Hi,

Here is the code I would like to complete:

with(plots):
theta:= s -> -2*Pi*n*s/ell;
v:=s->piecewise(And(0<=s,s<=ell/2), c*s, ell/2<s, c*(ell-s));
ell:=1;
c:=1;
n:=2;
spacecurve([cos(theta(s)),v(s),sin(theta(s))],s=0..ell,colorscheme = ["valuesplit",???????]);

What to put in place of the question marks so that the color of the curve is, for example, red if s is between 0 and ell/2, and green if s is between ell/2 and ell?

Thanks.

Hi senior, i am trying to customize the range for horizontal axis means in my case y axis but got error, also trying to give different color for outcomes. Please help in this regards.

Axis_Help.mw

I desire to find the summation value of errors from EA1 to EA19. After finding the summation, i want to find the average error. Can any of experts show how the maple should be done?

Download error_pc-bbdf_forward_formula.mw

When I look for petrov type II vacuum solutions in the Metric search, one of the metrics i get is Stephani [33,8,3].

But when I load the metric and calculate the Ricci or the Einstein tensor, they are not identically zero.
Am I using the metric search wrong or is there a glitch in the program?

Download Temp.mw

How can an equation containing a logarithmic function be converted into a polynomial?

Hi,

I have a data structure/plotting question. How do I plot the 3 lambdas (singleaxis) and the 6 betas (dualaxis) for 12 calibrations (1000 runs each)? All the details are in the script 230523_different-calibrations.mw. Thank you!

For the beta plots and subplots, please follow the dualaxis example output format at the bottom of my script for each of the 12 calibrations.

For the lambda plots, I'd like to combine a few of them as follows (each plot with lambda_1 subplot, lambda_2 subplot, and lambda_3 subplot - note that the lambda plot example at the bottom of the script is dualaxis but I just need singleaxis):

PLOT 1 (singleaxis): lambda_1, _2, _3 for ncal2 and ncal3 (superimposed, 2 data series for each subplot)

PLOT 2 (singleaxis):  lambda_1, _2, _3 for ncal7 and ncal8 (superimposed, 2 data series for each subplot)

PLOT 3 (singleaxis):  lambda_1, _2, _3 for ncal4, ncal5, ncal6 (superimposed, 3 data series for each subplot)

PLOT 4 (singleaxis):  lambda_1, _2, _3 for ncal9, ncal10, ncal11 (superimposed, 3 data series for each subplot)

 I run the attached code, but after waiting for a few minutes, there is no response, does anyone know the reason?

 It only shows Evaluating!!!!

 sy01.mw

I know trig functions are hard to simplify in general but was wondering if there was any simplification command that comes in handy for trig functions of the following form.

sin(theta)^(A - 2)*cos(theta)^2 - sin(theta)^(A - 2) + sin(theta)^A

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).

Download Pulsar_temp.mw

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

120523_problem_parallel.mw

Last execution block is not producing any output. Why?

The 3x3 nonlinear system I am trying to solve is already a stylized version of my problem, as I already:

1. Calibrated my equations before attempting to solve for them (search for "Calib_1" in my script)
2. Split the original 6x6 system into two 3x3 sub-systems (since 3 out of 6 variables only appear in 3 out of 6 equations) and solved for one sub-system

What else can you think of? Should I instead use the parallel solver on the whole 6x6 system rather than just the unsolved 3x3 sub-system?

How to find, if exist, singular solutions? That is, some valuation of some parameters that will yield a solution that cannot be obtained by applying the same valuation to a general solution. Carl Love (who I cannot tag) once mentioned: "The parameter valuations that lead to singular solutions can often be guessed by using valuations that would produce zeros in denominators in the general solution. A singular solution can't be expressed as any instantiation of a generic symbolic solution. By instantiation I mean an assigment of numeric values to some parameters. Here's an example:"

#2x2 matrix and 2x1 vector. 5 parameters (a, b, d, x, y). The 2 decision variables are
#unseen and unnamed in this pure matrix-vector form. Their values are the two entries 
#in the solution vectors S0 and S1.

A:= <a, b; 0, d>;  B:= <x, y>;

#Get a generic solution:
S0:= LinearAlgebra:-LinearSolve(A, B);

#Instantiate 3 parameters (a, d, y) to 0 and solve again:
S1:= LinearAlgebra:-LinearSolve(eval([A, B], [a, d, y]=~ 0)[]);

#Note that no possible instantiation of S0 can produce S1.

Thank you!

Hello Everyone;

Hope you are fine. I I have make a code but there is error and dsolve comand is working. I also need to plot. Kindly help me. I am waiting kind response. Code is attached.

Download Question1.mw

Thanks

I think some form of simplify() would do but I am not sure how.

See the following script for more details:

Download rearrangingterms.mw

It must be something similar to this https://www.mapleprimes.com/maplesoftblog/201455-Rearranging-The-expression-Of-Equations, but my case is slighty different.

Dear all:

    I am using maple2022 to learn Fourier Series package - Maple Application Center (maplesoft.com) . the author provide the package here:

cgi.math.muni.cz/kriz/xsrot/fourierseries/  I use the lastest version: Package FourierTrigSeries version 0.41 

there is no .mla so I do not know how to use this package.(the package is a little old). 

please enlight me if you know how to install this old package.

but the author provide the code inside fourierseries-structs.mws 

here is what I do:

1. first delete some lines which is not useful(which I shared in the attachment as FourierTrigSeries.mw)

and remain everything inside module and save as .mw (maybe the orginal .mws is a old version of maple files)

2. export as .FourierTrigSeries.mpl (also attached)

3. use the examples.mws (the code also from author)

I got error as:

the package can be recognized, but the first line wil give some error which is out of my knowledge field.

everything mentioned above is here, including the original author's files.

fouriertrigseries_0_41en_mapleprime.zip

Could you please have a look. your idea is valuable to me.

PS: this package is not available The Fourier Series package for Maple - Maple Application Center (maplesoft.com) whenI try to learn  Teaching Fourier Series with Maple II 

if anyone keep it before, please share it.

thanks for your help.

rockyicer 

restart;
with(plots);
with(plottools);
with(DEtools);
N := S(t) + In(t) + C(t);
                    N := S(t) + In(t) + C(t)

eqn1 := diff*(S(t), t) = lambda - (lambda + sigma)*S(t) - (beta + Zeta)*S(t)*In(t) - beta[1]*S(t)*C(t), S(0) = ic1;
 eqn1 := diff (S(t), t) = lambda - (lambda + sigma) S(t)

    - (beta + Zeta) S(t) In(t) - beta[1] S(t) C(t), S(0) = ic1

eqn2 := diff*(In(t), t) = beta*S(t)*In(t) - (lambda + gamma)*In(t), In(0) = ic2;
 eqn2 := 

   diff (In(t), t) = beta S(t) In(t) - (lambda + gamma) In(t), 

   In(0) = ic2

eqn3 := diff*(C(t), t) = Zeta*In(t) + Zeta*In(t)^2 - (rho + lambda)*C(t) - Zeta*C(t)*In(t), C(0) = ic3;
                                                     2
     eqn3 := diff (C(t), t) = Zeta In(t) + Zeta In(t) 

        - (rho + lambda) C(t) - Zeta C(t) In(t), C(0) = ic3

lambda := 0.117852;
                       lambda := 0.117852

mu := 0.035378;
                         mu := 0.035378

beta := 0.11;
                          beta := 0.11

beta__1 := 0.05;
                        beta__1 := 0.05

g := 1;
rho := 0.1;
                           rho := 0.1

zeta := 0.02;
                          zeta := 0.02

sigma := 0.066;
                         sigma := 0.066

ic1 := 2390000;
ic2 := 753;
ic4 := 358500;
                         ic1 := 2390000

                           ic2 := 753

                         ic4 := 358500

dsol := dsolve([eqn1, eqn2, eqn3], numeric);
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
 

I have this tedious looking function that I want to write in terms of the other expression but the command i usually use does not work here because the expressions are not polynomials. I am wondering if there is an alternative to doing this manually.
Temp.mw