The expression X^n, for an interger power n and any X, can be computed using the following formulae, which represent a negative power in terms of a positive power (-n), and a positive power in terms of a smaller non-negative power (either n/2 or n-1), and use only multiplication and division: 
                                    
                          X^n = 1/X^(-n)                      if n < 0 
                          X ^n = I*d                             if n = 0
                          X ^n  = X^(n/2) * X^(n/2)      if n is even
                          X^n  = X*X^(n-1)                  if n is odd.
These formulae lead to an efficient recursive algorithm for computing integer powers using the minimal number of multiplications. 

(a) Write a procedure MatPow(X,n::integer) to implement this algorithm for computing powers of matrices. Test MatPow(<<1|2>,<3|4>>,12) and MatPow(<<1|2>,<3|4>>,-12).

(b) Write a procedure PolyPow(X,n::integer) to implement this algorithm for computing powers of numbers and polynomials. Your procedure needs to exapnd each product of polynomials in order to be effective. Test PolyPow(123,12), PolyPow(123,-12), PolyPow(x^2+1,12) and PolyPow(x^2+1,-12). 

Write a procedure using the variable args that will take an unspecified finite number of numbers, delete the smallest and the largest, and return the average of the rest as a floating point number. If there are fewer than 3 arguments have an error message say: "There are not enough arguments. There should be at least three." 

You should have no input parameters in the definition of the procedure. You may write it directly or you may use the Maple command sort as a part of your program. Do ?sort to see how sort works. Test your procedure with each of the following argument sequences:  

   50,40,40, 40, 40, 10

   1,2

   seq(100 - i, i = 1..100)

   seq(modp(n,111), n=1..1000).

If n people (numbered 1 to n) stand in a circle and someone starts going around the circle and eliminating every other person till only one person is left, the number J(n) of the person left at the end is given by 

    J(n) = 1                           if n = 1
    J(n) = 2*J(n/2) - 1          if n > 1 and n is even
    J(n) = 2*J((n-1)/2) + 1   if  n > 1 and n is odd

(i) Write a recursive procedure to compute J. [As a check the first 16 values (starting with 1) of J(n) are 1,1,3,1,3,5,7,1,3,5,7,9,11,13,15,1]. 
(ii)Compute the value of J(10000). 
(iii) Can you explain why this is so much faster than our recursive procedure to compute the n-th Fibonacci number?

Has anyone installed and run maple under ubuntu installed the Windows Subsystem for Linux?   We are having trouble doing this: specifically running programs with text input files, etc.

I have a say sum(F(k) ,k=1..n)  It fails unless n is an actual integer.  But sum(F(k), k=1..a) works. Then then eval(%,a=n) completes it. That is probably correct but not necessarily a valid assumption. Details in attached. Also it is hard to understand the error message.
 

Download Summation_problem.mw

Dear Users!

Hope you would be fine. I want to construct system of equations by comparing the likes powers of x^i*y^j*t^k1*exp(k2*eta) for an expression H1 present in attached file. Please see the fix my problem. I shall be very thankful for your kind help. 

Help.mw

From  time to tiime Malel emits a sort of "Boiing" noise when I make a keyboard error. I am not sure exaclty when it does this, but it is loud. Is it possible to turn it off? I have looked quite extensively and cannot find out anything.

In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you

PROBLEM.mw

I have a problem writing a program for the numerical solution of nonlinear volterra integral equation using the method of reproducing kernel space. I have my algorithm as well as the program I tried to write, though they are full of error messages. Please could anyone give me a clue on how to go about my challenges. The algorithm is as follows:

Step 1. Fix 𝑎 ≤ 𝑥 and 𝑡 ≤ 𝑏.
If 𝑡 ≤ 𝑥, set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑡.
Else set 𝑅𝑥(𝑡) = 1 − 𝑎 + 𝑥.
Step 2. For 𝑖 = 1, 2, . . . , 𝑚 set 𝑥_i = (𝑖 − 1)/(𝑚 − 1).

Set 𝜓_i(𝑥) = 𝐿_t𝑅𝑥(𝑡)|𝑡=𝑥_i .
Step 3. Set 𝑢₀(𝑥₁) = 𝑢(𝑥₁).
Step 4. For 𝑖 = 1, 2, . . . , 𝑚 set 𝛾_ij = [𝜓^-1]_ij.
Step 5. 𝑛 = 1.
Step 6. Set S_n = Σ𝑛
𝑘=1 𝛾_nk𝑢_k-1(𝑥_k).
Step 7. Set 𝑢_n(𝑥) = Σ𝑛
𝑖=1 S_i𝜓_i(𝑥).
Step 8. If 𝑛 < 𝑚then set 𝑛 = 𝑛 + 1 and go to step 6.
Else stop.

So I have this system of equations with which I am not sure if the result is the same or not using "series" and "limit" or what is going on here.

I hope it is clear what I mean.

Download Mapleprimes_-_Ionproduct.mw

is there example data that can verify maxwell equations?

How to calculate determinant of a cube matrix ?

is there function to calculate 3x 3x 3 cube determinant?

How to proof classical and quantum both p summation equal to one in maple?

is possible to solve these partial differential equations in maple via pdsolve?

Thanks

In an unrelated thread, I provided the OP with some 1-D code, which contained the Array definition

TC:= Array(0...1001, fill=0)

Note the existence of three '.' characters in the range specification. This was a typo on my part, or my '.' key bounced, or something. The code containing the above definition "worked" with no problem, which, presumably, was why I didn't notice.

The Maple help does state (my emphasis)

Note that more than two dots in succession are also parsed as the range (..) operator.

although I wasn't making use of this fact - I just screwed up when typing the original.

The OP preferred to use 2-D input, and used cut-and-paste to transfer the above code, resulting in 2-D input, which is where the fun started. It seems(?) that when using 2-D input, more than two dots in succession is only interpreted as a straightforward range, if the total number of dots is even.

If the total number of dots is odd, then it appears(?) as if the 'final' dot is associated with the second number in the range as a 'decimal point', (so producing .1001 in the above example). This is then 'coerced/rounded' to an integer - ie it becomes '0', and the above Array definition is interpreted as

TC:= Array(0..0, fill=0)

Consequences in the following code are left to your imagination

Worth an SCR?