Let E all triplets as X=(p,q,r) such as p^2+q^2=r^2. We define the application f of E dans C complex as X in E f(X)=(p+Iq)/r=Z. Calculate abs(Z). Show that in E the law noted * defined by
X1*X2=(p1*p2-q1*q2,p2*q1+p1*q2,r1*r2) is an internal law. Calculate f(X1*X2). Then if X0=(3,4,5), find
X0*X0, X0*(X0*X0).Thank you for the help.

help me for solve the error of plot

p1.mw

I'm using Maple to solve academic problems.
At a certain stage, I need a loop to perform numerical calculations, from where I extract a graph. However, each step takes a long time and therefore, I would like to evaluate the performance of the result at each step of time.
To simulate my calculation, I created a test code:

restart:                                                                  # Restart
with(Threads):                                                      # To use Sleep()
a := 2*((ceil(rand()/10^10)-50)*(1/10)):                # Random Value
b := 2*(ceil(rand()/10^10)-50):                             # Random Value
c := 2*ceil(rand()/10^10)-100:                             # Random Value
f := proc (x) options operator, arrow; a*x^2+b*x+c end proc;                  # Generic function that i'm ploting.
np := 10:                                                              # Number of Points i'm ploting
vmax := 10:                                                         # Maximum funcxtion value
VAR1 := Matrix(np+1, 2, proc (m, n) options operator, arrow; if n = 1 then (m-1)*vmax/np else 0 end if end proc):       # Declaring VAR1 as a "null" matrix

for i to np+1 do                                                  # Loop Start
VAR1[i, 2] := f((i-1)*vmax/np):                           # VAR1 value update
print(plot([VAR1], x = 0 .. vmax,  gridlines)):                           # Ploting VAR1
Sleep(.25):                                                         # Simulating longer processing time
od;

However, all graphs are displayed simultaneously after the last step of the for loop.
I would like to print the result (output) after each time step, plotting a new graph for each time an iteration ends.
Would anyone know how to do this?

Thank you for your help.

Can anyone help me to frame the equations in Fractional Reduced Differential Transform Method 

system of nonlinear ordinary differential equations
ds/ dt = b−γ s(t)− (δ s(t)(i(t) + βa(t)) /N − ε s(t) m(t) 
de/ dt = δ (s(t)(i(t) + βa(t))/ N + ε s(t) m(t) − (1−ϑ) θ e(t) − ϑ α e(t) − γ e(t) 
di/ dt = (1−ϑ) θ e(t) − (ρ + γ) i(t)
da/ dt = ϑ α e(t) − (σ + γ) a(t)
dr /dt = ρ i(t) + σ a(t) − γ r(t)
dm /dt = τ i(t) + κ a(t) − ω m(t) 

Good day to all.

I have a function, z(x,y), that I am interested in exploring. The contour plot returns the z-contours on the x-y grid (see attached).

Can anyone suggest a way in which I can now assign z to the vertical axis (instead of y), x to the horizontal axis, and plot the contours for various y-values?

Thanks in advance.

Contour_Plot_MaplePrimes.mw

Dear experts

I am interested to solve the following equation numerically by Maple. I would appreciate it if you let me how I can do and what the boundary conditions and initial values are needed

eq:= diff(2*diff(eta(x,y,t),t)+3*eta(x,y,t)*diff(eta(x,y,t),x)+(1/3-1/epsilon/B)*diff(eta(x,y,t),x,x,x),x)+diff(eta(x,y,t),y,y)-1/sqrt(Pi*R)*int(diff(eta(x+zeta,y,t),x,x)/sqrt(zeta),zeta=0..t/epsilon)=0;
where

1) epsilon, B and r are constant

2) 1/epsilon/B is not equal to 1/3 at all

how to show which region of the plan belongs to the argument points between 0 and Pi/2 and the module points between 0 and 2 ?

Can anyone please help me out with the following integration

                      f(x) = tanh(x)/sqrt(x^2+1)

limits x_initial =1, x_final =100

Thanks

I am trying to work through an example in a textbook, but its a few years old and uses maple 2015. I am currently using the 2018 edition of maple. The code is an example of how to generate the points on an elliptic curve given a specific input. 
Here is the example code from the textbook:

epoints := proc(ec, x, ub, p)
    local ecurve, z, pct, k, i;
    pct := 0;
    for k from 0 to p-1 while pct <= ub do
        z := subs(x=k, ec) mod p;
        if z = 0 then
           pct := pct+1;
           ecurve[pct] := [k,z];
        fi:
        if z &^ ((p-1)/2) mod p = 1 then
           z := z &^ ((p+1)/4) mod p;
           ecurve[pct+1] := [k,z];
           ecurve[pct+2] := [k, -z mod p];
           pct := pct+2;
        fi:
    od:
    if pct > ub then
       pct := ub:
    fi:
    seq(ecurve[i], i=1..pct):
end:

Here is my code, written to work with Maple 2018:

ecpoints := proc (ec, x, ub, p) local ecurve, z, pct, k, i;
      pct := 0; for k from 0 to p-1 while pct <= ub
         do z := `mod`(subs(x = k, ec), p);
         if z = 0 then pct := pct+1;
            ecurve[pct] := [k, z] end if;
         if `mod`(z^((1/2)*p-1/2), p) = 1 then
            z := `mod`(z^((1/4)*p+1/4), p) = 1;
           ecurve[pct+1] := [k, z];
           ecurve[pct+2] := [k, `mod`(-z, p)];
           pct := pct+2 end if
   end do;
   if ub < pct then pct := ub end if;

   seq(ecurve[i], i = 1 .. pct)
end proc

The problem is with the output. The output should be [0, 5], [0, 14], [2, 4], [2, 15], [3, 6], [3, 13], [4, 6], [4, 13], [6, 0], [10, 16], [10, 3], [12, 6], [12, 13], [14, 16], [14, 3], [18, 17], [18, 2].
What I get is [0, 5 = 1], [0, 14 = 18], [2, 4 = 1], [2, 15 = 18], [3, 6 = 1], [3, 13 = 18], [4, 6 = 1], [4, 13 = 18], [6, 0], [10, 16 = 1], [10, 3 = 18], [12, 6 = 1], [12, 13 = 18], [14, 16 = 1], [14, 3 = 18], [18, 17 = 1], [18, 2 = 18]. 
Any hints on what I could be doing wrong here or what is going on?

Dear All, 

I am trying to solve the following differential equation, which is a kind of Spherical Harmonics. Can anyone please help me out how to solve this?

((D@@2)(y))(r)+(D(y))(r)/r-sin(y(r))*cos(y(r))/r^2+sin(y(r))^2/r-sin(y(r))-sin(2*y(r)) = 0

Thanks 

Dear all

I use Maple 2018 and have following problem:

I define following procedure and want to plot it. However Maple displays the coordinate system but does not plot anything nor gives and error message. Hope you can help.

Thanks

Murad

b:=proc(n)
local b,i:
 for i from 0 to n do
  if i=0 then
   b[0]:=0:
  elif i=1 then
   b[1]:=1:
  else
   b[i]:=(b[i-1]+b[i-2])/2:
  end if:
 end do:

return b[n]

end proc:

plot(b,0..10)

Maple 2018  has recently has  become sluggish to start up  -and very slow to respond to input. Can anyone suggest remedies?  I have plenty of space and CPU. Other apps seem to start fine.  Can any suggest a diagnosis and/or solution?

Melvin

Good day.

Reading through the Fuzzy C-Means routine (attached) written by the one-and-only Carl Love, I was wondering if anybody can tell me how to specify which points in the data belong most strongly to the assigned cluster. 

In the attached routine, there are 2 cases considered; two and three clusters. 

It would be interesting to obtain a list of all points that are assigned to each respective cluster.

Thanks for reading!

Fuzzy_clusters.mw

Any integer in [129,129+13^2[ 1s written as the sum of squares of separate integers equal to or less than 12.
examples:: 129=10^2+5^2+2^2, 130=11^2+3^2... 132=9^2+5^2+4^2+3^2+1^2...
179=12^2+5^2+3^2+1^2...297=12^2+10^2+7^2+2^2. Thank you.