This worksheet attempts to implement figures in Section 3 of the book "Indra's pearls" by Mumford, Series and Wright using the  command complexplot.

The worksheet seems to display Figure 3.1 on page 63 accurately but fails to correctly display Figure 3.4 on page 67.

Can complexplot be coded to accurately display this figure?

Indras_pearls_spirals.mw

Initially I have a system of w(x,y,t) and f(x,y,t). I have a set of two partial differential equations with this system. Later on, the system is modified into w(x,y,t,z) andf(x,y,t,z) where x and z are related due to the presence of boundary layers. Because of this, the partial differential expressions with respect to x has to change.

For example, initially: diff(w(x,y,t),x)=diff(w(x,y,t),x)
Later on, when the system gets modified in the presence of boundary layers on application of chain rule: diff(w(x,y,t,z),x)=diff(w(x,y,t,z),x)+diff(w(x,y,t,z),z)*diff(z,x)

This change has to happen for all higher order derivatives of x. In my case, I have upto 4th order derivative in x. How do I achieve these changes in the expressions in Maple in an elegant manner?

I want to create a random polynomial using randpoly() with coefficients in a given list A := [1,1,2,5,6].

For that, I need to create a function that works as rand(1..9) but that when called returns a random element of A instead of a random number between 1 and 9.

What I have tried so far is

r := rand(1..numelems(A))
A[r()]

However, that returns a random element of A, not a function that returns a random element of A.

I've also tried

rand(A(1..numelems(A)))

But that gives an error.

One way of solving this problem would be to find out how to create a `..` type with the desired elements, something that works as 1..9 but with the elements of A. But convert(A,`..`) doesn't work and the rest of the things I tried don't work either.

Hi..

OK, so my real-life example is I have a 3m gap between the house and the garage which I want to hang a sunshade. 
The hanging point on the house is 2.6m high and on the garage 2.1m (above ground). 

I have a choice between 2 sun sails, and I want to know -approximately- what sag I can expect from each.

I realise this is not exactly the same as the hanging wire problem i posted before.. but it my attempt anyway. Can anyone improve?

Sails.mw

there is this ref

https://www.mapleprimes.com/questions/147809-Real-Solution-For-Catenary-Differential-Equation

Hi. following on from

https://www.mapleprimes.com/questions/232817-Solving-Hanging-Cable-#comment281577

Second case: unequal poles.

I tried to work with vv's solution, but I got a problem... the required formula is

y=10.85378553130*cosh(0.0921337534371039*x) - 10.85378553130

Uneven.mw

Hi

I am trying to follow this paper

http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf

Lets start with the easier problem, equal poles. Assume that the length of the cable is 120m and the two poles have equal height of 50m. Our goal is to determine the minimum distance between the two poles that will prevent the cable from touching the ground.

I was trying to get Maple to agree with their derived formula, namely

y(x)= 11*cosh(1/11*x) - 61,

but I think I have not set the IC's correctly. or provided for the length of the cable.

restart:
int(sqrt(1+diff(y(t),t)^2),t=0..x)=120/2

//can't solve the above directly, or maybe someone clever here can

//a is a constant
DIV := diff(y(x), x, x) = a*sqrt(1 + diff(y(x), x)^2);
RV := y(0) = 0, D(y)(0) = -50;
dsolve({DIV});
Opl := dsolve({DIV, RV}, y(x));
allvalues(%)
 

Hi,

I'd like to know, if it is possible to define any sort of range for parameters in NonlinearFit. E. g. I know that one of parameters should be somewhere between 0.2 - 0.4. I know there is a possibility of initalvalues, but using it doesn't lead into this range.

Thanks.

Hi!

I am so pleased to be here to look for help in using Maple.

I am trying to find solutions to a set of nonlinear systems of equations using fsolve.

This code I am tried to solve is shown as follow:

 nonlinearsystemforallsolution.mw

I can get one solution for three variables, however, it's clear there are some solutions missed.

My questions are listed as:

1) How do I get all solutions for a fixed variable of sigma?

2) How do I create a  loop to obtain the solutions for various values of sigma?

3) How to plot solution of each variables versus sigma? 

3) How do I determine the stability of each solution?

Many thanks in advance.

sincerely

Hi Mapleprimes,

I am having difficulties trying to evaluate the following integral

int(-(C__A*K + 1)/(k*C__A), C__A = C__A .. C__A0, numeric = false)

Where the limits are undefined(unknown) symbolic limits, C_A0 is intial concentration, CA is actual concentration. Maple returns the same equation when I try it. I haven't loaded any packages.

I could of course just evaluate the indefinite version and manually substitute but I think that defeats the purpose of using maple.

Any thoughts will be greatly appreciated.

Maple 2020.1

The worksheet below contains an example of the tiling of the hyperbolic plane.

I would like to produce this and other hyperbolic plane tilings from Maple worksheets, but I don't know the math technique for doing so.

Please direct me to a source of the requisite knowledge or an example worksheet which I can study and imitate.

Hyperbolic_Plane_Tiling.mw

I create a table of 3D points in one worksheet and would like to use these values at a later time in a separate worksheet.

What is the simplest way to do this?

Download plotting_elements_of_matrix.mw

I would like to know how to make a graph like the attached. The Figure IV is showing the changes in the evolution of the rate of technological progress (a topic in economics).

I would like to make a graph exactly like the image attached where it clearly shows the name of the x- and y-axis; the name of the functions; the 45-degree line; the transition from "theta_1" to "theta_2" with the arrows, etc. (In fact, I want to have everything the same from the graph). 

I have attached a PDF document with the definition of the functions and the figure itself. I have also attached the image of the figure on this thread. 

IMG_633.pdf

For examples, they are two non-commutative variables x and y, and i use "Setup(noncommutativeprefix={x,y})" to define.
 As the previous results have shown that AntiCommutator(x,x)=0 and AntiCommutator(y,y)=0, so i just define Setup(algebrarules={%AntiCommutator(x,x)=0, %AntiCommutator(y,y)=0}).
When i am calculating AntiCommutator(x,y), the maple automatically simplifies the results and returns AntiCommutator(x,y)=0, as variables x and y are thought to be GrassmannParity =1 variables.

Consider two  3*3 matrix e23 and e32, the AntiCommutator of (e23, e23)=(e32,e32)=0, but the AntiCommutator(e23,e32)= e22+e33.

So how the algebrarules work and why there is the contradiction ?

The file is attached.

Download err.mw

The command 'coeff' doesn't work.