Hello,

I'm seeking an efficient solution to a particular problem. To illustrate, I'll provide a simplified example, though in practice, I'm handling lists with millions of elements.

Let's take the list, l: [1, 2, 3, 4, 5, 6, 7, 8]. Each element in this list has a corresponding twin. For instance, 1 has twins [4, 5], and 2 has twins [9, 12] (note that 12 is not in the original list, but that's not problematic). The complete list of twins is represented as t: [[4, 5], [9, 12], [6, 8], [1, 5], [1, 4], [3, 8], [13, 14, 17], [3, 6], [2, 12], [11, 12, 15]], and the twins are made available as they are needed.

The objective is to remove all twins starting from the first element of the list. Once a twin is removed, there's no need to check for twins for that particular element. For example, consider the first element, 1; the twins [4, 5] are removed, and there's no need to find the twins for those elements. The desired outcome would be the list [1, 2, 3, 7,10].

My solution utilizes a combination of a while loop and sets. However, it's painfully slow when dealing with lists larger than a few hundred thousand elements. 

Many thanks.  

Dear Power Users, I am trying to master Maple coming from another software. I encounter a problem in finding a simple way to find the best parameters for a fitting function. Would someone be so kind to help me out? Thank you in advance for your willingness to help.

FindOptimizedParametersFit.mw

Hi,

I am looking to refine my animation. I would like to add a condition on the colors to illustrate the periodicity of the sine function: the first circle in red, and the curve in red from 0 to 2π, then the second circle in blue and the curve in blue from 2π to 4π, etc. Any ideas? Thank you very much in advance.

AnimSinusCouleurs.mw

I am a new Maple user. I have a system of differential equations and I want Maple to solve the system such that if one of the solutions (dependent variable) is larger than a certain value, one of the differential equation will be described in a different way. I will describe it with an example:

restart;
with(plots);
# imagine we have two differential equations:
eqn1 := diff(T(x), x) = x + T(x)/10 + q(x)/2;
eqn2 := diff(q(x), x) = T(x)^2/10 + 3*q(x);
#The solution is given by:
sol := dsolve({eqn1, eqn2, T(0) = 0, q(0) = 0}, {T(x), q(x)}, numeric, method = mebdfi);
odeplot(sol, [x, T(x)], x = 1 .. 3);

#what I want to do is to write a conditional differential equation that depends on the solution T(x) of the system. For exmaple, if the value of T(x) is larger than 4, the solver sould use a different equation to solve the system. Say for example instead of eqn1 it will use something else like: eqn1:=diff(T(x),x)=x+T(x)^2/200+q(x)/300.

#Internally after each iteration, the solver should check the value of the solution T(x), and depending on it it will choose a different differential equation to use in the next step x.

I tried defining the differential equation as piecewise but I was not successful.

Maple gives solutions that do not satisfy the equation. Wondering what do I need to change.  

restart;
n:=3;m:=2;
eqx:=x^(n/m)=a;
maple_sol:=[PDEtools:-Solve(eqx,x)]; #also tried solve()
F:=map(X->eval(eqx,X),maple_sol);
map(X->evalb(X),F);

I always verified in Mathematica

Any thought what is going on and what do I need to change in my Maple code to make it give the solution x=a^(2/3) only?  

It is also possible that Mathematica is the one who is skipping the two complex solutions, but then I need to verify these in Maple, and so far I can't. Only the first solution is verified by Maple.

Even simplification with assuming a>0 do not verify these two extra solution given with complex values. I also tried RealDomain package but this also had no effect. I tired assuming real also and tried simplify with symbolic option.

Anything else I should try?

Maple 2024 on windows 10

update

As I said, I tried RealDomain but with PDEtools:-Solve. With solve it works. Is this a bug? worksheet below

Download real_domain_solve_vs_PDEtools_Solve.mw

I have used "colour" as my spelling on optional inputs to procedures in my package.  How can I also handle the alternative spelling "color"?  
 

Download 2024-03-21_Q_colour_or_color.mw

Details here: non-dimensionalization.mw. Thanks!

In short, I want to plot all the ten roots of a 10th-degree polynomial in _Z with 4 or 5 primitive parameters. To do so, I need to find that combination of parameters that allows me to transform/scale/non-dimensionalize the original polynomial in a polynomial in _Z with just (1) one parameter or at maximum (2) two parameters. In the case of (1), I can plot its roots in a standard 2D plot against the single parameter. In the case of (2), I can plot the roots in a standard 3D plot against the two parameters.

May be someone can come up with a way to simplify this ode solution? I used the option useInt but the solution can be written in much simpler way than Maple gives.  Below is worksheet showing Maple's 2024 solution and my hand solution.

(having trouble uploading worksheet, will try again).

Download simpler_solution.mw

I keep losing the edits I do. I post screen shot. Click submit, then find all my changes are lost. Will try one more time and give up:

This is Maple solution

This is implified version

Both versions are verified correct by odetest. The question is there is a way to obtain the simpler form from Maple.

What is the result of this system command:


This is a bit long. What is the explanation here?

Hi,

I need your insights on two technical questions regarding my BoxPlot:

1) How to adjust the color of the text (Title and caption)

2) How to remove only the y-axis

Thank you

S5StatBoxPlotBtest.mw

I want to export plots as PNG but found in the past that when using commands to automate the process (and explicitly controlling for image quality) some symbolic notation on the axes or in the plots themselves are translated to 1D.

Anyway, regardless of the reason just provided, I have a preference for exporting plots as PNG manually rather than automatically in some of my scripts. How to do this while ensuring the best quality? By default, manual exports into PNG have quite bad quality. 

I was wondering why Maple do not give this simpler solution to this ode. It solves it as exact. But if solved as separable, the solution is much simpler.

I solved this by hand and Maple verifies my solution. You can see the separable solution is much simpler. Any tricks to make Maple gives the simpler solution?

Download why_not_this_simpler_solution.mw

Hand solution

Maple 2024

Hi

A padel group organises doubles tournaments with the following structure: 16 players participate in four rounds, with each round consisting of four doubles matches. Players switch partners after each round.

So what I require is some code to generate the first round matches, the second round, the third, the nth .....

note the worksheet I bastardised from Tom Leslie's work. 

2_man_teams_doubles.mw

it took me hrs to find this as my solution was failing verification and I did not know why.

What logic do you think Maple used to simplify this:

expr:=sqrt(1 + sin(x))/x;
simplify(expr)

To this

How could the above be simpler than

?

Compare to Mathematica

And this is what I expected. I am now scared to use simplify in Maple as I do not know what I will get back.

Is there a way to tell Maple not to do such strange "simplification"? I am doing this in code, and the code does not know what the expression is.

To see an example of the side effect of this, here is one, where if solution to an ode is simplified first, it no longer verifies by odetest without adding extra assumptions:

One does not expect that simplified solution no longer verfiies the ode.

Sure, I can do

          odetest(simplify(sol),ode) assuming real;

and now it gives 0. But the point is that the first one did not need assumptions.

Download simplify_with_odetest.mw

Maple 2024 on windows 10.

I am trying to tidy up cases where a proc returns multiple values. Have being trying Tabulate. I can get it to work when called after the results are returned. I would the procedure to do this but  keep acces to the name(s) assigned to the returned values.

A,B,C:= proc(...)  .....  return a, b, c    end proc. 

So basically display a tabulated of a, b, c.
 

Download 2024-03-18_Q_Format_Returned_Results_into_a_Table..mw