To keep upgrading Maple in our university we need to justify it's usage. We have an unlimited floating license. How can we track the usage of Maple by our students, faculty, etc?

Dear All

I am trying to use differential operator two times in sucession but I am not getting desired differentiation. Please see content below:

Download operator_for_differentiation.mw

G := 6.6743*10^(-8);

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

g(r) = 1-s(r)/0.06123;

j(r) = e^(-(1/2)*w(r))*(1-2*G*v(r)/(r*c^2))^.5

sys := diff(v(r), r) = 4*pi*r^2*eps/c^2, ics=v(0)=0

diff(u(r), r) = -G*(eps+u(r))*(v(r)+4*Pi*r^3*u(r)/c^2)/(c^2*(r^2-2*G*r*v(r)/c^2)),u(0)=1.3668*10^34

diff(w(r), r) = 1.485232054*10^(-28)*(v(r)+4.450600224*10^(-21)*pi*r^3*u(r))/(r^2-2*G*r*v(r)/c^2), conditions: w(0)=0,iterate it to find w(688240)=-2.05684, it solve must satistfy the both conditions.

diff(r^4*j(r)*(diff(g(r), r)), r)+4*r^3*g(r)*(diff(j(r), r)) = 0, conditions dg(r)/dr =0  at r=0, g(688240) =0.87214

diff(J(r), r) = (8*pi*(1/3))*(eps/c^2+u(r)/c^2)*(g(r)*j(r).(r^4))/(1-2*G*v(r)/(r*c^2)) condition J(0)=0.

I am trying to apply window functions from the SignalProcessing package to arrays. However, some window functions (e.g. Hann) appear to operate on a [0..N-1] index basis, others (e.g. Welch) work on [1..N].

I don't know how to make the latter ones work correctly, since after applying the windowing function the first entry in the array is not zero, as it should be.

Best regards

I have made an algorithm for producing random walks (only possible to walk one step to either direction except downwards(EDIT: It is possible to go downwards, but it has to be when making a turn to the right or left). The walks are determined by the rand function:

R3:=rand(1..3): (1: go straight on; 2: turn right; 3: turn left)
M:=15; N:=1500;

Randwalk3:=proc(R3)
  local i,j,r,X,Y,L;
  for j from 1 to M do
    X[0,j]:=0;                                # Initialization
    Y[0,j]:=0;
    X[1,j]:=1;                                # The first step should still be taken to the point (1,0)
    Y[1,j]:=0;
    for i from 2 to N do
      r:=R3();
      if r=1 then X[i,j]:=2*X[i-1,j]-X[i-2,j]; Y[i,j]:=2*Y[i-1,j]-Y[i-2,j];                   # go straight on
      elif r=2 then X[i,j]:=X[i-1,j]+Y[i-1,j]-Y[i-2,j]; Y[i,j]:=Y[i-1,j]-X[i-1,j]+X[i-2,j];    # turn right
      else X[i,j]:=X[i-1,j]-Y[i-1,j]+Y[i-2,j]; Y[i,j]:=Y[i-1,j]+X[i-1,j]-X[i-2,j];             # turn left
      end if;
      if (X[i,j]=X[j,j] and Y[i,j]=Y[j,j]) then L[j]:=i; break; end if; (This is wrong)
    end do;
  end do:
  return [X,Y,L];
end proc:
 

The question from is like this:
Modify the algorithm such that it stops at r[i] if r[i] = r[j] for any 0 <= j <= i-2. r=(xi,yi). M is the number of random walks and N is the number of steps. The length of the paths should be stored in L[m] (m=1..M). How do I implement the if-test correctly?

Dear All

Please see my query below:

Download Summation.mw

Hello,
When I try to put the Gcdex in a procedure and start maplemint, then there occurs an error.

Gcdex(x^2 - 1, x - 2, x ,'s','t') mod 3;

--> works

But:

restart;
a := proc()
    Gcdex(x^2 - 1, x - 2, x ,'s','t') mod 3;
end proc;
maplemint(a);

Then there is an error I don't understand.

Error, (in maplemint/expression) not implemented POLY

By the way I have a fundamental problem to understand, where the values s and t are saved after calling Gcdex (or Quo, Rem, etc.). Till now I thought, that variables s and t are created, but when I declare s, t at the beginning as local variables and start maplemint, then there is something like:

    These parameters have the same name as constants:
      3
    These local variables were used before they were assigned a value:
      r::name, (-x-1)::name, (x-1)::name

So the names of s and t changed, they don't assign a new value? I don't understand that.

Hi everyone,

I need some help with the following error,

How can i solve this problem?

Thanks for your time

Best regards,

Canberk

I having a hard time with defining a vector, in order to store in it some data, then plot it and export it to a file, I copied all what's in the help instructures but it doesn't work everytime, please it's urgent for my PhD thesis !

Maple returns this: and I want to move the exp out of root so it becomes exp(

Ex3 := Pi*sqrt((4/mu+4/r)*exp(-r/mu))

and I want to move the exp out of root so it becomes exp(-r/2*mu), and I want to take the 4s out so it become 2*Pi instead of just Pi.  How do I do it? thank you for all the help

I'm trying to write some simple code to help plot an approximation of a solution to the heat equation. On one set of axes I want to plot the temperature characteristic of a 1-D bar at different temperatures. I am able to do this easily enough, but the code uses a for loop and my core i7 is not being utilized properly. To rectify this I have tried to use threads, but after many hours of playing around I cannot get it to work fully. The first time I run my code I am faced with the error "Error, (in plot) cannot determine if this expression is true or false: not fHwLibraryInitialized".

Then after this I can run my code a few more times and it will produce a graph, but each time the graph will be different, meaning most of them are incorrect. After running my display command several times I am then faced with the error "kernel connection has been lost", and I need to restary. I have never played with threads before and have very little understanding of how it works.

with(Threads);
with(plots);

para := proc (A, B)
return [op(A), op(B)]; 
 end proc;

HeatP := proc (f, g, n, lambda, X, N, M, T)
 local k, u, i, L, a; 
u := proc (x, t) options operator, arrow; sum((int(sin(k*lambda*x)*g, x = 0 .. 1))*exp(-k*lambda*t)*sin(k*lambda*x), k = 1 .. n) end proc;
 L := [];
 if N-X < 3 then for i from X to N do
 L := [op(L), plot(u(x, (i*T-T)/M), x = 0 .. 1)] 
end do; 
return L;
else a := floor((1/2)*(N-X))+X; 
Threads:-Task:-Continue(para, Task = [HeatP, f, g, n, lambda, X, a, M, T], Task = [HeatP, f, g, n, lambda, a+1, N, M, T])
 end if
 end proc;

g := piecewise(x <= 0, 0, 0 < x and x < 1, exp(-2/(1-(x-1/2)^2)), x >= 0, 0);

display(Threads:-Task:-Start(HeatP, 0, g, 5, Pi, 1, 8, 8, 2));

I cannot see where the problem is, but there is obviously at least one. Any help would be appreciated.

Hi, I have a big system with 27 polynomial equations in 16 unknowns: f_1=...=f_27=0.  I can store these equations but I cannot calculate a Grobner basis of the ideal  J generated by my polynomials (allocation problem) - I use the library "with(FGb)"-  What interests me is whether my system is minimal in the following sense.

If, for example,  I remove f_1, is the ideal generated by (f_2,...f_27)  J again ? That is to say, is f_1 in the ideal generated by f_2,...,f_27 ? I would like to get an answer "yes" or "no" for each removed  f_i.

My question: can we solve the problem above  without calculating a Grobner basis of J?

Thanks in advance.

is there a possibility to display the partial derivative of f(x,y) wrt. y as

and second order / cross-partials accordingly?

thx

jo

Hello,

my problem is, that the time or profiling results are not fine enough.

For example time is only measureable in a 16ms step on my system. Is there any way to measure time more fine, perhaps in a 1ms step or nanoseconds?

I consider  100 .100 real matrices A,B=Matrix(100,100,(i,j)->rand()) (with 12 significant digits).  In general, ConditionNumber(A) is <10^5; also I choose Digits:=17.Theoretically, the complexity of the calculations of Determinant(A), CharacteristicPolynomial(A,x), A.B and MatrixInverse(A) are similar (~n^3). Yet, the times of these calculations are respectively: 0"13, 0"67, 0"60 and, what surprises me, 75" (moreover, I don't display any result).

My question: concerning the calculation of the inverse, where does this factor 100 come from ? Would Matlab  be 100 times faster ? I do not see why this would be the case; in particular, the standard methods for the calculation of the inverse are  easily programmable.

Thanks in advance.