I have an equation were build with many unfixed numbers of variables as below:

eq:=f(U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]), i,j=0,1,2,...(changing during the program running)

How do you suggest to calculate the first derivative of such equation with respect to U[i,j],V[i,j],W[i,j],S[i,j],T[i,j]?

Suppose that i,j=22, in this way to calculate the metioned derivative with respect to U[0,0] only, I must write:

diff( eq(U[0,0],U[0,1],U[0,2],...U[22,22], V[0,0],V[0,1],...,T[22,22]), U[0,0])  ( More than 2420 terms)

As you see it needs cumbersome writings if i,j be constants, and because the i and j are changing during the program, I dont know how to cope with this derivatives in Maple??

What is the total number of the characters in "Vanity Fair" by William Thackeray?
How to determine it with Maple, making use of StringTools and EssayTools? I think an electronic version of this novel is free. 
AFAIK, there are about 600 personages in "And Quiet Flows the Don" by Mikhail Sholokhov.

PS. It happened to me to collaborate with Dr. I. Kulchytskyi on text analysis, but the asked problem is new for me.

PPS. Here is a link to the plain text.

Import("http://www.gutenberg.org/cache/epub/599/pg599.txt");

Hellow.
Is Maple understand the symbol f(i,j), f[i,j], f:=-->(i.j) and f_{i,j}  in the same way or in different way.

How to convert a system of differential equations to a matrix?

can infolevel show this matrix during the process?

Using plottools[line], the option for coords does not work.  It remains in cartesian coordinates regardless of the coords specification.

I have a procedure, and I want to use it so many times whthin my equations, because all notation in my equations are in indicial format, it will be so nice if I can call the procedure in indicial form rather than paranthesis form.

Is there anyone knows how is it possible in Maple?

Rr is my procedure that accepts 2 inputs, So there is no problem to call it using Rr(x,y), I am trying to call it with Rr[x,y] (indicial form

)

Is it possible to do so in Maple? It will be so great to do so.

Dear Maple experts,

I am struggling with a difference between the symbolic and numerical solution of an eigendecomposition of a symmetric positive definite matrix. Numerically the solution seems correct, but the symbolic solution puzzles me. In the symbolic solution the reconstructed matrix is different from the original matrix (although the difference between the original and the reconstructed matrix seems to be related to an unknown scalar multiplier.

restart;
with(LinearAlgebra);
Lambda := Matrix(5, 1, symbol = lambda);
Theta := Matrix(5, 5, shape = diagonal, symbol = theta);
#Ω is the matrix that will be diagonalized.
Omega := MatrixPower(Theta, -1/2) . Lambda . Lambda^%T . MatrixPower(Theta, -1/2);
#Ω is symmetric and in practice always positive definite, but I do not know how to specify the assumption of positivess definiteness in Maple
IsMatrixShape(Omega, symmetric);

# the matrix Omega is very simple and Maple finds a symbolic solution
E, V := Eigenvectors(Omega);

# this will not return the original matrix

simplify(V . DiagonalMatrix(E) . V^%T)

# check this numerically with the following values.

lambda[1, 1] := .9;lambda[2, 1] := .8;lambda[3, 1] := .7;lambda[4, 1] := .85;lambda[5, 1] := .7;
theta[1, 1] := .25;theta[2, 2] := .21;theta[3, 3] := .20;theta[4, 4] := .15;theta[5, 5] := .35;

The dotproduct is not always zero, although I thought that the eigenvectors should be orthogonal.

I know eigenvector solutions may be different because of scalar multiples, but here I am not able to understand the differences between the numerical and symbolic solution.

I probably missed something, but I spend the whole saturday trying to solve this problem, but I can not find it.

I attached both files.

Anyone? Thank in advance,

Harry

eigendecomposition_numeric.mw

eigendecomposition_symbolic.mw

Ho, I try series taylor of tanh, but I want that result is in function of tanh(sqrt(q)*z/y) and not exponential e.

f1 := taylor(tanh(sqrt(q)*z/y+x*m/y), m, 2)

f1 := ((exp(sqrt(q)*z/y))^2-1)/((exp(sqrt(q)*z/y))^2+1)+4*(exp(sqrt(q)*z/y))^2*x*m/(((exp(sqrt(q)*z/y))^2+1)^2*y)+O(m^2)

That is, it should look like:

tanh(sqrt(q)*z/y+.....+tanh^2(tanh(sqrt(q)*z/y)m

Regards.

Hello, I'd like to generate some data from an audio file, like get the amplitude and the time, so that I can plot it with x = time and y = amplitude, do you know how to do that ?

restart:
tf:=2:
n:=2:
X[1]:=t->t^2:
A[1]:=diff(X[1](t),t,t):
plot(A[1](t),t=0..tf,labels=["Time t","n times derivative of X[1](t)"]);

I have a code like above. I run it. Then,

in the labels; it was written "n times derivative of X[1](t)"] why not "2 times derivative of X[1](t)"]) ? and why was not the subscript appeared ? I mean that I want to see X₁ instead of  X[1]?

Help me please.

Thank you.

Hi Maple Community,

I just got my Maple licence and currently I'm going thorugh some basic tutorials in which I've encountered a problem I can't seem to fix:

I'm trying to use the 'LinearSolve' solver as it is shown in the examples on the Maplesoft.com support page:

But I can't seem to get Maple to display a result like it is shown in the picture above.

Instead Maple displays this:

I would be very grateful if someone could tell me what I'm doing wrong.

regards, Alex

Hi, I´m try take out common factor with "collect"

collect(-(1/4)*G*r^2/eta-(1/4)*G*(ri^2-ro^2)*ln(r)/(eta*(ln(ri)-ln(ro)))-(1/4)*G*(ln(ri)*ro^2-ri^2*ln(ro))/(eta*(ln(ri)-ln(ro))), -(1/4)*G/eta)

  But this does not work well.

Regards.

I want to use the solutuion of a DE as a function, including the possibility to plot it.

I have found out that the following comands work, but I cannot undesrtand why. Is there a simpler way?

Truly, Roberto R. Baldino

sol := dsolve({eq, icon}, i(t));
i := unapply(eval(i(t), sol), t);
plot(i(t), t = 0 .. 20, view = [-1 .. 20, -3 .. 3], gridlines);

If not define a procedure

just pass day(hello(a,b), c)

as parameter how to get hello , this function name and day this function name

Hello everybody,

i'm searching for a data-structure similar to the C++ std::unordered_map, so that the access time is konstant O(1) and no matter about the order. What access time does a table() in Maple have, it seems to be not O(1).