Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

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__A0 .. C__A)

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?


 

restart

with(LinearAlgebra)

InvT := Matrix([[c^2, s^2, -2*s*c], [s^2, c^2, 2*s*c], [s*c, -s*c, c^2-s^2]])

Matrix(%id = 18446746411704779590)

(1)

T := Matrix([[c^2, s^2, 2*s*c], [s^2, c^2, -2*s*c], [-s*c, s*c, c^2-s^2]])

Matrix(%id = 18446746411704773678)

(2)

c := cos(p)

cos(p)

(3)

s = sin(p)

s = sin(p)

(4)

Q := Matrix([[Q11, Q12, 0], [Q12, Q22, 0], [0, 0, Q66]])

Matrix(%id = 18446746411704759470)

(5)

Q11 := E1/(-v12*v21+1); Q12 := E2/(-v12*v21+1); Q66 := G12

E1/(-v12*v21+1)

 

E2/(-v12*v21+1)

 

G12

(6)

E1 := 0.233e12; E2 := 0.231e11; v21 := 0.2e-1; v12 := .2; G12 := 0.717e10

0.233e12

 

0.231e11

 

0.2e-1

 

.2

 

0.717e10

(7)

R := Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 2]])

Matrix(%id = 18446746411704747062)

(8)

Qbar := Matrix([[Qb11, Qb12, Qb16], [Qb12, Qb22, Qb26], [Qb16, Qb26, Qb66]])

Matrix(%id = 18446746411704742726)

(9)

InvR := MatrixInverse(R)

Matrix(%id = 18446746411704745726)

(10)

eq1 := Qbar = InvT.Q.R.T.InvR

Matrix(%id = 18446746411704742726) = Matrix(%id = 18446746411704732718)

(11)

plot(Qb11, p = 0 .. 9)

Warning, expecting only range variable p in expression Qb11 to be plotted but found name Qb11

 

 

NULL


 

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.

Hi,

What am I doing wrong? Seems like some unit compatibility problem when tryaing to solve simple task with momentum conservation rule...

with(Units);
Automatically loading the Units[Simple] subpackage


m__2 := 0.400*Unit('kg');
m__1 := 0.300*Unit('kg');
x__w := 0.700*Unit('m');

v__2p := 0.000;

v__1p := 2*Unit(('m')/('s'));



Download zadanie_z_jednostakim_-_problem.mw

m__1*v__1p + m__2*v__2p = m__1*v__1k + m__2*v__2k;
                                               /s\
             0.6 = (0.3 v__1k + 0.4 v__2k) Unit|-|
                                               \m/


subs(v__2p = 0, 0.600 = (0.300*v__1k + 0.400*v__2k)*Units[Unit](s/m));
                                               /s\
             0.6 = (0.3 v__1k + 0.4 v__2k) Unit|-|
                                               \m/

v__1k := solve(0.600 = (0.300*v__1k + 0.400*v__2k)*Units[Unit](s/m), v__1k);
                                                  /m\
           v__1k := (-1.333333333 v__2k + 2.) Unit|-|
                                                  \s/

 

1/2*m__1*v__1p^2 + 1/2*m__2*v__2p^2 = 1/2*m__1*v__1k^2 + 1/2*m__1*v__2k^2;


Error, (in Units:-Simple:-+) the following expressions imply incompatible dimensions: {.1500000000*(-1.333333333*v__2k+2.)^2*Units:-Unit(J)+.1500000000*Units:-Unit(kg)*v__2k^2}

Sitting and trying find solution in help and on forum but no chance.

I hope if someone copy code into maple it will look lik on my screen. Anyway I have uploaded file and below You have screen picture.

If I remove units from variables on the top all is working like a charm.

Please help me find an error guys.

Reagrds

Marcin

Hello,

 

I have a complex transfer function.  I've defined everyting as "real" via:

assum := Rsrc::real, C1::real, Lp::real, C2::real, f::real, RL::real, 0 < Rsrc, 0 < C1, 0 < Lp, 0 < C2, 0 < RL, 0 < f

I'm expecting simplify to reduce the following transfer function so that the denominator is real, but I can't get it to do it:


I have every variable defined as real, so I am not sure why it won't simplify this expression.

 

Thank you

 

 

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