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Please either refer me to or show me a valid proof.

  *** I have tried to upload my worksheet using the green arrow but the insert link operation of the upload failed ***

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int(int(x^(alpha + 1)*y^(beta + 1)*exp(-(x^2 + y^2)/(4*Pi))/sqrt(x^2 + y^2), x = -R .. R), y = -R..R) assuming x>0, y>0, R>0;

I am trying to evaluate the above symbolic integral but Maple returns the same input in Symbolic form without evaluating it at all. Is there something wrong with my approach?

This is another bizzar behaviour of objects. I created a basic object of type person.  Noticed that after issuing the call copy(object,deep) and not doing anything at all with the result. Just made the call only, then I am not longer able to create new objects of this class. I had to restart the session to be able to create new objects again.

Why?  This seems like something went messy with memory layout. I put a print message in the constructor, and see that this message no longer show up  after the call copy(object,deep) even though this call was not used for any purpose as you see, but to only to see its effect on the session.

Any explanation why one can no longer create new objects after doing this?  Here is the workseet

Download deep_call_problem.mw

I  generated some graphs via maple and would like to put them in my paper. So I am going to convert the following worksheet to pdf.

with(GraphTheory):
Graphs:=[NonIsomorphicGraphs(6,8,output=graphs,outputform = graph)]:
num_g:=nops(Graphs):
num:=ceil((num_g)/5.):
M1:=Matrix (num,5,(i,j)->`if`((i-1)*5+j<=num_g, DrawGraph(Graphs[(i-1)*5+j],size=[250,250] ,overrideoptions ,showlabels=false,style=planar, stylesheet =  [
 vertexcolor     = orange
,vertexfontcolor = black
,vertexborder    = false
,edgethickness   = 0.6
,edgecolor       = MidnightBlue
,vertexshape     =  "circle"
,vertexfont      = [Arial, 4],
vertexthickness=5], caption = cat(H__,5*(i-1)+j),captionfont=["ROMAN",7]),plot(x = 0 .. 1, axes = none))):
DocumentTools:-Tabulate (M1[1..5,.. ],widthmode=percentage ,width=80 , exterior =all) :

But there was a problem with the exported pdf. There was some mosaic stuff at the vertices of all those graphs. It was strange. (I want to reduce the size of vertices of the graphs in order not to look crowded.)

• TST.mw
• TST.pdf

Only when I insert the option vertexpadding and set a large enough size  of vertex (for this example, we set vertexpadding=7),  it won't go wrong. However, in fact, we often need make vertice‘s size smaller , especially when there are more vertices.

Using a pdf viewer, it seems that after exporting, there is a box above each vertex.

As I was trying things with Maple OOP, I noticed strange behavior which I do not understand. I'll explain the problem in words first then given an example.

I have Person class. Then made one instance of it. In this class, there is one method which is defined to take in an object of same type as the class itself.

I found when I pass the object itself to its own method, it gives an error that the method expects a second argument of type person which is missing. But it is not missing.

Then when creating a second object of same type, and passing the second object, it worked! 

Why?  Here is MWE. Attached worksheet.  I would have expected same behavior in both cases. EIther both work, or both do not work. As as long as the object being passed is the correct type (person).

It seems in the first case, Maple noticed the object being passed to the method happened to be same object where this method is, and it did not pass it. Hence the missing second argument.  Is this a documented behaviour somewhere? (I made sure to make all method static though, so same code is used by all instances of the class. This is strange error message).
 

Download why_first_call_fail.mw

Update

Ok, I am all set. I found a good way to do this. i.e. pass the object to one of its method. One has to make a copy of the object first and pass the copy. Can't use the same object. This is how I do it now. 

restart;
person:=module() 
    option object;
    export name::string:="";  

     export ModuleCopy::static:= overload( 
     [ 
         proc(_self,proto, $)option overload;
            print("Enter 2 args constructor of person");  
            #do nothing    
         end proc,

         proc(_self,proto, name::string, $) option overload; 
             print("Enter 3 args constructor of person");      
             _self:-name := name;
        end proc
     ]);

    export process::static:=proc(_self, the_input::person,$)
       print("the_input:-name = ",the_input:-name);
    end proc;
    
end module; 


p:=Object(person,"me");
#p:-process(p);  #instead of this do the following
o:=Object(p);
p:-process(o)

Which works and gives

              "Enter 3 args constructor of person"
                  p := Object<<2370600065568>>
              "Enter 2 args constructor of person"
                  o := Object<<2370600048288>>
                   "the_input:-name = ", "me"

So I am now able to pass the object (or rather copy of it) as explicit argument to other methods and other modules.  I am not sure why it does not work when using the object itself and had to make a copy. 

How to integrate the below function from 0 to eta.

A := P(eta)+S(H-2*`cosθ`(eta+1)*F)+`cosθ`*(2*F(eta)-2*H*F) = S(eta+1)*`sinθ`*F(theta)-`sinθ`(F*H(theta)-H*F(theta)+F(theta, eta))

Thanks in advance

How does one undo an overload?                                                                        

Download DynamicSystem-How_to_ODE.mw

Hi experts, I know built in command to solve definite integral by using simpson and trapezoidal rule but i need to show step which is given in the example to satisfy his students of grade 12. Please help me to solve this example

I have an animation in Maple that only works if I use the option frames=120, or anything >120. Anything less and it gives the error "Error, (in plots/animate) points cannot be converted to floating-point values". I don't understand why this restriction is happening, any advice is appreciated.

transparent_background_in_plots.mw

Is there a better way to impletment a transparent background when genereating plots?

Here I generate a plot with a yellow background.

plot(sin(x), x = 0 .. 4*Pi, background = yellow);


I want the background to be completely transparent instead of yellow.

plot(sin(x), x = 0 .. 4*Pi, background = none);

Error, (in plot) Unable to find image file, none

none is not an accepted color, so an error is returned. Is there such a color as "clear" that is fully transparent? Is there a better way to impletment a transparent background when genereating plots?

As we know, when every G_i is normal in G, then the series is called a normal series:

cs := CompositionSeries(DihedralGroup(8))

We can draw it:

DrawSubgroupLattice(DihedralGroup(8), labels = ids, highlight = cs)

And all G_i is normal in G:

IsNormal~(cs, DihedralGroup(8))

[true, true, true, true, true]

But why type(cs, 'NormalSeries') will get false.. It is a bug or do I have a misunderstanding?

I am still struggling understanding Maple Object  inheritance due to lack of good examples and sparse documenation.

This is what I am trying to do. I have base class Person, and then make Employee class which extends Person class and adds new field.   

The constructor to the Employee class then needs to call the constructor to the Person class (its base class) in order to initialize it. The base class constuctor takes care of initialization the fields in the base class.

I do not know how to do this. Actually it is not clear to me how the proto argument gets into play in all of this. I could not find one example that explains how to use proto with inheritance.

I am trying to implement this python example. I will show the code for the Python, and my Maple translation. The part I do not know how to do, it how to call the constructor for the base class from the sub class.  If I do not do this, then the fields of the base class will remain unitilized.

Python example is from https://www.geeksforgeeks.org/python-access-parent-class-attribute/

# parent class 
class Person( object ):     
    
        # __init__ is known as the constructor          
        def __init__(self, name, idnumber):    
                self.name = name 
                self.idnumber = idnumber 
                  
        def display(self): 
                print(self.name) 
                print(self.idnumber) 
    
# child class 
class Employee( Person ):            
        def __init__(self, name, idnumber, salary): 
                self.salary = salary 
    
                # invoking the constructor of the parent class  
                #----->>>>> HOW TO DO THIS IN MAPLE?
                Person.__init__(self, name, idnumber)  
          
        def show(self):
            print(self.salary)

# creation of an object
# variable or an instance 
a = Employee('Rahul', 886012, 30000000)     
    
# calling a function of the
# class Person using Employee's
# class instance 
a.display()
a.show() 

Here is the Maple code

restart;
person:=module() 
    option object; 
    #I made these exported instead of local for ease of printing from outside while
    #debugging , that is all.. These should otherwise be local

    export idnumber::integer:=0;  
    export name::string:="";  

    export ModuleCopy::static:= proc( _self, proto, name::string, idnumber::integer, $) 
        _self:-idnumber := idnumber;
        _self:-name := name;
    end proc;
 
end module; 
#---- extend the above class 

employee:=module() 
    option object(person); 
    export salary::integer:=0;  

    ModuleCopy::static:= proc( _self, proto, name::string, idnumber::integer, salary::integer , $) 
        _self:-salary := salary;
        # invoking the constructor of the parent class  
        # How to do that in Maple?

        #I could always manually do this. But I do not want to duplicate the code
        #done by the base class constructor.
        #_self:-name := name;
        #_self:-idnumber := idnumber;
        
    end proc;
 
end module; 

How does one do the Python example in Maple?

Someone should write a book on programming using OOP in Maple. I'll buy a copy in advance.

Maple 2022.1

How does one compute the location of the minimum algebraically (rather than numerically) of the following expression:
F:=((z^2+(z^2+2*z+2)^(1/2)*(z^2+1)^(1/2)+z+1)^(1/2)*(-z^2+(z^2-2*z+2)^(1/2)*(z^2+1)^(1/2)+z-1)^(1/2)-(z^2+(z^2-2*z+2)^(1/2)*(z^2+1)^(1/2)-z+1)^(1/2)*(-z^2+(z^2+2*z+2)^(1/2)*(z^2+1)^(1/2)-z-1)^(1/2)+2*z)/(2*z^2+2);

Write a Maple procedures called “biggest4” and “smallest4” to find
a) the biggest
b) the smallest
of the given numbers  a = -1/3, b = 0, c = 7/3, d = -2

i guess i need to use end proc for programing but i dont understand: