with(GlobalOptimization);

          [GetLastSolution, GlobalSolve, Interactive]

GlobalSolve(x3 - y3 - x + y, {x2 + 2*y <= 6}, x = 0 .. 5, y = 0 .. 5);
Error, (in GlobalOptimization:-GlobalSolve) finite bounds must be provided for all variables

I have the following expresion:

G_{ik}=|u_{i} - u_{k}|-(u_{i}-u_{k})^2

Where i, k=1,2,3,4. How can I write this expresion in maple? I want to be able to write G_{1 2} and in the RHS

Hi all, 

I am trying to plot the amplitude spectrum of a square wave. I plotted the wave by using its fourier series but I want to find the 5th harmonic which should be around 0.5 however, maplesoft retruns it as 0.7 for some reason. When the stem plot is plotted even that look likes 0.5 at the 5th harmonic but the F(5) is giving wrong value. 

Please have a look at the screenshot and file attached. 

Pulse_width_8us.mw

(Note: Maple was not giving wrong answer, I accidently uploaded the wrong file and have edited/updated the question)

I want to perform a numerical evaluation of sums of integrals of relatively complicated functions. I know about the evalf(Int( )) and evalf(Sum( )) commands to numerically evaluate both sums and integrals individually. My question is: what is the time-efficient way to numerically evaluate a sum of integrals? 

Here is a simplified sketch of what I have.

Say I define my complicated function F of the variable x (which will be integrated over) and of some constant parameter n.

I am interested in numerically evaluating in a time efficient way the following sum of integrals of F:

Where should I apply the evalf() command(s)? Should I go evalf(Sum( evalf(Int( )))) or evalf(Sum( Int())) or sum( evalf(Int( ))), or something else? I am not too worried about the accuracy here: it is for plots mainly. How to make this numercal evaluation fast?

Bonus question. If now I make F also depend on t, and wish to define a function G(t) out of a linear combination of such sums of integrals: is the method the same? I can have G(t) defined numerically with a t dependance. For example:

Thanks a lot!

PS: F is a complicated function in the sense that it is rationnal in some (non-usual) polynomials defined by a Rodrigues Rormula. The integrand has no singularity on the domain of integration. I have Maple 2018.

complexplot3d((z - 1)/(z^2 + z + 1), z = -4 - 4*I .. 4 + 4*I, view = [-2 .. 2, -2 .. 2, 0 .. 2], grid = [70, 70], shading = zhue)

How can I change this color of complex plot to take mirror image of my enhanced portrait? I see this is inverse but I don't know the source of this situation. I guess that zhue is indicaded by H = arg(f(z)) L = l(|f(z)|) S=1 in MAPLE but I don't know how to transfer and change this to the second picture coloring. I built the code for the second picture using codes from this post:

https://www.mapleprimes.com/questions/226790-Is-There-Any-Maple-Code-For-The-domain

I want to present this complexplot with the same coloring so thank for all yours advise.

temp.mw

Dear Users!

Hope everyone is fine here. I want to formulate the table like give bellow (Table 5.17) in maple so that I can copy it in word file and can edit.

The values of y[1,1],y[2,1],y[2,2],y[3,1],y[3,2],y[3,3]...y[nops(HAq),nops(HAq)] present in the following maple code. Thanks in advance

Refine_Extrapolation.mw

I'm a bit confused about set ordering.

According to help there are those features

1. object id (same kind of data-structures to be grouped togther)
2. object length
3. lexicographical or numerical orders
4. recurse on components
5. address

Have a look at the following set.

• If object length has higher priority than lexicographical order, why is HBSEVO before LBS?
• If lexicographical order has higher priority, which is HBSPLATEEVO after VGZEVO?

Download SetSortOrder.mw

restart;
T := diff(Phi(xi), xi);
                           d          
                          ---- Phi(xi)
                           dxi        
restart;
T := (p*a^(-Phi(xi))+q+r*a^Phi(xi))/ln(a);
                    (-Phi(xi))          Phi(xi)
                 p a           + q + r a       
                 ------------------------------
                             ln(a)             
u[0] := C[0]+C[1]*a^Phi(xi)+C[2]*a^(2*Phi(xi));
                         Phi(xi)         (2 Phi(xi))
            C[0] + C[1] a        + C[2] a           
u[1] := diff(u[0], xi);
               Phi(xi) / d          \      
         C[1] a        |---- Phi(xi)| ln(a)
                       \ dxi        /      

                      (2 Phi(xi)) / d          \      
            + 2 C[2] a            |---- Phi(xi)| ln(a)
                                  \ dxi        /      
d[1] := C[1]*a^Phi(xi)*T*ln(a)+2*C[2]*a^(2*Phi(xi))*T*ln(a);
         Phi(xi) /   (-Phi(xi))          Phi(xi)\
   C[1] a        \p a           + q + r a       /

                (2 Phi(xi)) /   (-Phi(xi))          Phi(xi)\
      + 2 C[2] a            \p a           + q + r a       /
u[2] := diff(d[1], xi);
      Phi(xi) / d          \       /   (-Phi(xi))    
C[1] a        |---- Phi(xi)| ln(a) \p a           + q
              \ dxi        /                         

        Phi(xi)\         Phi(xi) /
   + r a       / + C[1] a        |
                                 \
    (-Phi(xi)) / d          \      
-p a           |---- Phi(xi)| ln(a)
               \ dxi        /      

        Phi(xi) / d          \      \           (2 Phi(xi)) / d  
   + r a        |---- Phi(xi)| ln(a)| + 4 C[2] a            |----
                \ dxi        /      /                       \ dxi

          \       /   (-Phi(xi))          Phi(xi)\          
   Phi(xi)| ln(a) \p a           + q + r a       / + 2 C[2] 
          /                                                 

   (2 Phi(xi)) /    (-Phi(xi)) / d          \      
  a            |-p a           |---- Phi(xi)| ln(a)
               \               \ dxi        /      

        Phi(xi) / d          \      \
   + r a        |---- Phi(xi)| ln(a)|
                \ dxi        /      /
d[2] := C[1]*a^Phi(xi)*T*ln(a)*(p*a^(-Phi(xi))+q+r*a^Phi(xi))+C[1]*a^Phi(xi)*(-p*a^(-Phi(xi))*T*ln(a)+r*a^Phi(xi)*T*ln(a))+4*C[2]*a^(2*Phi(xi))*T*ln(a)*(p*a^(-Phi(xi))+q+r*a^Phi(xi))+2*C[2]*a^(2*Phi(xi))*(-p*a^(-Phi(xi))*T*ln(a)+r*a^Phi(xi)*T*ln(a));
                                              2                  
      Phi(xi) /   (-Phi(xi))          Phi(xi)\          Phi(xi) /
C[1] a        \p a           + q + r a       /  + C[1] a        \
    (-Phi(xi)) /   (-Phi(xi))          Phi(xi)\
-p a           \p a           + q + r a       /

        Phi(xi) /   (-Phi(xi))          Phi(xi)\\
   + r a        \p a           + q + r a       //

                                                         2       
             (2 Phi(xi)) /   (-Phi(xi))          Phi(xi)\        
   + 4 C[2] a            \p a           + q + r a       /  + 2 C[

      (2 Phi(xi)) /
  2] a            \
    (-Phi(xi)) /   (-Phi(xi))          Phi(xi)\
-p a           \p a           + q + r a       /

        Phi(xi) /   (-Phi(xi))          Phi(xi)\\
   + r a        \p a           + q + r a       //
expand((2*k*k)*w*beta*d[2]-(2*alpha*k*k)*d[1]-2*w*u[0]+k*u[0]*u[0]);
          2                         Phi(xi)
-2 alpha k  C[1] p + 2 k C[0] C[1] a       

                             2                      3     
                   / Phi(xi)\             / Phi(xi)\      
   + 2 k C[0] C[2] \a       /  + 2 k C[1] \a       /  C[2]

                      2             Phi(xi)
   - 2 w C[0] + k C[0]  - 2 w C[1] a       

                        2                     2
              / Phi(xi)\          2 / Phi(xi)\ 
   - 2 w C[2] \a       /  + k C[1]  \a       / 

                       4                                
           2 / Phi(xi)\       2              Phi(xi)    
   + k C[2]  \a       /  + 4 k  w beta C[1] a        p r

                                2    
        2             / Phi(xi)\     
   + 6 k  w beta C[1] \a       /  q r

         2              Phi(xi)    
   + 12 k  w beta C[2] a        p q

                                 2    
         2             / Phi(xi)\     
   + 16 k  w beta C[2] \a       /  p r

                                 3                          
         2             / Phi(xi)\           2              2
   + 20 k  w beta C[2] \a       /  q r + 4 k  w beta C[2] p 

                                                            2  
              2       Phi(xi)              2      / Phi(xi)\   
   - 2 alpha k  C[1] a        q - 2 alpha k  C[1] \a       /  r

                                                            2  
              2       Phi(xi)              2      / Phi(xi)\   
   - 4 alpha k  C[2] a        p - 4 alpha k  C[2] \a       /  q

                               3                         
              2      / Phi(xi)\         2                
   - 4 alpha k  C[2] \a       /  r + 2 k  w beta C[1] p q

        2              Phi(xi)  2
   + 2 k  w beta C[1] a        q 

                                3   
        2             / Phi(xi)\   2
   + 4 k  w beta C[1] \a       /  r 

                                2   
        2             / Phi(xi)\   2
   + 8 k  w beta C[2] \a       /  q 

                                 4   
         2             / Phi(xi)\   2
   + 12 k  w beta C[2] \a       /  r 
value(%);
          2                         Phi(xi)
-2 alpha k  C[1] p + 2 k C[0] C[1] a       

                             2                      3     
                   / Phi(xi)\             / Phi(xi)\      
   + 2 k C[0] C[2] \a       /  + 2 k C[1] \a       /  C[2]

                      2             Phi(xi)
   - 2 w C[0] + k C[0]  - 2 w C[1] a       

                        2                     2
              / Phi(xi)\          2 / Phi(xi)\ 
   - 2 w C[2] \a       /  + k C[1]  \a       / 

                       4                                
           2 / Phi(xi)\       2              Phi(xi)    
   + k C[2]  \a       /  + 4 k  w beta C[1] a        p r

                                2    
        2             / Phi(xi)\     
   + 6 k  w beta C[1] \a       /  q r

         2              Phi(xi)    
   + 12 k  w beta C[2] a        p q

                                 2    
         2             / Phi(xi)\     
   + 16 k  w beta C[2] \a       /  p r

                                 3                          
         2             / Phi(xi)\           2              2
   + 20 k  w beta C[2] \a       /  q r + 4 k  w beta C[2] p 

                                                            2  
              2       Phi(xi)              2      / Phi(xi)\   
   - 2 alpha k  C[1] a        q - 2 alpha k  C[1] \a       /  r

                                                            2  
              2       Phi(xi)              2      / Phi(xi)\   
   - 4 alpha k  C[2] a        p - 4 alpha k  C[2] \a       /  q

                               3                         
              2      / Phi(xi)\         2                
   - 4 alpha k  C[2] \a       /  r + 2 k  w beta C[1] p q

        2              Phi(xi)  2
   + 2 k  w beta C[1] a        q 

                                3   
        2             / Phi(xi)\   2
   + 4 k  w beta C[1] \a       /  r 

                                2   
        2             / Phi(xi)\   2
   + 8 k  w beta C[2] \a       /  q 

                                 4   
         2             / Phi(xi)\   2
   + 12 k  w beta C[2] \a       /  r 
simplify(%);
           2                         Phi(xi)
 -2 alpha k  C[1] p + 2 k C[0] C[1] a       

                     (2 Phi(xi))             (3 Phi(xi))     
    + 2 k C[0] C[2] a            + 2 k C[1] a            C[2]

                (2 Phi(xi))         2  (2 Phi(xi))
    - 2 w C[2] a            + k C[1]  a           

            2  (4 Phi(xi))            2       (2 Phi(xi))  
    + k C[2]  a            - 2 alpha k  C[1] a            r

               2       (2 Phi(xi))  
    - 4 alpha k  C[2] a            q

               2       (3 Phi(xi))                      2
    - 4 alpha k  C[2] a            r - 2 w C[0] + k C[0] 

                Phi(xi)      2              (2 Phi(xi))    
    - 2 w C[1] a        + 6 k  w beta C[1] a            q r

          2              (2 Phi(xi))    
    + 16 k  w beta C[2] a            p r

          2              (3 Phi(xi))    
    + 20 k  w beta C[2] a            q r

         2              Phi(xi)    
    + 4 k  w beta C[1] a        p r

          2              Phi(xi)          2              2
    + 12 k  w beta C[2] a        p q + 4 k  w beta C[2] p 

               2       Phi(xi)              2       Phi(xi)  
    - 2 alpha k  C[1] a        q - 4 alpha k  C[2] a        p

         2              (3 Phi(xi))  2
    + 4 k  w beta C[1] a            r 

         2              (2 Phi(xi))  2
    + 8 k  w beta C[2] a            q 

          2              (4 Phi(xi))  2      2                
    + 12 k  w beta C[2] a            r  + 2 k  w beta C[1] p q

         2              Phi(xi)  2
    + 2 k  w beta C[1] a        q 
collect(%, a^Phi(xi));
Error, (in collect) cannot collect a^Phi(xi)
 

Is it possible to auto close brackets in Maple? Like when I type "sin(pi" it would automatically create a closing bracket and I could just press enter to calculate

I am trying to find Lie subalgebra for finding optimal solutions directly with the help of MAPLE.  Please help me to find it. Share MAPLE code please.

Any good online training for maple soft to purchase 

How to solve this differential equation numerically

Hello everyone, I am very new to Maple so please bear with me. I have created a procuedure that rearranges 

NaturalNumbers:=proc(k)
[$1..2*k-1]
end proc;

Into 

eq_arrangement:=proc(k)  local i,j,a;  for i from 1 to k-1 do 
  a[2*i-1]:=k+i; 
  a[2*i]:=k-i; 
end do:
[k,seq(a[j],j=1..2*(k-1))];end proc; 

My question is how I can repeat this procudure the sufficient number of times until I get back to [$1..2*k-1] in that order. 

Thank you so much!

Hi,

I'm trying to plot the function below. However, I cannot get the plot to exceed 10 on the x-axis. I have tried changing the axis properties but the function is just "cut off". I have had the same problem with similar functions and ended up using other software.

The function should have valid values above 10.

Does anyone know how I can fix this?

h := x -> 1.23 + x*1*0.0001 + 0.12*log(50000*x) + abs((-1)*0.03*log(x/0.001))

Thank you in advance :)