My goal is to export images of curves where the output image has no background or equivalently, a fully transparent background. Is there a standard way to perform this task? I know that I can do this with the help of external software but I want to do it at the export stage in maple and avoid increasing the number of tools needed to perform the job. Eventually, I may want to generate many thousdands of curves/images with transparent backgrounds. 

Below I show how to make a plot while choosing a background with the color blue. I have found no way to select a fully transparent background. I expect this background transparency will be applied at the export image stage. 

how_do_I_plot_with_no_background.mw

To give an explicit example of what a plot with no background looks like, I make a plot in an unrelated software of a curve with no background. It's impossible to differentiate a white background from a transparent background in this environment, so we also show the same image embedded in an unrelated colored background also generated in an unrelated software.

In the image below, we can see how a image of a curve with a transparent background can be embedded over top of any other image without the blue square shown the the first example.

Hi,

I use Maple 2024 (X86 64 LINUX), and am trying to calculate the sum of the prime factors of integers.

My code is as simple as something like this:

SumPrimeFactors := proc(n)
    local f, L, p;
    f := ifactor(n);
    L := [op(f)];
    return add(convert(op(1, p), integer), p in L);  # Sum base primes
end proc:

However, the above code returns the following result when I set n = 360:

> SumPrimeFactors(360);
                                     5 +  (2) +  (3)

while what I had expected is just an integer, 10 (= 5+2+3).
It seems the operation convert(op(1, p), integer) is not working properly, and "(2)" is recognized as an expression, not an integer, even after the convert operation.

I have no idea how I should rectiy it.
I would be glad if someone gives me a way to get it solved.
Thank you very much.

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 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)

Hi

I'm trying to duplicate this graph in Maple. Any suggestions on how to place the textplot labels (n=0, n=1, etc.) to the right of 0.8, just like in the original graph?

how to place the textplot labels (n=0, n=1, etc.)

Thanks

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