Hi all,
i'm working with the confluent Heun function (Maple 2019).
Since for the case of an integer coefficient delta or gamma there are two integer Frobenius roots at the regular singularities 0 or 1, there is a logarithmic term in the Frobenius solution at these singularities. So, my question is the following:
When moving around this singularity in the complex plane, the value of the logarithmic term might depend on the choice of the complex logarithm's branch cuts. So, does anybody know just about how HeunC is implemented? Is there sth like a power series solution, which value would in my oppinion depend on this choice of a branch cut?
Or is there another implementation that preserves us from this ambiguity in the case of logarithmic singularities (i.e. integer coefficients in the confluent Heun equation)?

Many thanks,

This worksheet creates geodesics in the Poincare disk by transformation of a series of circles of diminishing radii in the complex plane.

The intersections of the geodesics are meant to create the first few pentagonal uniform tilings in the Poincare disk.

I do not know the mathematically correct way to create such a display, so the radii of the circles are only a trial and error approximation.

What Maple code will provide the radii of the complex circles which produce an accurate uniform pentagonal tiling?

Is there a better overall strategy for producing uniform tilings of the Poincare disk? 

HyperbolicTiling.mw

When I use Solve for a PDE with the option singsol=all, is Maple guaranteeing that I am getting all the solutions, and in partidcular , is it returning the *general* solution(s)? 

One of our users asks how they can find the Re ( sqrt(a+I*b)) where a, b are real.

They had tried entering the latter as "assume", without any luck. 

We told them that it may not be very intuitive, but such expressions can be evaluated by wrapping into evalc which implicitly assumes that free parameters are real-valued:

evalc(Re(sqrt(a+I*b)));

How is the matrix of the affinity of base the plan of equation x+2*y-z=1, of direction u <1,0,-1>and of ratio 2 determined? Thank you.

Hi,

I am trying to learn how to apply initial conditions to pdes with maple.  I have figured out how to do it with odes, but when assigning initial values to derivatives, I get weird results.  I have attached my Maple file, with the error, and a link to the document I am using as motivation for my analysis.

Test_1D_Wave_Equation.mw

https://personal.math.ubc.ca/~ward/teaching/m316/lecture21.pdf

I used to have this kind of code without problem:

myModule := module()
    option package;
    export myFunc;
    # local i;
    myFunc := proc()
        [seq(i, i in 1..10)]
    end proc;
end module;

But after upgrading to the latest version of Maple 2021, I get a warning

Warning, (in myModule:-myFunc) `i` is implicitly declared local |myModule.mpl:5|

I have to uncomment the local i declaration for the warning to go away. Has the behavior of seq changed in Maple 2021?

Maple returns to me an algebraic expression that involves many RootOf expressions and I have found it hard to get all solutions behind this expression (by using "allvalues") - this keeps on running without terminating. Is there a way to get the number of solutions without asking Maple to return all solutions explicitaly?

Dear Useres!

Hope everyone is fine here! I want to compare the coeficient of exp(k*eta[3]+m*eta[1]+n*eta[2]) for k=0,1,2,3,...,N,n=0,1,2,3,...,N and m=0,1,2,3,...,N for N=10 in the following attached file. But I got some error, please have a look and try to fix it as early as possible. Please take care and thanks

Compare_coeff.mw

In mathematica, CommunityGraphPlot attempts to draw the vertices grouped into communities. 

This function is very useful, for example, if I get a partition of vertices, such as the gallai-Edmonds decomposition below, I use  CommunityGraphPlot to easily see the overall layout of the graph. I don't know if Maple has a corresponding function.

Hi I have experienced another Maple 2021 error with those of my students who Maple 2021 Mac edition. 

Lets say their have saved a .mw on their main drive and tries to open the file from inside Maple. Maple gives an error like "file cannot be opened - please try to another". This also happens when trying to open the file from outside Maple. 

This never happens on the Windows version. So any idea what could be causing this ?

I have the following expression.

Maple will evaluate this to:

Screenshot:

Plotting these two in 2D on Desmos to demonstrate: https://www.desmos.com/calculator/tvp4rbzxzp

These two are not the same expression. Is Maple broken or am I doing something wrong?

Hi,

I solve numerically an ODE system which depends on 25 parameters.
I want to know the maximum value of the time at which a specific event is triggered, when these parameters vary (independently the one of the other) within a 25 dimensional hyperbox.

To solve this maximization problem, which I assume is local¹, I would like to use NLPSolve

The attached zip (I use Mac OSX) contains:

• a file that gives a full description of the problem (the original ".pages" file and its export as pdf),
• an m file wich contains the solution procedure plus a few other variables needed to solve the problem,
• the mw file which contains:
  • the reading of the m file,
  • the procedure (OBJ) which returns the trigerring time,
  • many attemps to find its maximum value using NLPSolve.

None of my attempts at using NLPSolve gave me the expected answer

Could you help me to fix this?

Thanks in advance

mw_and_m_files.zip

1: Initializing a local method (see the explanation file) with different points gave me different optimizers but all of them led to rather close values of the objective function. Thus the problem is either global instead of local, or convergence might not be achieved for all the initialization points (but keep in mind that I'm not interested in the location of the minimizer(s) but in the maximum value of if the time when the event is triggered).

When I was drawing a plane graph, I found that the labels  of vertices were not displayed  and some edges even overlap when drawing because they were too close due to embedding.

So I thought that  option  Interactive  can adjust the position manually, but  at the same time I found that the style of  edges, such as the color and thickness, etc., is lost.  How to handle it? Is this a bug?

Maple 2021.1 screen shot: property box too small to select properties

how it should look like

How do I get it back to normal?

Thank you