I am implementing the Fokas (unified transform) method for the heat equation on a finite interval [0,1]. The solution is expressed as a contour integral in the complex k-plane and I evaluate it numerically in Maple.

When I call plot3d I get the following error, even though approx_u(0.5, 0.1)

Is there a way to make plot3d work? Any help appreciated.

Download heat_equation_on_finte_interval.mw

Any one knows a trick to help Maple obtain this much simpler solution to this ode obtained using AI?

ode := 4*(-1 + sqrt(1 - 1/x^2)*x^2)*sec(4 + 4*x + 4*arccsc(x))^2 - sqrt(1 - 1/x^2)*x^2*diff(f(x), x) = 0

Download AI_sol.mw

given

ode:=2*x^(1/2)*diff(y(x),x)-y(x) = -sin(x^(1/2))-cos(x^(1/2)); 
ic:=y(infinity) = y__0; 
sol:=dsolve([ode,ic]);

It gives  

This solution satisfies the ode itself. Now cos(sqrt(x)) when x=infinity is  -1..+1

But IC says y(infinity)=y0  so odetest do not verify the IC and gives this

odetest(sol,[ode,ic]);

I think dsolve should not have returned a solution at all. 

What do the experts here think of this result?

Maple 2026.1 on windows 10

I'm trying to rewrite my initialization routines a bit, and want to find out if there are any other procedures with a certain name that should be called.
However there seems to be a problem with the scope. I'm trying to explain that with a little program.

The question is - why is InitSpecific not found by the InitCommon procedure here?

Download InitCommon.mw

The uploaded worksheet references two youtube videos.

The first one displays the animation of a simple device rotating about an axis tilted at a small angle from the device's principal axis having an intermediate moment of inertia.

The animation and accompanying verbal description demonstrate the Dzhanibekov effect.
The second video contains the first video's narrator's equations which produce the values used in creating the animation.

The uploaded worksheet contains my failed attempt to reproduce these values.

Please suggest the Maple 2020 compatible statements which correctly produce these values.

Dzhanibekov_effect.mw

I am new to evala (and the math behind).

On ?evala,Sqrfree at the first bullet point I was wondering if there isn't a "u" missing here

Can someone confirm?

I asked an LLM to provide an expansion of the MacDonald function of arbitrary order (a modified Bessel function of the second kind with purely imaginary order and positive argument), K(I*y,r), as a weighted sum of MacDonald functions of integer order. It came back with

         K(I*y,z)=2*sinh(Pi*y)/Pi* [K(0,r)/2*y+sum( (-1)^n*y*BesselK(0,r)/(y^2+n^2),n=1..infinity)]

(see below for more readable text)

I evaluated the LHS and RHS using Maple 2026 for various choices of y and r and found numerical agreement using both "sum" and "Sum".  I was very pleased until I realized that the RHS isn't a convergent series!

Can anyone explain to me how Maple pulls this off! 

(I asked Maplesoft Tech Support but they said it is above their pay grade... I suspect that Maple is using Borel summability to evaluate the RHS but I haven't been able to verify that)

I apologize, but I can't see how to attach a .mw file, so I've cut and pasted the code below

restart;

T := R(xi)*R(xi) + lambda;

u := A[0] + A[1]*R(xi) + B[1]/R(xi);

d[1] := A[1]*T - B[1]*T/R(xi)^2;

d[2] := 2*A[1]*R(xi)*T - 2*B[1]*T/R(xi) + 2*B[1]*(R(xi)^2 + lambda)*T/R(xi)^3;

expand(((-alpha^2*b^2 + a^2)*alpha^2)/(2*beta)*d[2] + (omega + alpha^2*(alpha^2*l^2 + k^2)/2 - a*C[1]/(-alpha^2*b^2 + a^2))*u[0]/(beta - 2*beta*a^2/(-alpha^2*b^2 + a^2)) + u[0]*u[0]*u[0]);

value(%);

simplify(%);

collect(%, R(xi));

      /      6  4    4      2\      3
 A[1] \-alpha  b  + a  alpha / R(xi) 
 ------------------------------------
             /     2  2    2\        
        beta \alpha  b  + a /        

                  /      6  4    4      2\         
      A[1] lambda \-alpha  b  + a  alpha / R(xi)   
    + ------------------------------------------ + 
                     /     2  2    2\              
                beta \alpha  b  + a /              

                         /                               /     
             1           |/                    B[1] \    |     
   --------------------- ||A[0] + A[1] R(xi) + -----|[0] |beta 
        /     2  2    2\ \\                    R(xi)/    \     
   beta \alpha  b  + a /                                       

                                                  2
   /     2  2    2\ /                    B[1] \    
   \alpha  b  + a / |A[0] + A[1] R(xi) + -----|[0] 
                    \                    R(xi)/    

      1  2  2      6   1 /  2  2    2  2\      4
    + - b  l  alpha  + - \-a  l  + b  k / alpha 
      2                2                        

                                                       \\
      /  1  2  2    2      \      2    2               ||
    + |- - a  k  + b  omega| alpha  - a  omega + a C[1]||
      \  2                 /                           //

                  /      6  4    4      2\
      B[1] lambda \-alpha  b  + a  alpha /
    + ------------------------------------
               /     2  2    2\           
          beta \alpha  b  + a / R(xi)     

            6  4       2         4      2       2     
      -alpha  b  lambda  B[1] + a  alpha  lambda  B[1]
    + ------------------------------------------------
                     /     2  2    2\      3          
                beta \alpha  b  + a / R(xi)           

WHen I open many worksheets at same time, say 10. The new UI do not stack them all (i.e. the tab at the top), forcing one to use the small arrow to navigate to each worksheet.

Is there a way to tell the UI to show all tabs (may be double rows and 3 rows as needed) to make it easier to jump from one worksheet to the other?

I do not know if this is new feature in the new ribbon UI or not. 

Here is screen show where I have 10 worksheets open

There is also a pull down menu, but it only shows 8 worksheets and one can have more open but they do not show. So have to scroll down looking for the rest. Even that does not work well. many times when I try to scroll down, the window closes. It will not give me time to move the mouse to the scroll bar to move it before it closes.

Both of these solutions are not good. Having to use the arrow key to look and navigate for a different worksheet is bad UI design.

How to see all tabs for all open worksheet in same UI?  If the tabs do not fit on one row, why not make second row? If two rows do not fit, make 3rd row. This should be an option for the user. But I did not see one so far. But will keep looking.

I find tabs where all worksheet show much better design that this UI design.   

I only use worksheet and not document mode. Windows 10.

To give you idea what I mean, These are examples found on the net of stacked tabs

Where in Maple, each tab above will have the name of the worksheet open. Font can be small, is OK.

Is it possible to have this in the new UI for open worksheets?

One option I might try to make my worksheets names much shorter. May be then they will fit all in same window.

The below problem has already occured several times to me. In all such instances Maple did not realise that extracting a factor from a square root is the key for further simplification. Doing this by hand is obvious and often easy when extracted factors are positive.  

Did I overlook something? Are there other ways avoid disassembling an expression with the op command?
Should simplify or other commands be improved to adress such problems?

Download Simplify_radical_02.mw

Help me rewrite the code to create visible Bar chart of different colors. I can't figure out why this code is not giving me a visible bar graph

Download Bargraph.mw

restart;
with(plottools);
with(plots);
a := 1;
b := 1;
c := 1;
k := 1;
l := 1;
omega := 1;
A[2] = 2;
alpha := 2;
beta := 1;
kappa := 0.5;
C[1] := 1;
lambda := -1;

omega := (-alpha^6*b^4*lambda + 2*alpha^6*b^2*l^2 - 2*a^2*alpha^4*l^2 + 2*alpha^4*b^2*k^2 + a^4*alpha^2*lambda - 2*a^2*alpha^2*k^2 + 4*a*C[1])/(-4*alpha^2*b^2 + 4*a^2);

a[0] := 0;

a[1] := sqrt(-(-alpha^2*b^2 + a^2)/(4*beta))*alpha;

b[1] := sqrt(-(alpha^2*b^2*lambda*sigma - a^2*lambda*sigma)/(4*beta))*alpha;

sigma := A[1]*A[1] - A[2]*A[2];

T := A[1]*sinh(xi*sqrt(-lambda)) + A[2]*cosh(xi*sqrt(-lambda)) + mu/lambda;

t := diff(T, xi);

S := t/T;

R := 1/T;

mu := 0;

A[1] := 0;

y := 0;

xi := k*x^kappa/kappa + l*y^kappa/kappa - omega*t^kappa/kappa;

  Error, recursive assignment

Dear all,

I'm reporting what seems to me as a bug in the SMTLIB library in maple. 

    |\^/|     Maple 2026 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2026
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> SMTLIB:-Satisfiable({x^2=2,y^2=2,x<y});
                                     true

> SMTLIB:-Satisfiable({x^2=2,y^2=2,y<x});
                                     false

> SMTLIB:-Satisfiable({x^2=2,a^2=2,a<x});
                                     true

The Satisfiable command do not output the correct decision on two formulas of equivalent realization by switching x<y (output SAT) to y<x (output UNSAT). I suspect this is because some alphabetical order depandance in the variables as for a<y we get SAT again.

I tried to feed Z3 with the code given by ToString on the problematic formula and I get two different outputs :

• on the Z3 version 4.8.12 from the ubuntu repository (apt install) I also get the wrong UNSAT output;
• one the Z3 version 4.17.0 build from the official github repository I finally get the correct SAT output.

Thus, I suspect a version problem in SMTLIB that do not take in account the last updates made in SMT solvers (Z3?).

Many thanks for considering my problem!

A little while ago, I created a video, Engaging and Enlightening Students with Maple Visualizations, that showed a sample of Maple visualizations that would be helpful in teaching math. Doing that allowed me to get reacquainted with some of Maple's plotting features that I hadn't used for a while. As a result, I made a second instructional video for my Maple tips series, Animating a Polyhedron in Maple. 

I chose this topic because I thought it would show several features in Maple that might not be known to all users. I list them below and encourage you to try them out.

• The plots:-polyhedraplot command allows you to create a 3-D plot of a polyhedron, including one of 138 polyhedra that Maple knows about.

• The list of named polyhedra available can be obtained by calling the plots:-polyhedra_supported command.

• The viewpoint option, which allows you to create an animation by varying the viewpoint through a 3D plot, can be used to rotate the polyhedron.

• Finally, the Export feature allows you to save the plot animation as an animated GIF.

restart;
solve({-alpha^4*b^2*lambda*mu*b[1] + a^2*alpha^2*lambda*mu*b[1] + 6*beta*lambda^2*sigma*a[0]*a[1]^2 + 6*beta*mu^2*a[0]*a[1]^2 - 6*beta*lambda*a[0]*b[1]^2 = 0, -alpha^4*b^2*lambda^2*mu*sigma - alpha^4*b^2*mu^3 + a^2*alpha^2*lambda^2*mu*sigma + a^2*alpha^2*mu^3 - 4*beta*lambda^2*sigma*a[0]*b[1] - 4*beta*lambda*mu*b[1]^2 - 4*beta*mu^2*a[0]*b[1] = 0, -alpha^4*b^2*lambda^2*sigma - alpha^4*b^2*mu^2 + a^2*alpha^2*lambda^2*sigma + a^2*alpha^2*mu^2 + beta*lambda^2*sigma*a[1]^2 + beta*mu^2*a[1]^2 - 3*beta*lambda*b[1]^2 = 0, -alpha^4*b^2*lambda^2*sigma - alpha^4*b^2*mu^2 + a^2*alpha^2*lambda^2*sigma + a^2*alpha^2*mu^2 + 3*beta*lambda^2*sigma*a[1]^2 + 3*beta*mu^2*a[1]^2 - beta*lambda*b[1]^2 = 0, -alpha^6*b^4*lambda^2*mu*b[1] + alpha^6*b^2*l^2*lambda^2*sigma*a[0] + alpha^6*b^2*l^2*mu^2*a[0] - a^2*alpha^4*l^2*lambda^2*sigma*a[0] + alpha^4*b^2*k^2*lambda^2*sigma*a[0] - a^2*alpha^4*l^2*mu^2*a[0] + alpha^4*b^2*k^2*mu^2*a[0] + 2*alpha^2*b^2*beta*lambda^2*sigma*a[0]^3 + a^4*alpha^2*lambda^2*mu*b[1] - a^2*alpha^2*k^2*lambda^2*sigma*a[0] - 6*alpha^2*b^2*beta*lambda^2*a[0]*b[1]^2 + 2*alpha^2*b^2*beta*mu^2*a[0]^3 - a^2*alpha^2*k^2*mu^2*a[0] + 2*a^2*beta*lambda^2*sigma*a[0]^3 + 2*alpha^2*b^2*lambda^2*omega*sigma*a[0] - 6*a^2*beta*lambda^2*a[0]*b[1]^2 + 2*a^2*beta*mu^2*a[0]^3 + 2*alpha^2*b^2*mu^2*omega*a[0] - 2*a^2*lambda^2*omega*sigma*a[0] - 2*a^2*mu^2*omega*a[0] + 2*a*lambda^2*sigma*C[1]*a[0] + 2*a*mu^2*C[1]*a[0] = 0, -2*alpha^6*b^4*lambda^3*sigma - 2*alpha^6*b^4*lambda*mu^2 + alpha^6*b^2*l^2*lambda^2*sigma + alpha^6*b^2*l^2*mu^2 - a^2*alpha^4*l^2*lambda^2*sigma + alpha^4*b^2*k^2*lambda^2*sigma + 2*a^4*alpha^2*lambda^3*sigma - a^2*alpha^4*l^2*mu^2 + alpha^4*b^2*k^2*mu^2 + 6*alpha^2*b^2*beta*lambda^2*sigma*a[0]^2 + 2*a^4*alpha^2*lambda*mu^2 - a^2*alpha^2*k^2*lambda^2*sigma - 6*alpha^2*b^2*beta*lambda^2*b[1]^2 + 6*alpha^2*b^2*beta*mu^2*a[0]^2 - a^2*alpha^2*k^2*mu^2 + 6*a^2*beta*lambda^2*sigma*a[0]^2 + 2*alpha^2*b^2*lambda^2*omega*sigma - 6*a^2*beta*lambda^2*b[1]^2 + 6*a^2*beta*mu^2*a[0]^2 + 2*alpha^2*b^2*mu^2*omega - 2*a^2*lambda^2*omega*sigma - 2*a^2*mu^2*omega + 2*a*lambda^2*sigma*C[1] + 2*a*mu^2*C[1] = 0, -alpha^6*b^4*lambda^3*sigma + alpha^6*b^4*lambda*mu^2 + alpha^6*b^2*l^2*lambda^2*sigma + alpha^6*b^2*l^2*mu^2 - a^2*alpha^4*l^2*lambda^2*sigma + alpha^4*b^2*k^2*lambda^2*sigma + a^4*alpha^2*lambda^3*sigma - a^2*alpha^4*l^2*mu^2 + alpha^4*b^2*k^2*mu^2 + 6*alpha^2*b^2*beta*lambda^2*sigma*a[0]^2 - a^4*alpha^2*lambda*mu^2 - a^2*alpha^2*k^2*lambda^2*sigma - 2*alpha^2*b^2*beta*lambda^2*b[1]^2 + 12*alpha^2*b^2*beta*lambda*mu*a[0]*b[1] + 6*alpha^2*b^2*beta*mu^2*a[0]^2 - a^2*alpha^2*k^2*mu^2 + 6*a^2*beta*lambda^2*sigma*a[0]^2 + 2*alpha^2*b^2*lambda^2*omega*sigma - 2*a^2*beta*lambda^2*b[1]^2 + 12*a^2*beta*lambda*mu*a[0]*b[1] + 6*a^2*beta*mu^2*a[0]^2 + 2*alpha^2*b^2*mu^2*omega - 2*a^2*lambda^2*omega*sigma - 2*a^2*mu^2*omega + 2*a*lambda^2*sigma*C[1] + 2*a*mu^2*C[1] = 0}, {omega, a[0], a[1], b[1]});