f(a).b;            #ok
                           (f(a)) . b

op(0, f(a).b);     #ok
                               .

lprint(f(a).b);    #ok
f(a) . b

f(7).b;            #???
                             f(7) b

op(0, f(7).b);     #???
                               *

lprint(f(7).b);    #???
f(7)*b

Hi! I need a help for solve PDE problem (diffusion problem) in bipolar system coordinates. Actually, to begin with, I wanted to try to solve the homogeneous diffusion equation in a bipolar coordinate system with given boundary conditions. The process is not stationary, for simplicity, the diffusion coefficient is a constant (or linearly depends on η). The source function is also specified on the right side. The problem is that I cannot construct a correct exact solution, and the PDESolve function gives a very strange solution. The question is whether it is possible to solve a homogeneous and then a non-homogeneous solution automatically, or will it be necessary to manually specify parts of the general solution (homogeneous and particular solution)?

A document with a brief description and code for solving the equation is provided in the file. I ask for help with solving this problem, any valuable comments will be useful!

PDE.mw

====UPDATE===
I try to set Neumann conditions for solve this problem, but get error:
Error, (in PDEtools:-Library:-NormalizeBoundaryConditions) unable to isolate the functions {u(0,eta), u(xi,1.1), u(2*Pi,eta)} in the given boundary conditions {u(0,eta) = u(2*Pi,eta), u(xi,1.1) = 0}

PDE_upd.mw

For practice, I would like to solve the following problem. It is from "Steven Weinberg, Gravitation and Cosmology, p. 7" and was posed in a NG. I planned to define coordinates (x_i; y_i), apply the Pythagorean theorem, and enter the tediously long terms as term1 and term2, respectively. The final result should be term1-term2=0, or "is" should be used. I failed to enter the coordinates - the error message "error=Null" appears.

Question:
How are coordinates and their names of the type described meaningfully defined and entered as term1 and term2, respectively?

The four points P_1, P_2, P_3, P_4 lie in the Euclidean plane. Let
(ij) be the square of the distance between P_i and P_j. Then, it must be proven that

(12)(12)(34)+(13)(13)(24)+(14)(14)(23)+(23)(23)(14)
+(24)(24)(13)+(34)(34)(12)+(12)(23)(31)+(12)(24)(41)
+(13)(34)(41)+(23)(34)(42)
=
(12)(23)( 34)+(13)(32)(24)+(12)(24)(43)+(14)(42)(23)
+(13)(34)(42)+(14)(43)(32)+(23)(31)(14)+(21)(13)(34)
+(24)(41)(13)+(21)(14)(43)+(31)(12)(24)+(32)(21)(14)

I have a contour plot, and I need to make the following modifications. Could anyone please guide me on how to change the syntax accordingly?
 

1. Remove grid lines (black lines) from my plot.

2. Swap the axes so that s2  appears on the Y-axis, ranging from 1000 to 7000. Currently, s2 is shown on the X-axis from 1 to 7.

3. Add a color scale (legend) for the contour values of stemp (with label), with formatted values like 1.47 × 10⁷ (scientific notation).
   
   Attaching my file with plot: S1_vs_s2_contour_plot.mw

I’ve attached (or described) a sample contour plot for reference.

When i paste the code , its not keeping its same outline as in the worksheet  ?
 using this 

I've tried changing typesetting from extended to standard, but nothing seems to work.  I got myself in some mode I cannot get out of.  I've restarted maple, and even rebooted.
 

Download sample.mw

here's a snapshot because the uploaded maple document looks  weird:

I am trying to display the results by substituting values into a table format after solving the KKT conditions. I attempted to do this using Maplet, but it did not give the desired output or flexibility.

Could you please guide me on:

• The correct way to capture and display substituted results in a table?

• Any alternative syntax or functions (other than Maplet) that are better suited for this purpose?

I would also like to confirm whether the substitution I made for the lower and upper bounds—specifically C_min value  and C_max value —has been done correctly. Could you please verify if this is the correct way to implement these bounds within the KKT formulation?

KKT_Table_Q-22.mw

I'm working on a system of coupled ordinary differential equations with multiple degrees of freedom. I would like to explore the existence of multiple solutions by using a bifurcation diagram. To this end, I tried using the built-in Bifurcation command in Maple. However, the command repeatedly returns errors and fails to produce the expected plots.

Has anyone successfully used the Bifurcation command in Maple for coupled ODE systems? Are there specific settings or prerequisites that I might be missing? I would greatly appreciate any guidance or example code demonstrating how to properly use this command for such systems.
bifurcation.mw

To organize windows, Windows 11 provides a new function "Snap Layout". The example screen shot below shows options to place the Maple 2025 Screen Reader window.  

Draging now Maple 2025.1 Screen Reader to the left window of the third option results in the following selection screen

where on the right a list of tasks to chose from is presented. In this list Maple 2025.1 is missing. However Maple 2025.1 was running as can be seen from the task bar.

Has anybody managed to position Maple 2025.1 windows with the Snap Layout (or alternatively with Win+Arrow keys) or at least reproduce what I see on my computer?

Why can a Maple 2025.1 window be adjusted by hand but Windows does not do this in Snap Layout?

(Dragging and adjusting a Maple window by hand is not an option. This is how we had to work before Windows 7.)

When optimizing with constraints, I’m getting an error: ‘NLP no feasible point’.

However, when I plot the graph, it shows a result — there appears to be a point where p1 is positive and s is maximized.

Could you help identify if there’s a syntax issue? Also, what’s the correct syntax to visualize the constraints in the plot?

Sheet: 07.mw

Hello,

I’m trying to solve a problem from Modern Mathematical Methods for Scientists and Engineers using Maple, specifically applying the Fokas method (Unified Transform) to the heat equation on the half-line. The problem setup matches Example 9.1 from the book.

Everything runs fine until I try to plot the solution using plot3d.
 

Download fokas_method.mw

Has anyone successfully handled similar integrals inside plot3d? Is there a better way to numerically evaluate the Fokas integral so Maple can plot it efficiently?

Dear Maple users

I can plot a pin diagram for the binomial distribution for say n = 20 and p = 0.3. It is one-dimensional, since only the number r of successes is relevant. Now I want to plot a diagram for the multinomial distribution for 3 categories. This means a two dimensional distribution. Let's say n = 20, p1 = 0.2, p2 = 0.5 (then p3 = 1 - p1 - p2 = 0.3). How do I make this plot? Pin diagram, but maybe even better: A Bar Chart. 

I hope someone can help.

Erik

I want to solve my PDE using Homotopy Perturbation Method. I have error while solving i dont know why it is showing error. If anyone knows the what mistake i have done in the code, kindly correct me. I want to find the equation of W(r,z) . dp/dz is a pressure terms which is independent of r. And the initial guess is taken as w0 := (-eta^2 + r^2)/2.  Help me to solve this.

restart;
PDEtools[declare](w(r, z));
               w(r, z) will now be displayed as w

N := 1;

w0 := (-eta^2 + r^2)/2:
w(r,z) := sum(p^i*w[i](r, z), i = 0 .. N)
                   w[0](r, z) + p w[1](r, z)

HPMEq := (1 - p)*diff(w(r, z), r $ 2) + p*(diff(w(r, z), r $ 2) + diff(w(r, z), r)/r - (1 + lambda)*(dp/dz + A2*M^2*w(r, z) + A1*w(r, z)/Da - m^2*UHS*BesselI(0, m*r)/BesselI(0, m*eta) + A3*sin(Phi))/A1);
                                                                /
                                                                |
        // d  / d            \\     / d  / d            \\\     |
(1 - p) ||--- |--- w[0](r, z)|| + p |--- |--- w[1](r, z)||| + p |
        \\ dr \ dr           //     \ dr \ dr           ///     \

  / d  / d            \\     / d  / d            \\
  |--- |--- w[0](r, z)|| + p |--- |--- w[1](r, z)||
  \ dr \ dr           //     \ dr \ dr           //

     / d            \     / d            \                       
     |--- w[0](r, z)| + p |--- w[1](r, z)|      /             /  
     \ dr           /     \ dr           /   1  |             |dp
   + ------------------------------------- - -- |(1 + lambda) |--
                       r                     A1 \             \dz

         2                            
   + A2 M  (w[0](r, z) + p w[1](r, z))

                                       2                    
     A1 (w[0](r, z) + p w[1](r, z))   m  UHS BesselI(0, m r)
   + ------------------------------ - ----------------------
                   Da                   BesselI(0, m eta)   

                  \
                \\|
                |||
   + A3 sin(Phi)|||
                ///

for i from 0 to N do
    equ[1][i] := coeff(HPMEq, p, i) = 0;
end do;
                     d  / d            \    
                    --- |--- w[0](r, z)| = 0
                     dr \ dr           /    

                           d                                   
                          --- w[0](r, z)      /             /  
 / d  / d            \\    dr              1  |             |dp
 |--- |--- w[1](r, z)|| + -------------- - -- |(1 + lambda) |--
 \ dr \ dr           //         r          A1 \             \dz

                                          2                    
          2              A1 w[0](r, z)   m  UHS BesselI(0, m r)
    + A2 M  w[0](r, z) + ------------- - ----------------------
                              Da           BesselI(0, m eta)   

                 \\    
                 ||    
    + A3 sin(Phi)|| = 0
                 //    

NULL;
cond[1][0] :=  D*w[0](0,z) = 0, w[0](eta,z) = 0;
for j to N do
    cond[1][j] := D*w[j](0,z) = 0,w[j](eta,z) = 0;
end do;
               D w[0](0, z) = 0, w[0](eta, z) = 0

               D w[1](0, z) = 0, w[1](eta, z) = 0

for i from 0 to N do
    dsolve({cond[1][i], equ[1][i]}, {w[i](r,z)});
    w[i](r,z) := rhs(%);
end do;
w(r,z) := evalf(simplify(sum(w[n](r,z), n = 0 .. N)));
convert(w(r,z), 'rational');
w(r,z) := subs(r = 0, w(r,z));
Error, invalid input: rhs expects 1 argument, but received 2
                    w[0](r, z) + w[1](r, z)

                    w[0](r, z) + w[1](r, z)

                    w[0](0, z) + w[1](0, z)

I tried to change my email adress but after submitting changes I still get my old email listed.

Additionally to only changing the email I also changed my password.

Nothing worked. What could I have done wrong?

Hello everyone,
Is it possible to load complete Maple packages into Maple Flow?

Regards,

Oliveira