## Differentiation of a matrix...

Dear Users,

I have a set of linear equations which can be presented as A(alpha,n) x(alpha)=b(alpha,n), where 'n' is the dimension of the square matric A.

For a particular value of "n" and "alpha", I can solve the unknown vector x. Further, I can differentiate Ax=b with respect to alpha to find out the rate of change of variable x with respect to alpha.

The above exercise reads, Ax'=b'-xA', which gives the unknown vector x', for a given value of alpha and n.

If I chose different values of n while fixing alpha=alpha0, the rate of change of x with alpha ( x' ) does not converge with 'n'. I noticed that x (alpha=alpha0) converges with n, also x(alpha=alpha0+ delta alpha) also converges with 'n'. I am interested in the query why x' does not converge, in spite of the fact that x converges? Any comments regarding the same are highly appreciated.

Thanks,

Grv

## Confirmation of Wynn's epsilon algorithm...

I'm new to Maple.  To get some practice, I'm trying to use Maple to confirm the validity of Wynn's epsilon algorithm in a simple case.  The reference is: Wynn, P. (1956); On a device for computing the e[m](S[n]) transformation; Mathematics of Computation. (I'm using Maple notation for subscripts.)  Let (x[t]) be a sequence of real numbers whose asymptotic form is c + a sum of m terms of the form a[k]*lambda[k]^t, where |lambda[k]| < 1 for k = 1,...,m.  Wynn's algorithm allows one to extrapolate to the limit c from 2*m + 1 consecutive numbers in the sequence.  I wanted to use Maple to confirm that this works when m = 2.  There are 2 cases to consider: (1) a[k], lambda[k] are real for k = 1,2, and (2) a[2] is the complex conjugate of a[1] and lambda[2] is the complex conjugate of lambda[1].  I succeeded in validating Wynn's algorithm in the real case, but in the complex case I encountered the following error message: Error, (in simplify/trig) numeric exception: division by zero.  If anyone wishes to help me, I can send you a PDF file describing the algorithm precisely, plus the two Maple files showing my computations for the real and complex cases.

## platform for running calculation...

Does maple provide any platform for running calculation something like cloud facility

## Severe basic bug in Maple 2019.1 in Document Mode?...

Dear Maple users

Some students have come to us to report, that something doesn't seem to work properly in Maple 2019.1 in Document Mode. And they seem to be right: writing an passive math formula by using Shift+F5 (the formula is gray, not blue), then using F5 to get out of that Math field and back into Text Mode. Using the Enter key to go to the next line: It doesn't work! The cursor stays in the same line. This behavior is new in Maple 2019. It worked properly in Maple 2018 and earlier. I assume it is not the intention?

I know it can easily be dealt with by making a new Paragraph by using the shortcut Ctrl+Shift+J. I call the assumed bug 'severe' though, because it will severely delay the workflow for many students. They are used to deliver a document mixed with formulas (active or passive) and text.

NB! I have tested it on several computers (Mac and Windows), and it doesn't work on any of them.

Regards,

Erik V.

## how to keep set members in order of addition...

i have a question about sets. how can i keep set members in order of addition not the defualt maple ordering.
in maple help, i saw the command setsort=0..8 but i do not know how to use it.
consider exmaple below:

 > restart
 > L:={}:
 > for j in [3,5,6,1] do birth:=j: L:=`union`(L ,{j}); od;
 (1)
 >

how can i keep L as order of addition? L={3,5,6,1}. thanks in advance

## Trouble converting units directly from evaluation ...

I've recently changed to maple 2019, from the 2016 version as my license for that product had expired.
However I find it really frustrating that often upon evaluating an expression I can't convert the units.

For instance I had a calculation that evaluated to:

2.114163508*10^7 [kg/s^2]

When I try to directly replace the units within maple to instead be [J/m^2] I recieve the following error message:

"Error, (in  Units:-TestDimensions) 'op(3, i) does not  evaluate to module"

There is no explanation for this error when I try to look it up. However if I once again manually write the answer:
2.114163508*10^7 [kg/s^2] and use the replace units function.
No problem.
I find this quite annoying and frustrating and I hope you can help.

Best regards

Anders Alexander Wagenblast

## how does Maple decide which is simpler expression?...

This is may be a philosophical question. But sometimes Maple suprises me when telling it to "simplify" expression. As in this example.

 > expr:=1/(y^3+1)^(2/3);

 > int(expr,y)

 > simplify(%)

 >

For me, the original result is "simpler". (Not only smaller leaf count, but it has one special function, vs. two: Legendre and Gamma). But may be Maple considers hypergeom always more "complex" than any other?

That is why I use simplify(expr,size) because I am scared of simplify without any option, as I have little idea how it decides which is simpler.

Any thoughts from the experts on how Maple decided to simplify something when no option is used? What kinds of rules it uses to decide how to transform the expression?

Maple 2019.1

## Web Camera feed for Video Components...

The video component is going to save me alot of hassle in that I was previously building external java applications for audio visual analysis purposes, with the downside of course being that I didnt have maple code at my disposal.

I read in the manual for the video component that I can provide a HTTP address for which a video is located, which would mean i could probably stream an IP camera, but I can I use the localhost IP address with some sort of extension that directs to the I/O of a webcamera connected to my local machine?

## Write suggestions for method (procedure) ...

Hi all, how to write description, suggestions for method (procedure) like image below. I tried searching for a solution but can't. Thank you very much

## Is there extendable combinatorics experiment archi...

Is there extendable combinatorics experiment architect system design

such as new method can combine or use with old method and find relationship between them , these kind of big data system design in combinatorics experiment design?

## ChangeOfVariables doesn't work...

How can I fix the error of ChangeOfVariables: Error, (in Student:-MultivariateCalculus:-ChangeOfVariables) unable to solve the change-of-variables equations for the original variables ?

Thanks!

## How to solve properly given system of ODE's?...

Hi

I have trouble with solving this ODE system using dsolve command:

and

This system have following solutions:

where

and

C's and A are constants of integration.

They're equations from this paper https://arxiv.org/abs/1710.01910 (45 and 47).

However, my solution differs from correct one - in output there are hypergeometric functions everywhere.

Is there any way to fix/convert this solution? Or to get rid of these functions (my f1 solution looks very close to original one but with coupled hypergeometric function).

sysode := 2*q*(3*q-1)*f1(tau)/tau^2+2*q*(diff(f1(tau), tau))/tau+diff(f1(tau), tau, tau)+(kappa^2+f2(tau))*(1+omega)*(tau/t0)^(-(3*(3+omega))*q) = 0, (54*q^3-30*q^2+4*q)*f1(tau)/tau^3+(24*q^2-4*q)*(diff(f1(tau), tau))/tau^2+11*q*(diff(f1(tau), tau, tau))/tau+diff(f1(tau), tau, tau, tau)-3*omega*(1+omega)*(kappa^2+f2(tau))*q*(tau/t0)^(-(3*(1+omega))*q)/tau = 0;

 (1)

simplify(dsolve([sysode], build));

 (2)

## solve PDE with Runge-Kutta method...

Hi everybody?

how can I solve this PDE with Runge-Kutta method and 2D plot in terms of w(x,t) , t and 3D plot in terms of t, x, w(x,t)?

code1.mw

## In python, call Maple and its toolbox....

I know you can call python from Maple, I am thinking if there is the other way around. That is use Maple (and its toolbox) as backend engine to do calculations (e.g. Global Optimization), and say manipulate the data in Python as the front-end.

## Chebyshev series in different intervals...

Hello,

My question is mathematical in nature, so it might be a little out of place but I though I would give it a shot.

You have a series of chebyshev coefficients in two connecting subdomains lets say S1 = [0,0.5] and S2=[0.5,1]. So far you are still in the spectral space. If you want to compute the solution in real space you can sum the coefficients with the Chebyshev polynomials.

Now imagine you change the interval to S1 = [0,0.6] and S2 = [0.6,1]. Is there a way to manipulate the Chebyshev coefficients from both initial subdomains to create a new set of Chebyshev coefficients that fit the solution in the new subdomains.

The brute force method would be to create the real solution of Chebyshev polynomials and then use that to form a new set of Chebyshev coefficients. Or you can use Clenshaw to compute the solution at several points, and then use the points to create new Chebyshev coefficients.

But what if we can stay in spectral space and create the new chebyshev coefficients. Is that possible? If so, how?

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