MaplePrimes Questions

I am trying to make a very rough animation of a rotating pulsar magnetosphere that would very roughly resemble this gif.
I was able to make a sphere and the dipolar field lines. I was wondering if anyone could provide any possible suggestion regarding.

1. How do i animate the rotation such that the rotation axis is not z but slightly misaligned to z.

2. Is there a better way to make the field likes from the poles (jets).

restart

[1.1, cos(theta), theta]

[1.1, cos(theta), theta]

(1)

sph := [.5, theta, phi]; c1 := [A*sin(phi)^2, 0, phi]; c2 := [A*sin(phi)^2, (1/6)*Pi, phi]; c3 := [A*sin(phi)^2, (1/3)*Pi, phi]; c4 := [A*sin(phi)^2, (1/2)*Pi, phi]; c5 := [A*sin(phi)^2, 2*Pi*(1/3), phi]; c6 := [A*sin(phi)^2, 5*Pi*(1/6), phi]

[A*sin(phi)^2, (5/6)*Pi, phi]

(2)

NULL

NULL

NULL

A := 2; plot3d([c1, c2, c3, c4, c5, c6, sph], phi = 0 .. 2*Pi, theta = 0 .. 2*Pi, coords = spherical, plotlist = true, scaling = constrained)

2

 

 

NULL

s1 := [sqrt(theta), 1, 1/10]; s2 := [sqrt(theta), 3, -1/10]; s3 := [sqrt(theta), 2, 1/10]; s4 := [sqrt(theta), 1.7, 1/7]

p := plot3d([sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], phi = 0 .. 2*Pi, theta = 0 .. Pi, coords = spherical, orientation = [-75, 58, 10], scaling = constrained, color = ["SkyBlue", "yellow", "yellow", "yellow", "yellow", "yellow", "yellow", "red", "red", "red", "red", "red", "red"])

``

NULL

NULL

plots[animate](plot3d, [[sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], theta = 0 .. Pi, phi = 0 .. 2*Pi, orientation = [B, 45, 52], coords = spherical], B = -180 .. 180)

NULL

 

Download Pulsar_temp.mw

3. Any other suggestions that could help with the aesthetics.

Maple 2023 still can't verify its own series solution. This happens with Frobenius method when the indicial root are repated. I think I mentioned or reported this long time ago but unable to find a link now.

My question is: Since this looks like it will not be fixed by Maplesoft anytime soon, any one could suggest an alternative method to verify this solution?

restart;

ode:=2*x^2*diff(y(x), x, x) + 2*x*diff(y(x), x) - x*y(x) =0;
sol:=dsolve(ode,y(x),'series');
odetest(sol,ode,'series')

Maple's solution is correct, I solved it by hand and get same solution.

Maple 2023 on windows 10.

I could not find a way to check whether or not a given value belongs to an interval expressed as RealRange (or a union of them e.g. RealRange(Open(-10),-5), RealRange(Open(-6),infinity).

Ideally, I would like a Boolean function that takes two arguments (i) a value v and (ii) a (union of) RealRange r, and returns true/false depending on whether or not value v is in/out of the range r.

hallo  every body 
please i have a simple question 
how do i calculate this sum in maple 18 
thank you 

[6600.0*theta(q)-17000.0*theta(q-1)+14400.0*theta(q-2)-4000.0*theta(q-3) = v(q)-.20*theta(q)+.20*theta(q-1)]

[6600.0*theta(q)-17000.0*theta(q-1)+14400.0*theta(q-2)-4000.0*theta(q-3) = v(q)-.20*theta(q)+.20*theta(q-1)]

(1)

isolate([6600.0*theta(q)-17000.0*theta(q-1)+14400.0*theta(q-2)-4000.0*theta(q-3) = v(q)-.20*theta(q)+.20*theta(q-1)], theta(q))

Error, (in isolate) invalid arguments for isolate

 

solve([6600.0*theta(q)-17000.0*theta(q-1)+14400.0*theta(q-2)-4000.0*theta(q-3) = v(q)-.20*theta(q)+.20*theta(q-1)], theta(q))[]

theta(q) = 0.1515105603e-3*v(q)+2.575709827*theta(q-1)-2.181752068*theta(q-2)+.6060422411*theta(q-3)

(2)

It works for h(x)  in help(isolate)


Download no_isolation.mw

I have access to a powerful GPU, a NVIDIA Tesla A100.

How to leverage it to solve my system of 3 nonlinear equations in 3 variables? Script: 160523_stylized_problem_GPU.mw

I don't think that it is just by adding the following two lines right before my solve() block, right?
CUDA:-Enable(true)
CUDA:-IsEnabled()

(https://www.maplesoft.com/products/maple/features/cuda.aspx)

I also read https://mcsr.olemiss.edu/docs/gpus-on-maple/ and https://www.mapleprimes.com/posts/36412-GPU-Programming-CUDA-OpenCL-And-Maple but it's still not clear to me. Thanks!

When trying to load/import/read an MPL file with Maple 2023, I get an error message of "Error, recursive assignment" which only links to a page which states "There is no help page available for this error."

https://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20recursive%20assignment

Presumably there is an error in the Maple syntax that prevents execution, but I cannot find a way to debug.  Maple Code Editor Diagnostics says "No Errors" but Maple Code Editor Console says "Error: recursive assignment."  The MPL file is 485 lines but I am assuming the error could be anywhere in the file.  Is there any way to fix this?

Update: I found the error by copying just a handful of lines at a time into Maple until the error was reproduced.  It was a typo of just one character out of 16,960 characters.  But this is very frustrating.  Why can't Maple 2023 tell me what line the error is on?  Is there a better way to debug MPL files?

How to solve an initial value or boundary value fractional differential equation problem by Maple or, a Maple code is required for solving fractional differential initial value or boundary value problem.

 

Hi, I am creating an activity to illustrate various rotations around different axes. My goal is to enhance the display by showing the axes (one portion as a dashed line and the other as a vector) and to insert the texts (Ox, Oy, Oz) in an optimal manner. Any ideas to optimize the rendering? Thank you.

uestionRevolution.mw

Why is a change in the text area component triggering an action three times in a row?

Download ThePostmanKnocksThreeTimes.mw

When using 

with(physics)

I can enter a metric tensor. If it is the Schwarzschild metric, it is easy enough to do

Geodesics(output=solutions)

to get a general geodesic solution. But is it possible, once I have entered the metric, to numerically integrate a specific geodesic and then plot it?

In this paper (see the footnote on the page), the authors pointed out:

We use -v16 as it is faster than the -v2019 for real root isolation on our benchmarks.

Since I don't have Maple 16 at present, I cannot confirm such an assertion personally. However, I'd like to ascertain if old Maple 16 (released in 2012) is still faster in that specialized realm now (i.e., in 2023). Is there any benchmark test that supports this claim (or tells an opposite story instead?)?

Note. Here I just try to justify the authors' statement (which has caused confusion). Incidentally, will this library be a part of Maple in some future version? (I find that some recent papers provide new "powerful"—in accordance with their "Experiment" sections—Maple packages to tackle difficult problems efficaciously, but such functionalities are not built into the Maple kernel as yet. (In fact, if Maple is a single integrated all-in-one technical platform, then I will no longer need to change tools and formats at each stage. :) ))

Is it even possible to use a replacement list as attempted below to convert a z-transform to a finite difference expression?

z-transformed impulse response (`sampletime = 1/20`)

(10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10)*U(z)/z+(exp(1/10)*(-3+10*exp(1/10)-7*exp(1/5))-(10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10))*U(z)/z^2-(-3+10*exp(1/10)-7*exp(1/5))*exp(1/10)*U(z)/z^3 = 8*Y(z)*exp(1/10)*exp(3/10)*exp(1/5)+(8*((-exp(1/5)-exp(3/10))*exp(1/10)-exp(3/10)*exp(1/5)))*Y(z)/z+(8*(exp(1/10)+exp(1/5)+exp(3/10)))*Y(z)/z^2-8*Y(z)/z^3

(10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10)*U(z)/z+(exp(1/10)*(-3+10*exp(1/10)-7*exp(1/5))-(10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10))*U(z)/z^2-(-3+10*exp(1/10)-7*exp(1/5))*exp(1/10)*U(z)/z^3 = 8*Y(z)*exp(1/10)*exp(3/10)*exp(1/5)+8*((-exp(1/5)-exp(3/10))*exp(1/10)-exp(3/10)*exp(1/5))*Y(z)/z+8*(exp(1/10)+exp(1/5)+exp(3/10))*Y(z)/z^2-8*Y(z)/z^3

(1)

deg_mx := 3

3

(2)

Replacements to get finite difference equation

[seq(U(z)/z^i = U[q+1-i], i = deg_mx .. 0, -1), seq(Y(z)/z^i = Y[q+1-i], i = deg_mx .. 0, -1)]

[U(z)/z^3 = U[q-2], U(z)/z^2 = U[q-1], U(z)/z = U[q], U(z) = U[q+1], Y(z)/z^3 = Y[q-2], Y(z)/z^2 = Y[q-1], Y(z)/z = Y[q], Y(z) = Y[q+1]]

(3)

Attempt to replace

algsubs([U(z)/z^3 = U[q-2], U(z)/z^2 = U[q-1], U(z)/z = U[q], U(z) = U[q+1], Y(z)/z^3 = Y[q-2], Y(z)/z^2 = Y[q-1], Y(z)/z = Y[q], Y(z) = Y[q+1]][1], (10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10)*U(z)/z+(exp(1/10)*(-3+10*exp(1/10)-7*exp(1/5))-(10*exp(3/10)-7*exp(1/5)-3*exp(2/5))*exp(1/10))*U(z)/z^2-(-3+10*exp(1/10)-7*exp(1/5))*exp(1/10)*U(z)/z^3 = 8*Y(z)*exp(1/10)*exp(3/10)*exp(1/5)+8*((-exp(1/5)-exp(3/10))*exp(1/10)-exp(3/10)*exp(1/5))*Y(z)/z+8*(exp(1/10)+exp(1/5)+exp(3/10))*Y(z)/z^2-8*Y(z)/z^3)

Error, (in algsubs) cannot compute degree of pattern in z

 

NULL

Download replace_Y_of_z_by_Y_of_q.mw

Dear all

I have an equation, I would like to introduce a variable R[0], how can I use subs in my equaiton 

subs_equation.mw

Thank you

This code fails in Maple 2023.  It used to work in earlier versions.  Did I miss something in the release notes?

restart;

kernelopts(version);

`Maple 2023.0, X86 64 LINUX, Mar 06 2023, Build ID 1689885`

with(plots):

setoptions3d(font=[Times,roman,12]);

arrow(<1,1,1>);

Error, (in plottools:-rotate) invalid arguments for 3-D transformation

 

First 93 94 95 96 97 98 99 Last Page 95 of 2322