Hello everyone!

I want to construct column vector which elements should be square matrices (m x n each one). So, i use cycle "for" to set such construction.

My question is: what is the fastest way to construct matrices if each matrix elements are independent from each other and also they are results of numerical integration, like is shown in attached file?

Acceleration.mw

how I can solve this PDE equation with four boundary conditions mentioned in the attached file?

It seems that this pde needs four boundary conditions. One of them is defined on a curved domain that its function is provided.

Data related to function phi in boundary condition is attached as an excel file.

a similar procedure is provided in this paper

townsend.pdf

Thanks

pde.mw

Book1.xlsx

By considering matrix A and having three conditions mentioned in maple file, Matrix A  has four zero eigenvalues ​​and one non-zero eigenvalue that are reported in maple file by applying three conditions.

The goal is to obtain five Eigenvectors (V__1` ,`V__2` ,`V__3` ,`V__4` ,`V__5`) corresponding to these five eigenvalues ​​such that they have following form.

1-The first Eigenvector should be v1 = [-, -, -, 0,0] that the three dashes can be whatever, but the last two numbers must be 0 and 0.

2- The second Eigenvector should be v2 = [-, -, -, 0,0] where the three dashes can be anything but the last two numbers must be 0 and 0.

3- The third Eigenvector must be v3 = [-, -, -, 1,0], which three dashes are whatever , but the last two numbers must be 1 and 0.

4-The fourth Eigenvector should be v4 = [-, -, -, 0,1] that those three dashes can be whatever, but the last two numbers must be 0 and 1.
 
5-The fifth  Eigenvector should be v5 = [-, -, -, 0,0] that those three dashes can be whatever, but the last two numbers must be 0 and 0.

for more details please see maple file.

How I can find this Eigenvectors by considering mentioned points.

Thanks

EIGENVECTOR.mw

I find by my hand some equations have four integer solutions.

How can I tell Maple to do this? For what the values of integer numbers k, m, n, a, b, c, d so the equation
k/(x^2 + a x  + b) +  m/(x^2 + a x  + c) + n/(x^2 + a x  + d) = 0 have four integer solutions?

Good day.

I am interested in forecasting using the (trend-adjusted) exponential smoothing process and I have found Maple's Time Series Analysis function helpful.

However, can anyone tell me how to extract the values of the smoothing factors, alpha and beta, used in the computations? 

Please see the attached example using 8 data points; the forecast value for the 9th period is computed by Maple.

Thanks for reading!

Time_Series_Trial_Apr_3.mw

I have a long expression stored in a variable. The expression contains different orders of the derivative of a function u(x,y,z). Is it possible to find all the derivatives of u appearing in the expression? For example, if my expression is 3 u_xx - 3 u_xy + 4 x u - 7 x u_z + u u_xx, then I would like to get {u_xx, u_xy} if I specify order 2 and {u_z} if order 1.

Make the below graph more graph more presentable it is planar too

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0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]]"

B := SubstituteAll(A, ". ", ",");

B := SubstituteAll(B, ".]", "]");

B := SubstituteAll(B, "]][[", "],[");

C := Matrix(parse(B));

IsPlanar(Graph(C));

true

DrawGraph(Graph(C), layout = planar);

THis is very very bad presntation of vertices and edges and graph is also planar

kind help in better presentation with some changes good style and program

How to plot u(t)= z'(t) with respect to x, y, z?

  Here,  z(t)=y'(t), y(t)=x'(t).

where, x(t)= z^3(t), y(t)= z^3(t)/2, z(t) = (a- b), a, b are time interval.

Trajectories.mw

How to solve the matrix for u(t) and plot phase trajector?

I want to plot3d this function :
(2*Int(3*piecewise(x < 1, x, 1 < x, 2 - x)*piecewise(y < 3/2, y, 3/2 < y, 3 - y)*sin(Pi*x/2)*sin((2*Pi*y)/3), [y = 0 .. 3, x = 0 .. 2]))/3
 

So, I wrote : 

plot3d((2*Int(3*piecewise(x < 1, x, 1 < x, 2 - x)*piecewise(y < 3/2, y, 3/2 < y, 3 - y)*sin(Pi*x/2)*sin((2*Pi*y)/3), [y = 0 .. 3, x = 0 .. 2]))/3, x = 0 .. 2, y = 0 .. 3)

and I get :

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

I am totally new with integrals and I think there is a pb related to a bad writing of them.
Thank you for your answers.

I have numpy matrix say A

I want to print the matrix into a

A.txt.   file  phyton coding

Hi there.

I noticed some little bug:

example.mw

As you can see the second term in serie C looks like -M/sqrt(-M^2 + E) - k, but not like M*k/sqrt(-M^2 + E).

Hi Users!

Hope everyone is fine here. I want to find the values of M and L for any functions f(x,y) and y(x) such that

abs(diff(f, y))       for all a ≤ x ≤ b, -∞ < y < ∞ and

abs(diff(y, x, x, x))   for all a ≤ x ≤ b, -∞ < y < ∞

For example for

f:=y-x^(2)+1; 0 ≤ x ≤ 2, -∞ < y < ∞ and

y:=(x+1)^2-.5*exp(x); 0 ≤ x ≤ 2, -∞ < y < ∞

the values of L = 1 and M = 0.5exp(2)

I want to use python which has some added installtion inside my system in maplesoft itself as code is it possible

It may use networkx package say.

with(Python)

ImportModule("networkx");
Error, (in Python:-ImportModule) unable to start Python: could not create process, C:\Program Files\Maple 2020\bin.X86_64_WINDOWS\mpython

Python out will be as below it can be any arbitray Matrix of this for 

A:= [[0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 1. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 1. 0. 1. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 1. 1. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 1. 0. 0. 1. 1. 1. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]

we can observe the ". " is their which we need to replace by , and at the end of each ] inside it should need to be ],

If anyone can give a direct code like if i copy paste the above matrix it will output the maple type matrix for my input

Now A becomes

A:=[[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

To remember the progam should work any arbitary such matricies not for this only case.