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First I know that the Newton-Raphson formula gives N(z)=z-(f(z))/(f'(z)). If f(z)=z^+1, then N(z)=(z^2-1)/2z


Then the Question asks me to first define two important functions which I did:

1)T(z)=z-i/z+i where is i is imaginery number, 2)N(z)=z^2-1/2z. Hence, I wrote the following in maple:



Then I was asked to show that T(N(z))=(T(z))^2, so I wrote the following commands:


>T(N(z))-(T(z))^2 (I got zero for their difference, so they are equal)

next, the question said the same wave verify that T(N^2(z))=(T(z))^4, so i wrote:

>T(N^2(z))-(T(z))^4 (but I got 0.3239121662-1.392199407I which is a complex number, not zero but WHY?)

and the rest of the questions are as follow:

1) What will be the general result? <-I don't what does it mean by general result :S

2) T(N^k(z)) will be what power of T(z)? <-Is it power of 2k?I have no ideas.

3) Try T(N^3(z)).<-which I know that T(N^3(z))=T(N^2(N(z))), so does T(N^2(N(z)))=(T(z))^6 then?


It would be appreciated If anyone could help me with this/clear up my confusion with questions. thanks.




Hi everyone,

I need to write a program to save some files in both Windows or Unix System.

The structure of the path files is different from windows to Unix, so i want to something like this

if (WindowsOS) then

        pathFILE := "\\MyDirectory\\blabla.txt";

elif (UnixOS) then

       pathFILE := "\/MyDirectory\/blabla.txt";

end if;


Thanks for help.

Dear Mapleprimes members,

I am trying to understand some known classical theorems of geometry (thales intersection thm, ceva, menelaus ) from the perspective of affine geometry and projective geometry.(my paper/pencil work is ok.. But I would like to use  Maple to visualize -if possible - geometrically some theorems and properties in a graph)

How could I do it in maple? Where may I get some examples?

thank you,



Hi there,

i want to generate some plots in files in this example:

this code doesn't work. but without restart; it works fine. i passed 2 days to figure out that "restart;" was the problem.

my questions are :

1. why i have to eliminate the first line of restart;

2. how can i save my files in a directory that is in the current directory. For example i have a directory in current directory named "plotFILES".

thanks in advance for your help

Hello all, 

During my last attempt to solve ODE system (autonomous system which includes 3 first order diff. equations) with initial conditions, Maple had performed the solution which includes d_z1 parameter as follows below (I present the solution of one of the equations):

S(t)=S(0)∫(QN_z1+A)d_z1, where integral ∫ is defined integral from 0 to t, S(0) is the initial value of S, Q, N and A are the parameters. I would like to ask, what does it mean _z1 and d_z1? Why if the ODE system is only time dependent, I received the integral with other differential, that is d_z1? Does it mean that the integral can't be evaluated or maybe something else?

Thanks in advance,




Dear Experts,


Analytical integration is not a choice for the integrals listed here. Hence, Maple is not able to find the numerical integration for the following oscillatory functions. However mathematica can. However, before I take the mathematica results, just need to check with you.

Following link shows that for a diverging series, the (Numerical) integral is finite.




eval(int(r^2 BesselJ(1,r)* BesselJ(0,r), r = 0..infinity)) 



NumberForm[ NIntegrate[BesselJ[0, x]*BesselJ[1, x]*x^2, {x, 0, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>



2)  Maple:
       eval(int(r* BesselJ(0,r), r = 10..infinity)) 



NumberForm[ NIntegrate[BesselJ[0, x]*x, {x, 10, Infinity},   AccuracyGoal -> 20], 15]

SequenceLimit::seqlim: The general form of the sequence could not be determined, and the result may be incorrect. >>



Any conclusions on the result.

a) Why maple not able to evaluate the integrals.  b) Are the result of the Mathematica can be considered as appropriate.


Attached is the maple file for your consideration. 


Lookinf forward to your reply.



I've been having trouble plotting in polar coordinates. My code is included below:

The ouput prints the 10 terms of the sum but the plot does not produce anything.

I also would like to know a method that I could use to plot with a going from zero to the size of the radius.

Thank you for any help.


Am trying to convert a vector projection to matrix type output.

Attached is a sample worksheet. 


Dear Maple forum,


given A, B real numbers,

and after defining the recurrent sequence


x(0) = A

x(n) = 0.5* x(n-1)^3 + B


I would like to see a graphic of x(n) on the plane x(n) - n.

how could I implement in maple 16?


thank you for your help.



Dear sirs/madams,

I tried to use my MAPLE in a MacBook with a quiet large screen...however I see the letter sizes of my Maple16 very small (the same wiht the font size on input and ouput sheets..and everywhere)..

Is there some way to "see larger and bigger"?

Thanks for your attention,



I was asked to transform (x+y)^2+(1)/x+y into ((x+y)^3+1)/x+y, I have tried nomer/denom, but i don't how to factorise the nomer bit into (x+y)^3+1 because maple factorise it differently by default. therefore, it would be grateful if anyone can help me with this...please?

How do I define a function from a graph in a plot? 

Or how do I find the intersection between two lines? I have to find the intersection of 2 lines in a graph, while one of these lines consists of 2 different equations dependent from the same variable. 


Thanks in advance. 

I am trying to sort a list of symbolic values:

v := [x, 1/3-(1/3)*x] 

However, Maple can't do it because of the assumptions. Is there a function I can pass to sort() that would sort such a list correctly? I thought that sort(v, (a,b)->is(a>=b)) would work because it takes into consideration values which are equal to each other, but it doesn't - I get [1/3-(1/3)*x~, x~] no matter what ordering function I use.

Thank you.

I have a variable with some assumptions: assume(0<=W<=1).

Now, when I make a list and sort it, everything goes fine:

k := [W, (1/3)*W, (1/3)*W, (1/3)*W]:
sort(k, (a,b)->is(a>b))

I get [(1/3)W, (1/3)W, (1/3)W, W] as expected.

Now I try this:

k:= Vector[column]([W, (1/3)*W, (1/3)*W, (1/3)*W]) 
sort(k, (a,b)->is(a>b))

And Maple gets stuck on this computation. I have tried on both Windows and Linux, on several different computers.

Hello everyone,

I have a system of PDEs






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