MaplePrimes Questions

i do same trasnformation but i don't know what is issue  the result is near to same but parameter (t) appear in my which that make my ode  not be correct so  i can't see the problem in here  and i am intrested in finding this, regarding to this i will put here my result and the papers result rregarding to resolve the issue 

pde1

pde2

 

T1.mw

I was trying to use the debugger into a proc that has this call

P:=plots:-contourplot(RHS,':-colorbar' = false,':-contours' = L):

Even though the proc has : at its end, and the above call to plots also ends with :, the debugger insists in printing to the debugger window the contour cuves lines. i.e the value of P

Is there a way to tell the debugger not to do this? i.e. not show the value of P. It seems it does that automatically.

Here is the worksheet. Simply evaluate the call foo(); this will open a debugger windows. Then click on next button and now debugger will print  the output of plots:-contourplot(RHS,':-colorbar' = false,':-contours' = L): 

restart;

kernelopts('assertlevel'=2):
kernelopts(numcpus=1);

32

interface(version);

`Standard Worksheet Interface, Maple 2026.1, Windows 10, April 28 2026 Build ID 2011354`

foo:=proc()
local L := [$ -4 .. 4]:
local RHS:=y/tan(x):
local P,T:

DEBUG();
P:=plots:-contourplot(RHS,':-colorbar' = false,':-contours' = L):
T:= timelimit(60,plottools:-getdata(P,'rangesonly')):
end proc:

 

foo();  #this will open a debugger window

 

Download hang_maple_2026_1_on_timelimit.mw

Here is screen shot

In my main actual code, the output was so large that it hanged Maple UI when stepping into the debugger and hitting that line.  I had to kill Maple from task manager as Java UI got stuck due to large output.

Why is it showing value of P when I have : at the end? Is there an option to turn automatic display of variables in debugger as one steps in?

I have a rather involved double summation which I am trying to evaluate for various values of the four parameters. Is there a straightforward way that Maple can evaluate this summation?

For example, lambda=nu= +1/2 and/or -1/2 and kappa=mu=1/2 for a start. I would like an expression as a .mw file into which I could put various values and get varying degrees of simplification, rather than trying to do "handraulic" evaluations.

regarsd, RJH

The integral shown in the attached file "test" was posted on another forum for calculation. I unsuccessfully attempted to apply Green's theorem in Maple and—as befits a Maple beginner—failed. Does Maple offer a sequence of commands to carry this out? I would appreciate some advice. If this is possible, I would then tackle the line integral using the residue theorem.

restart

NULL

NULL

 

``

Download test.mw

This is a follow-up question from here concerned with rearraging (not simplifying) an expression for an easier visual comparision.

restart

In a Maple document I want to demonstrate (easier to follow from the output without the knowledge of Maple commands) that the following expression

expr := sqrt(2)/(sqrt(-beta^2+1)*sqrt(2+(-x-1)*beta^2))

2^(1/2)/((-beta^2+1)^(1/2)*(2+(-x-1)*beta^2)^(1/2))

(1)

can visually match the integrand of this ellpitic integral

FunctionAdvisor(definition, EllipticF)

[EllipticF(z, k) = Int(1/((-_alpha1^2+1)^(1/2)*(-_alpha1^2*k^2+1)^(1/2)), _alpha1 = 0 .. z), MathematicalFunctions:-`with no restrictions on `(z, k)]

(2)

This can be done with following substitution

x = 2*k^2-1

x = 2*k^2-1

(3)

subs(x = 2*k^2-1, 2^(1/2)/((-beta^2+1)^(1/2)*(2+(-x-1)*beta^2)^(1/2)))

2^(1/2)/((-beta^2+1)^(1/2)*(-2*beta^2*k^2+2)^(1/2))

(4)

simplify(2^(1/2)/((-beta^2+1)^(1/2)*(-2*beta^2*k^2+2)^(1/2)))

1/((-beta^2+1)^(1/2)*(-beta^2*k^2+1)^(1/2))

(5)

Since the substitution comes without explanation, I though about rearranging expression (1) by Maple commands in a way that facilitates visual pattern matching.
How to collect the factor 1+x in (1) leading to  sqrt(2)/(sqrt(-beta^2+1)*sqrt(2-(1+x)*beta^2))

It looks as one would write by hand.

 

At a glance, this much easier suggest that k^2 = (1+x)*(1/2).

Download Collect_one_plus_x_-_02.mw

(Maple 2025.2 only for easier editing. Results are the same with Maple 2026)

Original Post - Collect_one_plus_x.mw

The title says it all. Nevertheless, I am doing some symbolic computation/manipulations with tensors in the Physics pacakge. When I type out my expressions and execute it changes some positions of the indices -- example below. Why? 
**Sorry, contents will not post. 

Download IndexQuestion.mw

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.

restart; with(plots)

V := exp(-k^2*t)*((-4*k*(sin(k*x)/exp(1)+sin(k*(1-x)))*(k^2-1))*(1/((k^2+1)*(k^4+1))))/((2*Pi)*(exp(I*k)-exp(-I*k)))

-2*exp(-k^2*t)*k*(sin(k*x)/exp(1)+sin(k*(1-x)))*(k^2-1)/(Pi*(exp(I*k)-exp(-I*k))*(k^2+1)*(k^4+1))

(1)

L := 3/4; k1 := proc (r) options operator, arrow; L+(3/4)*I+r*exp(((1/6)*I)*Pi) end proc; k2 := proc (r) options operator, arrow; -L+(3/4)*I+r*exp(((5/6)*I)*Pi) end proc; k3 := proc (s) options operator, arrow; s+(3/4)*I end proc; dk1 := D(k1); dk2 := D(k2); dk3 := D(k3)

3/4

 

proc (r) options operator, arrow; L+(3/4)*I+r*exp(((1/6)*I)*Pi) end proc

 

proc (r) options operator, arrow; -L+(3/4)*I+r*exp(((5/6)*I)*Pi) end proc

 

proc (s) options operator, arrow; s+(3/4)*I end proc

 

proc (r) options operator, arrow; exp(((1/6)*I)*Pi) end proc

 

proc (r) options operator, arrow; exp(((5/6)*I)*Pi) end proc

 

1

(2)

integrand1 := Re((eval(V, k = k1(r)))*dk1(r)-(eval(V, k = k2(r)))*dk2(r)); integrand3 := Re((eval(V, k = k3(s)))*dk3(s)); integrand2 := simplify(evalc(integrand1)); integrand4 := simplify(evalc(integrand3))

approx_u := proc (x, t) local temp1, temp2; temp1 := Int(eval(integrand2, [:-x = x, :-t = t]), r = 0 .. infinity, method = _d01amc); temp2 := Int(eval(integrand4, [:-x = x, :-t = t]), s = -L .. L, method = _d01ajc); evalf(temp1+temp2) end proc

approx_u(.5, .1)

.6536368264

(3)

``

forget(`evalf/int`); forget(evalf); CodeTools:-Usage(plot3d(approx_u, 0 .. 1, 0 .. 2*Pi, grid = [10, 10], axes = boxed, labels = ["x", "t", "u(x,t)"], title = "Fokas Method of solution", shading = zhue))

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

memory used=14.27GiB, alloc change=-16.00MiB, cpu time=92.96s, real time=88.85s, gc time=8.99s

 

 

 

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

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;

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

maple_sol:=dsolve(ode);

f(x) = c__1+Int(8*(-1+(1-1/x^2)^(1/2)*x^2)*x^6/((1-1/x^2)^(1/2)*(-8*((x^2-1)/x^2)^(1/2)*x^7*sin(8+8*x)+x^8*cos(8+8*x)+x^8+80*((x^2-1)/x^2)^(1/2)*x^5*sin(8+8*x)-32*x^6*cos(8+8*x)-192*((x^2-1)/x^2)^(1/2)*x^3*sin(8+8*x)+160*x^4*cos(8+8*x)+128*((x^2-1)/x^2)^(1/2)*x*sin(8+8*x)-256*cos(8+8*x)*x^2+128*cos(8+8*x))), x)

odetest(maple_sol,ode);

0

AI_sol:=f(x)=_C1+tan(4*(1+x+arccsc(x)));

f(x) = c__1+tan(4+4*x+4*arccsc(x))

odetest(AI_sol,ode)

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?

Module1 := module()

 

``

Module2 := module()

Module1:-InitCommon()

"false"

(1)

Module2:-InitSpecific()

"InitSpecific"

(2)

NULL

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.

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