Trajectories.mw

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

I have numpy matrix say A

I want to print the matrix into a

A.txt.   file  phyton coding

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

Use Maple to find all quintic polynomials f(x) such that f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 6, f(5) = 10. Is there a cubic polynomial satisfying the conditions? If so, give this polynomial.

Use the bisection method in a while loop to estimate the root of f = (x − 1/9)(x − 2)(x − 3) which lies between 0 and 1 to an accuracy of 10^−4 .  

with(plots);
a := -Pi;
b := Pi;
implicitplot3d(1/2*(sin(2*x)*cos(y)*sin(z) + sin(2*y)*cos(z)*sin(x) + sin(2*z)*cos(x)*sin(y)) - 1/2*(cos(2*x)*cos(2*y) + cos(2*y)*cos(2*z) + cos(2*z)*cos(2*x)) + 0.15 = 0, x = a .. b, y = a .. b, z = 1/2*a .. 3/2*b, grid = [70, 70, 70], style = patchnogrid, shading = xy, lightmodel = light2);
 

Hi! Is it possible to get more clear mesh plot when the grid is such large? 

to make this image I have just defined

f := (x, y) -> piecewise(y <> 0, 2*arctan((sqrt(y^2 + x^2) - x)/y), 0 < x and y = 0, 0, x < 0 and y = 0, Pi, x = 0 and y = 0, undefinied)

contourplot(f(x, y), x = -1 .. 1, y = -Pi .. Pi, color = black, numpoints = 10000);

ofc I could define z:=x+I*y and take

contourplot(argument(z), x = -1 .. 1, y = -Pi .. Pi, color = black, numpoints = 10000);

but I don't know how to delete this "tail" , I want to show only the ray (I thought that definition of argument in MAPLE is problematic so I redefined it but it doesn't matter)

I need this to create phase portrait and make better visualisation for complex function in MAPLE, so I would like to make and argument of function as two variable function which is modified such that this "tail" disappeared, thanks in advance

Hi.

I experience "broken links" in Maple. That is when I've used the the search field Alt+S or visited the help pages, very often thereafter I have to restart Maple in order to use e.g. the Help again, a task or whatever is essentially a link. Is this a known problem in Maple and if what do I do remedy it.
Thanks in advance.

Instead of the nice output from the help, I get the following message:

I asked before how to determine whether a graph is  outerplanar graph.  vv  and  Carl Love  provided very good guidance. 

https://www.mapleprimes.com/questions/229128--How-To-Determine-If-A-Graph-Is-Outerplanar

 Today I tried to use the previous code to further determine whether a plane graph is maximal outerplanar graph.

A maximal outerplanar graph is an outerplanar graph that cannot have any additional edges added to it while preserving outerplanarity.

I feel that the  above adding edges in programs is a bit inefficient.

So I wonder if there is a better way.  Then I want to start from property of this graph class.

Some Properties:

1. Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges.
2. A graph on  n (>=3) vertices  is  maximal outerplanar graph  if and if  every bounded face of a maximal outerplanar graph is a triangle and boundary of  unbounded face  is  Hamiltonian cycle. 

I noticed the second one. I don’t know if it can be achieved through programming. 

I want to get some information about the degree sequence of the face with the help of the dual graph . But I know  dual graph not unique   since  there are different plane embeddings  for not 3 connected  planar graphs. 

Or is there a more efficient way？

Is it possible to auto close brackets in Maple? Like when I type "sin(pi" it would automatically create a closing bracket and I could just press enter to calculate

Any good online training for maple soft to purchase 

How to solve this differential equation numerically

Comparing the following 2 outputs, all done using worksheet mode. They are same expression. But one is generated using assignment and one using function definition (with arrow).

restart;
expr:=sinh(Pi)/Pi*(1+  Sum( (-1)^n/(1+n^2)*(cos(n*x)+n*sin(n*x)),n=1..m)):
f1:=expr;
f2:=unapply(expr,x);

Why Maple 2D display shows small dot for multiplication in the second case, but not in the first? Is there a way to remove this dot? I do not like it and find it distracting.  I looked at options->display and see nothing there to affect this.

Maple 2021 on windows 10