021.0, but yet I am having similar problems on that machine with other cases.

Here's a slightly simpler example in which gfun[ratpolytocoeff] induces a "division by zero" error ("Error, (in convert/fullparfrac/normal_only) numeric exception: division by zero"):

with(PolynomialIdeals):
url := "https://api.combopal.ru.is/garpur_run/61e5f7acf2e929ff811caad3":

latex:-Settings(useimaginaryunit=i):

data := URL[Get](url):
json := JSON[ParseString](data):
json := JSON[ParseString](data):

debug_gfun := gfun[ratpolytocoeff](1/(1-x), x, n);

After the division by zero error, if I press Ctrl+D to close the Maple command line, it prints
"GC Thread signalAbort 0x7000019a5000 Execution stopped: Stack limit reached.".

Is this an internal Maple bug? Is there any workaround? I am pulling my hair out and would be very grateful for any help.

Hello guys,

I want to find exact form of a(t) in following differential equation:

-diff(a(t), t)^2*_C1*6^(-1/(-1 + 2*alpha))*((diff(a(t), t, t)*a(t) + diff(a(t), t)^2)/a(t)^2)^(-1/(-1 + 2*alpha))/(4*(diff(a(t), t, t)*a(t) + diff(a(t), t)^2)*(-1/2 + alpha)) = (6*diff(a(t), t, t)*a(t)^2*alpha + 6*a(t)*diff(a(t), t)^2*alpha + k^2)/a(t)^3

please guide me,

Has someone tried to connect Grasshopper with Maple yet?

Grasshopper is a visual programming environment on Rhino.

https://en.wikipedia.org/wiki/Grasshopper_3D

Dear esteem Colleagues,

Please how do I modify the following two files (though similar) to get consistent errors? I am not sure where I made the mistake.

Any modifications would be appreciated.

Thank you all for your time and mentorship. Best regard

Biratu_Mapleprimes.mw

DDE_2_Mapleprime.mw

Download contourintegraal_vraag1.mw

Can someone confirm, that autosave is not implemented for workbooks?

The only thing I can restore form a workbook session are specific worksheets of the workbook that I was working on.

None of the Maple codes are saved for example.

This is a major issue, folks. If you haven't implemented it, you need to tell us about it in the help document.

IN CAPITAL LETTERS!

I following a example of products multiplication like this one

u:=n->Product(2*k-1,k=1..n)/Product(3*k-1,k=1..n)*x^n;

Calculating with  this with maple 1d input is correct, but when i convert a maple 1d input  to 2D input ( i did somewhere) and use this then there is difference with the maple 1d calculation

Seems to be not a advisable to use converted maple 1d to 2 D input for calculation : ( for a mixed calculation(maple input/2D input)  or solely 2d input) , but only for purpose of seeing what the expression in maple input is standing for.   

Note: i did the calculation again with mixed input and now the correct sequenze of answers shows up ?

Just wanted to post that I had some data loss because I opened two different workbooks with the same name from different locations.

This could lead to loss of data.

I had code attachments from the "old" workbook implemented in the "new" workbook, while the new code was gone.

Thought always that the round d is reserved for function of two variables x,y , but  that seems to be not the case here ?

Download Controleren_dezelfde_antwoord_voo_expressies.mw

I have defined a function II1norm of one variable. The variable has units "microns". It plots perfecting using a range defined in microns, but gives an error when I try to find the root using NextZero. If I just leave off the "microns" in the second argument, NextRoot just reports "FAIL". If I rewite the worksheet without units, then the NextZero executes fine. Why? How to I use units when finding roots?

This is so useful to see geometrical mapping diagram to visualize Complex analysis

Something that also can be made for Maple 

Mapping Diagram for Cauchy Integral Formula – GeoGebra

Using GeoGebra for visualizing complex variable. (google.com)

I highly encourage everyone interested in complex variable to read Tristan Needham „Visual Complex Analysis” and try to solve problems with or without aid of GeoGebra. I hope that in this workshop we will manage to get a feeling of complex functions and as a final point understand how complex integration works. It is a common misconception that complex integration can't be visualized, and using Tristan Needham's ideas we will try to explore this idea. It's a pity that we don't have a lot of time, thus we will skip a lot of important information and construct only some graphs. 

There is so much experimenting with Geogebra software and doing too this in Maple ?