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Hi I was wondering if anyone can help me with the following procedure, i am trying to write a procedure that can encrypt/decrypt messages encrypted using the method of ELGamal my current procedure runs but it takes too long to compute, and it can only decrypt.
 

 


My procedure is as follows:

   


my procedure for part c is as follows it seems to run but it takes a long time to carry out the procedure when i try to decrypt.


               Elgamal := proc (ciphy, hkt, p, a, b)
               local i, icdarray, s, q;
                 icdarray := Array(5 .. 388);
                   for i from 5 to 388 do 
                   s := ciphy[i];
                   q := `mod`(1/hkt^proc3(a, b, p), p);
                   icdarray[i] := s*q;
                   end do;
                   return convert(icdarray, bytes);
                  end proc;

where proc3 is as follows

                      proc3 := proc (alpha, beta, p)
                   local k, R, i, j, N, A, t;
               Description "baby step giant step procedure";
                 N := floor(sqrt(p-1))+1;
                 A := Array(0 .. N);
                 for j from 0 to N do
                 A[j] := `mod`(alpha&^j, p);
                end do;
          for i from 0 to N do
             t := `mod`(beta*alpha&^(-N*i), p);
            for k from 0 to N do
            if t = A[k]
           then return k+N*i;
         end if; 
         end do; 
           end do; 
         end proc;

                      header := 9681348997

ciphertext: 
[12432485341, 2579085006, 13736574369, 4105371047, 9573017222, 

  7824534168, 10017411248, 13292180343, 2356887993, 9573017222, 

  10017411248, 13765667419, 9795214235, 10017411248, 2801282019, 

  608404939, 4105371047, 13765667419, 11572790339, 13765667419, 

  11765894302, 10017411248, 13765667419, 4549765073, 10017411248, 

  13736574369, 2579085006, 4549765073, 10017411248, 4549765073, 

  13765667419, 2801282019, 830601952, 4105371047, 10017411248, 

  7824534168, 13765667419, 13736574369, 2801282019, 7824534168, 

  10017411248, 830601952, 9573017222, 4327568060, 13765667419, 

  6076051114, 8268928194, 13292180343, 10017411248, 7824534168, 

  386207926, 2801282019, 4105371047, 2579085006, 6076051114, 

  608404939, 13765667419, 6076051114, 830601952, 13765667419, 

  4105371047, 11765894302, 10017411248, 13765667419, 13292180343, 

  13736574369, 10017411248, 608404939, 10017411248, 7824534168, 

  2134690980, 13765667419, 4105371047, 11765894302, 2801282019, 

  4105371047, 13765667419, 2579085006, 608404939, 13292180343, 

  11543697289, 2579085006, 7824534168, 10017411248, 4549765073, 

  13765667419, 4994159099, 5853854101, 6076051114, 830601952, 

  4327568060, 6076051114, 5853854101, 10017411248, 7824534168, 

  13765667419, 4105371047, 6076051114, 13765667419, 9573017222, 

  13292180343, 10017411248, 13765667419, 4105371047, 11765894302, 

  10017411248, 13765667419, 5853854101, 6076051114, 7824534168, 

  4549765073, 13765667419, 11572790339, 13765667419, 4105371047, 

  11765894302, 2801282019, 4105371047, 13765667419, 4105371047, 

  11765894302, 10017411248, 13765667419, 4327568060, 2801282019, 

  608404939, 4549765073, 13292180343, 13736574369, 2801282019, 

  11543697289, 10017411248, 13765667419, 5853854101, 2801282019, 

  13292180343, 13765667419, 11765894302, 6076051114, 7824534168, 

  7824534168, 2579085006, 8268928194, 4327568060, 2134690980, 

  13765667419, 11543697289, 7824534168, 10017411248, 13736574369, 

  2579085006, 11543697289, 2579085006, 4105371047, 6076051114, 

  9573017222, 13292180343, 2385981043, 13765667419, 3245676045, 

  9573017222, 2801282019, 2579085006, 608404939, 4105371047, 

  6105144164, 13765667419, 5853854101, 11765894302, 10017411248, 

  608404939, 13765667419, 9573017222, 13292180343, 10017411248, 

  4549765073, 13765667419, 4105371047, 6076051114, 13765667419, 

  4549765073, 10017411248, 13292180343, 13736574369, 7824534168, 

  2579085006, 8268928194, 10017411248, 13765667419, 4105371047, 

  11765894302, 10017411248, 13765667419, 6076051114, 13736574369, 

  13736574369, 2801282019, 13292180343, 2579085006, 6076051114, 

  608404939, 2801282019, 4327568060, 13765667419, 386207926, 

  2579085006, 4327568060, 4327568060, 2801282019, 6298248127, 

  10017411248, 13765667419, 4105371047, 11765894302, 7824534168, 

  6076051114, 9573017222, 6298248127, 11765894302, 13765667419, 

  5853854101, 11765894302, 2579085006, 13736574369, 11765894302, 

  13765667419, 4105371047, 11765894302, 10017411248, 2134690980, 

  13765667419, 11543697289, 2801282019, 13292180343, 13292180343, 

  10017411248, 4549765073, 6105144164, 13765667419, 9795214235, 

  10017411248, 2801282019, 608404939, 4105371047, 13765667419, 

  830601952, 10017411248, 386207926, 10017411248, 7824534168, 

  11572790339, 7824534168, 2579085006, 4549765073, 4549765073, 

  10017411248, 608404939, 13765667419, 2801282019, 608404939, 

  4549765073, 13765667419, 4105371047, 9573017222, 9795214235, 

  8268928194, 4327568060, 10017411248, 4549765073, 6076051114, 

  5853854101, 608404939, 2385981043, 13765667419, 4994159099, 

  5853854101, 6076051114, 830601952, 4327568060, 6076051114, 

  5853854101, 10017411248, 7824534168, 13765667419, 5853854101, 

  2801282019, 13292180343, 13765667419, 2801282019, 13765667419, 

  4105371047, 6076051114, 9573017222, 7824534168, 2579085006, 

  13292180343, 4105371047, 6105144164, 13765667419, 4105371047, 

  11765894302, 10017411248, 13765667419, 830601952, 2579085006, 

  7824534168, 13292180343, 4105371047, 13765667419, 10017411248, 

  386207926, 10017411248, 7824534168, 13765667419, 13292180343, 

  10017411248, 10017411248, 608404939, 13765667419, 6076051114, 

  608404939, 13765667419, 4105371047, 11765894302, 10017411248, 

  13765667419, 5438553125, 2579085006, 13292180343, 13736574369, 

  5853854101, 6076051114, 7824534168, 4327568060, 4549765073, 

  2385981043, 13765667419, 4994159099, 6076051114, 9573017222, 

  7824534168, 2579085006, 13292180343, 4105371047, 6105144164, 

  13765667419, 8713322220, 2579085006, 608404939, 13736574369, 

  10017411248, 5853854101, 2579085006, 608404939, 4549765073, 

  13765667419, 11765894302, 2801282019, 4549765073, 13765667419, 

  4549765073, 10017411248, 13736574369, 2579085006, 4549765073, 

  10017411248, 4549765073, 6105144164, 13765667419, 9795214235, 

  10017411248, 2801282019, 608404939, 4105371047, 13765667419, 

  8075824231, 2579085006, 4549765073, 2579085006, 6076051114, 

  4105371047, 8075824231, 2385981043]


  [1]: https://i.stack.imgur.com/xY3zd.png
  [2]: https://i.stack.imgur.com/0eYFM.png
  [3]: https://i.stack.imgur.com/PMk7s.png

dy/dx=sqrt(1+(a*x)+(2*y))

for the case a=1, y=1 and x=0 construct a program for the runge-kutta method of order 2 with formulae as follows where f(x,y)=dy/dx.

k_1=h*f(x_n,y_n)

k_2=h*f(x_n+h,y_n+k_1)

y_(n+1)=y_n+1/2(k_1+k_2).

 

After creating a program obtain value of y correct to 4 decimal places when x=1 for h=0.1 and h =0.05.

Meanwhile, thank you so much for everything.
I know I'm asking a lot but if you have time, you can help me do this?

Building a system of interactive components that, taken a function, two points 'a' and 'b' values ​​and an integer n, the calculations point between a and b in which the function assumes the minimum value by using the following procedure:

• It divides the values ​​between a and b into n equal parts (these will distance the one with the other (b-n)/2);
• calculates the function in each of these points;
• located between these values,  what is the minimum (in case of a tie, take the one closest to a)

I think i have to create a vector for each  part and  prehaps with a fcycle for, calculate the function, finelly i'll use minimize with all function.
Do you think is the correct procedure? If yes, how can I do it?

How can i answer iv on Maple?

A family of curves has polar equation r=cos^n (theta/n), 0<=theta,n*pi, where n is a positive even integer.

Previously Using t = theta as the parameter and finding  a parametric form of the equation of the family of curves it was shown that 

dy/dx = (sin(t)sin(t/n)-cos(t)cos(t/n)) /( sin(t)cos(t/n)+cos(t)sin(t/n)).

Is it possible to show on Maple with a program that there are n+1 points where the tangent to the curve is paralell to the y axis?

I need help to create a program that will find all the positive integers n, where n < 1000, such that
(n 􏰀-1)!= 􏰁 􏰀-1 (mod n^2 ) . program has to be in full and state the values of n obtained. 

How could i show wilsons theorom on maple?

(p-1)!=-1(modp) if and only if p is prime.

Hi I have the question where i have to create a program in Maple

to find all the solutions to x^2 = -1(mod p) where 0 <= x < p . 

The progam has to be tested with different p values. 

 

So i got this code, im trying to iterate with jacobi and gaussseidel method.

H := HilbertMatrix(n, n, 1); b := Matrix(n, 1, proc (i) options operator, arrow; add(1/(i+j-1), j = 1 .. n) end proc); A := Matrix(n, 1, 1); Multiply(H, A); norm1H := norm(H, 1); norm2H := norm(H, 2); normHinf := norm(H, infinity); norm1b := norm(b, 1); norm2b := norm(b, 2); norminfb := norm(b, infinity); IterativeApproximate(H, initialapprox = Vector(n, 0), tolerance = 10^(-7), maxiterations = 10, method = gaussseidel)

 

But sadly no iteration gave me an answer, anyone knows wheres my mistake? i really help with this! 


thanks in advance

Q1: Pascal’s Matrix of order n is given by:
Sij =(i + j)!/ i!*j!
Use Mable to produce Pascal’s Matrix of order 8.

Q2: Study the Matrix decomposition (i.e. QR, LU, and LLT), then use Maple to produce these decompositions for a random Matrix of order 6.

Q3: Write one paragraph of your own to explain Moore-Penrose Inverse of a Matrix. Use Maple to find Moore-Penrose Inverse for a random Matrix of order 8.

Q4: Use Maple to find Jordan Canonical form for a random Matrix of order 10.

Q5: Use the seq command to generate the triple [i,j,k] for all possible values for 1 ≤ i,j,k ≤ 10, then plot this triple. i.e. Use nested seq .

Q6: Let F[n] be the set:
F[n] = {p / q: 1 ≤ q ≤ n,p ≤ p ≤ q}
Use Maple to find F[6].

here is my homework, i am new to maple and need some help!

Consider the logistic equation:

dP/dt = 3/100 * (P(M - P)),

with seasonally varying population constraint

M(t) = 20 + 1.54sin(pi t / 6)

use maple to plot the solution curve for P(0) = 25

If a particle that moves in only one dimension is subject to a force Fi between the time

steps ti and ti+1, the velocity vi and position xi of the particle is:

 

v[i] := v[i − 1] +(1/m)*F[i]*Δt

x[i] := x[i − 1] + 0.5 (v[i − 1] + v[i])                   

 

Use the mean of v between ti and ti+1 when updating xi, since the value may change

a lot from step to step. In the subsequent, we set the mass m = 1 and the time steps

are Δt = 1, since we could absorb m and Δt in the expression for the force Fi anyway.

 

Write a procedure that computes xi and vi for a particle subject to random forces Fi,

uniformly distributed on the interval [-0.5..0.5].

 

I`ve written a procedure that generates random forces (F[i]) in the given interval. How can I write a for – procedure that computes xi and vi ?

I have to generate a code for carrying out the matrix form of the revised simplex method. I have a code in place but am struggling to convert the constraints into canonical form and introduce the penalty function. If anyone has any ideas I'd be very grateful!

Best Regards

Hello dear Maple,

My name is Bulat, I'm student of Kazan National Research Technical University ( Russia). In our High Program we used your product ( Maple V, Release 4). Now I have two problems and I haven't no idea how I resolve their. I am forced to ask for your help. I upload PrintScreen of my two problems. Please help me to solve them. I' ll be grateful for your help. Sorry for my English :(.

Yours very truly, Bulat

I Could Not Write An If Then Or Ifelse Statement. Please Help Me.

f := unapply(x^2-2, x); a := 1; b := 2; n := 10; Digits := 10;
      2    
x -> x  - 2
                               1
                               2
                               10
                               10
c := evalf(eval((a*f(b)-b*f(a))/(f(b)-f(a))));
                          1.333333333
if  f(c)*f(a)<0 then ;
          "      k:=evalf(eval(|(f(c))/(b-c)|)) and "

                          /(1 + k) a f(b) - b f(a)\
             x[i] := evalf|-----------------------|
                          \  (1 + k) f(b) - f(a)  /
            "     elif f(x[i])*f(a)<0 then b:=x[i]"
                 "     else b:=c and a:=x[i] "
                  "     if f(c)*f(a)>0 then "
                 "      k:=|(f(c))/(b-c)|and "

                          /a f(b) - b f(a) (1 + k)\
             x[i] := evalf|-----------------------|
                          \  f(b) - f(a) (1 + k)  /
            "     elif f(x[i])*f(a)>0 then a:=x[i]"
              "     else a:=c and b:=x[i] end if"

Error, unterminated 'if' statement
     Typesetting:-mambiguous(Typesetting:-mambiguous(

       if fApplyFunction(c)sdotfApplyFunction(a)lt0 then , 

       Typesetting:-merror("unterminated 'if' statement")))

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