tzeng

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3 years, 152 days

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These are questions asked by tzeng

Dear All,

I am having trouble with doing integration of a complex integrand with Maple 2016. The code is shown below. For simplicity, I have used a real function Psi00, but in general, it should be a complex function. Although I have assumed r to be real, in the final output, there is still an overhead bar on r^1/4. It is not recognized as real and is not multiplied on the r^5/4 factor to give r^3/2. May I ask you for help in solving this problem? Any of your help is highly appreciated!

Best,

Toby

assume(r, real); assume(phi, real);
Psi00 := exp(-(1/2)*r^2)/sqrt(Pi);
                             /  1  2\
                          exp|- - r |
                             \  2   /
                          -----------
                              (1/2)  
                            Pi       

int(int(conjugate(Psi00*r^(1/4))*Psi00*r^(1/4)*r, r = 0 .. infinity), phi = 0 .. 2*Pi);
    /   /             2 ______                          \\   
    |   |/   /  1  2\\   (1/4)  (5/4)                   ||   
    |   ||exp|- - r ||  r      r                        ||   
    |   |\   \  2   //                                  ||   
  2 |int|----------------------------, r = 0 .. infinity|| Pi
    \   \             Pi                                //   

Dear All,

I am trying to calculate a product of a complex function and its complex conjugate, for instance, conjugate(exp(I*phi))*exp(I*phi), and integrate phi from 0 to 2*pi. The product is supposed to be 1 and the integral should be 2*pi. However, with the following code:

phi::real; simplify(conjugate(exp(I*phi))*exp(I*phi))

I obtain the result as shown in the attached figure. It still gives a bar over one phi and does not give 1. Could you please tell me how I can fix this problem? Any of your hellp is appreciated.

 

Best regards,

Toby

 

Dear All. I am a beginner of using Maple. My calculation gives a complex expression as shonw in Line (23) in the attached figure. I used "simplify" to simplify it. However, the result is not the simplest form. The numerator can be divided by the denominator. Could you please tell me what command I can use to further simplify the expression? Any of your help is highly appreciated!

Best regards,

Toby

Dear All,

 

I am a new Maple user and I am still unaware of a lots of fancy features of Maple. I have a problem of simultaneous fitting polynomials. I wish that I could have help from you. Say, we have two polynomials of two variables,

f1(x,y)=a1+a2*x+a3*y+(a4+a5)*x2+(a4-a5)*y2;

f2(x,y)=b1+b2*x+b3*y+(a4-a5)*x2+(a4+a5)*y2.

Note that a4 and a5 are shared by the two polynomials. I would like to fit the two polynomials against their respective data set. Is there anyway I can do it using Maple? Any of your help is highly appreciated!

 

Best regards,

 

Toby

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