Maple_lover1

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These are replies submitted by Maple_lover1

Thank you @dharr,

yes the distance between two points z1=x1+I*y1 and z2=x2+I*y2 is abs(z1-z2) = sqrt((x1-x2)^2+(y1-y2)^2).
All right, why do we prefer abs(z1-z2)^2 instead of the distance which is abs(z1-z2) ? Could you explain more?

As I see, in the 3D plots of the complex functions, abs(f(z))^2 is commonly used (instead of abs(f(z))). I think it is also same logic. But I don' t understand the logic behind it.  

 

Thank you @dharr,

 I have some questions:

-Yes, I understand your code but I don't understand what can be the logic behind getting just the numerator of the expression and setting P=1. What do you think?

-Why do you use 

solve(eqns,{mu,a[0],a[2]},explicit); #set 1
solve(eqns,{mu,a[0],a[1]},explicit); #set 2

 

instead of

solve(eqns,{mu,a[0],a[1],a[2]},explicit);  

The results of these codes are different. Why?

 

-And also where is d_1?

Dear @vv,

I am so sorry, there are some typos in the question. I edited it. 

@Carl Love 

I removed the first row which includes some texts, I edited other all cells as "number format" in Excel, but the result is the same.  

Yes, parse is the only option now.

  

Thanks for your interest @Carl Love,

There are still quotes. 

@Kitonum 

Yes, the command parse works in your example. But in my example, I got the following error

Dear @nm, this is amazing. Thank you very much. 

Dear @tomleslie,

thanks for your suggestion. It is very attractive. 

What do you use to convert the table into LATEX? 

 

The code below doesn't convert well.

latex(A)

 

Thanks, dear @nm,

Yes, generating Latex code with Maple is very useful.

But when I run the following code,

	
printf("%s",s)

 I get the following error:

Error, (in fprintf) string expected for string format

I don' t understand the reason of the error.

yes, adding "option remember" may be useful. Thanks again @acer

Have a nice day.

 

Thank you very much dear @acer.

Lastly; 

I want to make some assumptions in the following procedure functionB. (May be my friends use the package. So, I want to be clear.)

  1. epsilon, gamma>-1
  2. k, M ∈ N,
  3. n = 1, 2,...,2^(k-1)
  4. m = 0, 1, 2,..., M-1

Could you help me pls.?

functionB:=proc(k,M,epsilon,gamma) local K,h,n,m,x;
    K:=2^(k-1):
    h:=simplify(2^(epsilon+gamma+1)*GAMMA(epsilon+m+1)
                *GAMMA(gamma+m+1)/((2*m+1+epsilon+gamma)
                                   *m!*GAMMA(epsilon+gamma+1)))
         assuming n::posint, m::posint;
    unapply(piecewise((n-1)/K <= x and x <= n/K,
                      'simplify'(2^(k/2)*h
                                 *JacobiP(m,epsilon,gamma,2^(k)*x-2*n+1)),
                      0),
            [n,m,x]),
    unapply((1-x)^(epsilon)*(1+x)^gamma, [x]);
end proc:

 

Thank you @Carl Love. I got the answers to all my above questions :)

Yes, you are right. We didn't use uppercase M up to now. But I will expand the package, so we will use uppercase M in the next steps.

Lastly; 

I want to make some assumptions in the following procedure functionB. (May be my friends use the package. So, I want to be clear.)

  1. epsilon, gamma>-1
  2. k, M ∈ N,
  3. n = 1, 2,...,2^(k-1)
  4. m = 0, 1, 2,..., M-1

Could you help me pls.?

functionB:=proc(k,M,epsilon,gamma) local K,h,n,m,x;
    K:=2^(k-1):
    h:=simplify(2^(epsilon+gamma+1)*GAMMA(epsilon+m+1)
                *GAMMA(gamma+m+1)/((2*m+1+epsilon+gamma)
                                   *m!*GAMMA(epsilon+gamma+1)))
         assuming n::posint, m::posint;
    unapply(piecewise((n-1)/K <= x and x <= n/K,
                      'simplify'(2^(k/2)*h
                                 *JacobiP(m,epsilon,gamma,2^(k)*x-2*n+1)),
                      0),
            [n,m,x]),
    unapply((1-x)^(epsilon)*(1+x)^gamma, [x]);
end proc:

 

 

 

Thanks @acer.

I have some questions about your answer.

  • Is there any difference between w:=(x)->1; and w:=x->1;
  • What is the difference between
 A:=unapply(piecewise((n-1)/K <= x and x <= n/K,
                      (sqrt((m+1/2)*2^k))*LegendreP(m,2^k*x-2*n+1),
                      0),
            [n,m,x]),

and 

 A:=unapply(piecewise((n-1)/K <= x and x <= n/K,
                      (sqrt((m+1/2)*2^k))*LegendreP(m,2^k*x-2*n+1),
                      0),
            n,m,x),
  •  If I want to use some packages in procedure (or module), what do you suggest me? For example, I want to use Hermite polynomial (function H(n,x)  )  in orthopoly package. I wrote the following code by uses orthopoly in the procedure. But it doesn' t work. 
    FunctionC:=proc(k,M) local K,x,w;
    uses orthopoly: 
        K:=2^(k-1);
    
        unapply(piecewise((n-1)/K <= x and x <= n/K, 2^((k+1)/2)/sqrt(Pi)*H(m,2^(k)*x-2*n+1), 0),
                [n,m,x])
      end proc:
    

Thank you @tomleslie.

Lastly, what do you suggest Contour plot in 3-D space in Maple as follows?

Surface Contour Plot

Thanks @Rouben Rostamian,

I love it :) 

What do you suggest to add colorbar in Maple like Matlab=?

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