Please download 1.txt.

Integrand := parse(FileTools[Text][ReadFile]("1.txt")):

int(Integrand, [z = -R .. R, y = 0 .. R], numeric);

plots[implicitplot3d](Phi = phi, z = -R .. R, y = 0 .. R, Phi = 0 .. 0.1e-1, color = ColorTools[Gradient]("Red" .. "Blue", best)[4], grid = [50, 50, 20]);

Why the integrand has positive real amounts in the domain [z = -R .. R, y = 0 .. R] for R=0.5, but the integral value is negative?

Hi guys

I've created a joint display which plots a spacecurve and an arrow which represents the tangent to the curve:

I've written this in the animation format so I can move the tangent arrow along the curve, however when I replace

arrow(subs(s=0,p),subs(s=0,ptan),width=0.3,length=4)

with

arrow(subs(s=A,p),subs(s=A,ptan),width=0.3,length=4)

I get the error:

Error, (in Plot:-AnalyzeData:-StandardizeData) points cannot be converted to floating-point values

I have tried animating the arrow alone(see below) and this works fine, so the problem is coming from try to pass the animation parameter A into the display array of multiple plots.

DG.mw

Thanks

Hi

I have trouble with solving this ODE system using dsolve command:

and 

This system have following solutions:

where

and

C's and A are constants of integration.

They're equations from this paper https://arxiv.org/abs/1710.01910 (45 and 47). 
               

However, my solution differs from correct one - in output there are hypergeometric functions everywhere.

Is there any way to fix/convert this solution? Or to get rid of these functions (my f1 solution looks very close to original one but with coupled hypergeometric function). 
 

Download question.mw

When I apply the uses function with the Physics package in a procedure, the commands in this package are not restricted to the inside of the procedure, but are applied globally. See the example below:

gds := proc(LL, qi, t)

 local ta,i;  

uses Physics;

ta := sec(diff(diff(LL, diff(qi[i](t), t)), t), i = 1 .. nops(qi));

RETURN(ta) end:

sxy := diff(x(t), t)^2 + diff(y(t), t)^2:

gds(sxy, [x, y], t);

Error, (in Physics:-diff) name expected for external function
 

On the other hand, when I apply the uses function with the LinearAlgebra package in a procedure, the commands in this package are restricted to the inside of the procedure only.
dst:=proc(MM) 

local DA; 

uses LinearAlgebra;

DA:=Determinant(MM); 

RETURN(DA) end:

dst(<<1 | 2>, <3 | 4>>);

                  -2

Determinant(<<1 | 2>, <3 | 4>>);

                         Determinant(Matrix(2, 2, [[1, 2], [3, 4]]))

This could be a bug in Maple 2019?

Hello, I am wondering if Maple is capable of generating a subgraph for a directed, weighed graph with the GraphTheory package. The online resources I can find only include undirected, unweighed graphs. 

can you please include an example with commands that is able to perform the said task?

hi everyone:

how can I solve this below equation?

w:=(x)->sin(lambda*x)+b*cos(lambda*x)-sinh(lambda*x)-b*cosh(lambda*x);

b := -(sin(lambda*L)+sinh*lambda*L)/(cos(lambda*L)+cosh*lambda*L);

L:=10;

equation:=int(w(x)^2,x=0..L)=1;

lambda=????

tnx..

Hi everybody?

how can I solve this PDE with Runge-Kutta method and 2D plot in terms of w(x,t) , t and 3D plot in terms of t, x, w(x,t)?

code1.mw

how this integral can be calculated in the simplest form ? the second question is what exactly is done when using assuming? for example when using assuming real, all the functions or parameteres are affected? thanks in advanced

 

Download error_function.mw

This post is closely related to the previous one  https://www.mapleprimes.com/posts/210930-Numbrix-Puzzle-By-The-Branch-And-Bound-Method  which presents the procedure  NumbrixPuzzle   that allows you to effectively solve these puzzles (the text of this procedure is also available in the worksheet below).  
This post is about generating these puzzles. To do this, we need the procedure  SerpentinePaths  (see below) , which allows us to generate a large number of serpentine paths in a matrix of a specified size, starting with a specified matrix element. Note that for a square matrix of the order  n , the number of such paths starting from [1,1] - position is the sequence  https://oeis.org/search?q=1%2C2%2C8%2C52%2C824&language=english&go=Search .

The required parameter of  SerpentinePaths procedure is the list  S , which defines the dimensions of the matrix. The optional parameter is the list  P  - this is the position of the number 1 (by default P=[1,1] ).
As an example below, we generate 20 puzzles of size 6 by 6. In exactly the same way, we can generate the desired number of puzzles for matrices of other sizes.

For some reason, these 20 examples and their solutions did not load here.

 Edit. I separately inserted these generated 20 puzzles as a picture:

Download SerpPathsinMatrix.mw

I know you can call python from Maple, I am thinking if there is the other way around. That is use Maple (and its toolbox) as backend engine to do calculations (e.g. Global Optimization), and say manipulate the data in Python as the front-end.

The following differential equation:

sy := (dsolve({T*diff(y(x), x, x) + rho*omega^2*y(x) = 0, y(0) = 0, y(L) = 0}, y(x)) assuming (0 < T, 0 < omega, 0 < rho))

                                                                 sy:=y(x)=0

Maple only returns the trivial solution. Should return other expressions:
Thank you

Hello,

My question is mathematical in nature, so it might be a little out of place but I though I would give it a shot. 

You have a series of chebyshev coefficients in two connecting subdomains lets say S1 = [0,0.5] and S2=[0.5,1]. So far you are still in the spectral space. If you want to compute the solution in real space you can sum the coefficients with the Chebyshev polynomials. 

Now imagine you change the interval to S1 = [0,0.6] and S2 = [0.6,1]. Is there a way to manipulate the Chebyshev coefficients from both initial subdomains to create a new set of Chebyshev coefficients that fit the solution in the new subdomains. 

The brute force method would be to create the real solution of Chebyshev polynomials and then use that to form a new set of Chebyshev coefficients. Or you can use Clenshaw to compute the solution at several points, and then use the points to create new Chebyshev coefficients.

But what if we can stay in spectral space and create the new chebyshev coefficients. Is that possible? If so, how?

step := t −> piecewise(t sum( (−1)∧n * step(t−n) , n=0..50);

Consider the following forced D.E. L d 2x dt2 + R dx dt + 1 C x = 200 ∗ f(t/3)

where R = 20 , C = 0.01 , L = 10 , x(0) = 10 , x 0 (0) = 0.

a. Graph the solution curve in the phase plane on Maple.

b. Graph x(t) over the interval 0 ≤ t ≤ 25 on Maple .

For the DE solution below, Maple returns only one option. I can't get the others. Can anyone help?

wW := unapply(piecewise(0 <= x and x < L/2, 0, L/2 <= x and x <= L, w[0]), x):

eq := k*diff(y(x), x$4) = wW(x):

dsolve({eq, y(0) = 0, y'(0) = 0, y''(L) = 0, y'''(L)=0}, y(x)) assuming 0 < L

          y(x) = -L*w[0]*x^3/(6*k) + L^2*w[0]*x^2/(4*k) + w[0]*x^4/(24*k)

Obrigado.
Oliveira