I am new to Maple will appreciate any advice.

I am trying to write a procedure to solve a cubic equation using fsolve, print the root at each stage, and store results in a table for later use.  

I have restricted the range of fsolve, but I know from other sources that there is a solution within this range.

The instructions work if entered manually line by line, but not as a procedure.

The code is copied below.  Thanks for any suggestions.

Stephen Martin

Reg_IV := proc (beta, n) local alpha, b, c, d, k, `αL`, 

   `αR`, delta, eqn, x; `αL` := 3+beta-6*beta^(1/2);\

   `αR` := 1-beta; delta := (`αR`-`αL`)/n; 

   print(`β = `, evalf(beta, 5), `n = `, evalf(n, 5)); 

   print(`αL = `, evalf(`αL`, 5), ` αR = `, 

   evalf(`αR`, 5), `δ = `, evalf(delta, 5)); 

   print(``); for k from 0 to n+1 do alpha := `αL`+k*delta\

  ; b := -5+alpha-3*beta; c := 8-4*alpha-6*beta+2*beta^2-2*alpha\

  *beta; d := -(4*beta+4)*(1-alpha-beta); eqn := proc (b, c, d, 

   x) options operator, arrow; {x^3+b*x^2+c*x+d} end proc; x[k] 

   := fsolve(eqn, 0 .. 2); print(evalf(x[k], 5)) end do; 

   print(``); print(evalf(x, 5)) end proc

Reg_IV(0.2, 4);
                    β = , 0.2, n = , 4.

 αL = , 0.51672,  αR = , 0.8, δ = , 0.070820

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

                      fsolve(eqn, 0 .. 2)

   TABLE([0 = fsolve(eqn, 0 .. 2), 1 = fsolve(eqn, 0 .. 2), 

     2 = fsolve(eqn, 0 .. 2), 3 = fsolve(eqn, 0 .. 2), 

     4 = fsolve(eqn, 0 .. 2), 5 = fsolve(eqn, 0 .. 2)])

Verification_24_09_2024.mw

In the attached file, in the subsection named #Transmittance calculation I had an issue with the absolute value calculation. The calculation in the first part for the expression a1 was carried out although with addition of some strange t parameter in the exponent power. The second one just didn`t. I will be more than grateful for some help and advice. In addition, I have been struggling with that for a long time so if you have in mind some book or youtube lesson that clarifies all of that I will be more than happy. Nothing valuable was found on the web so far :(

Hello everyone,

I successfully plotted the intersection point of two linear equations using a matrix-based approach. Still, I’m facing an issue when trying to achieve the same result using the second method — solving the system symbolically and plotting without matrices.

The Matrix-Based Approach (Working): I used the following steps to plot both equations and mark the intersection point (solution). However, when I switch to solving the system symbolically without matrices, I can plot the two lines, but I'm unable to plot the intersection point correctly.

It seems that the symbolic solution isn't being properly converted to a numeric form for pointplot, even though I’m using evalf.

Any help would be greatly appreciated!

Download Linear_System.mw

On my journey of discovery in the Maple world, which is new to me, I have now looked at the linear algebra packages. I am less interested in numerics than in symbolic calculations using matrices. I would like to illustrate this with the following task:

Let A be any regular (n; n) matrix over the real numbers for natural n. The regular (n; n) matrix X that solves the equation

X - A^(-1)*X*A = 0 for each A is to be determined. In this, A^(-1) is the inverse of A. Is there perhaps a symbolic solution for a specifically chosen n?

The solution to this old exercise is known. X is every real multiple of the unit/identity matrix, i.e. the main diagonal is occupied by a constant and all other matrix elements are zero.

Error.mw
As the title, I try to solve an ODE:

y(x) = (x - 1)*(x - 3)*diff(y(x), x) + f((x*y(x)^2 - 4*x*y(x) + 3*x - y(x)^2 + 4*y(x) - 1)/(x - 3))
And it seems that the ODE can be solved using Lie Symmetry method. But as I choose f to be a simple exponential function, dsolve fails to give the solution. I also try the DEtools[symgen] and receive the same result.

Can anyone tell me what's the problem? Is there some internal bug?

I thought I had post with collection showing timelimit still hangs in Maple. But can't find it searching. I wanted to add this to it.

If someone finds such post, please let me know and I will append this to that post and delete this.

I just found another example where int() hangs all of Maple, using timelimit. I put timelimit of 30 seconds. After 2 hrs it is still running.

Maple 2024.1 on windows 10. This shows clearly that timelimit in Maple still does not work when It was supposed to have been fixed in Maple 2021?

For me, if there is anything that will make me stop using Maple for good, it is this timelimit issue.

Because with timelimit not working all the time, my program keeps hanging. It is not possible to do antything then. Having to keep checking if the program is still running or have hanged and restarting it is not a way to develop software.

Software that have been in development for almost 45 years now like Maple, should have figured by now how to implement timelimit that works. 

Note that, with smaller timelimit it is possible it will  not hang, because longer time limit makes it end in the code path which causes the hang. When I tried 5 seconds for example instead of 30 second, it did not hang With 30 it does. so if you try it and it does not hang, please increase the timelimit a little and it will surely hang. Just make sure to do restart each time, since Maple remembers last result.

maple's server.exe was running at full cpu also.

Download int_hangs_with_timelimit.mw

Just one more small geometry task to get to know Maple a little better:
In the 1st quadrant, point A is on the y-axis and points B, D, C are at a positively increasing distance from the origin on the x-axis. Let BD = DC = s/2 and angle ADB = 45°. Point D is therefore the center of BC. The area of ​​triangle ABC is 60, line AD = x and the length of AC = 19. We are looking for the length of line AB = y.

A student wakes up at the end of the lecture and just catches the professor saying:
"... and the roots form an arithmetic sequence."

On the board there is a 5th degree polynomial as homework, but unfortunately the student only manages to write down
x^5 - 5x^4 - 35x^3 +
before the professor wipes the board.

But the student still finds all the roots of the polynomial.

And the roots now have to be calculated.

I have and input parameter to a procedure called shift:=05. It sets the position of test between to points.

this particular procedure has two potential sets of text one in Q and the other in vec.
Can Q and vec have the own individual values for shift?

I have shown the input to the procedure and what it outputs. The procedure itself to too long and akward to the post.

Also given is the input definiton of the procedure and how I could possibly find a shift in a list.

Download 2024-09-18_Select_name_and_Value_from_List.mw

In this post, I would like to share some exercises that I recently taught to an undergraduate student using Maple. These exercises aimed to deepen their understanding of mathematical concepts through computational exploration and visualization. With its powerful symbolic computation capabilities, Maple proved to be an excellent tool for this purpose. Below, I present a few of the exercises and the insights they provided. Interestingly, the student found Maple to be more user-friendly and efficient compared to the software he usually uses for his studies. Below, I present a few of the exercises and the insights they provided.

One of the first topics we tackled was the Fourier series. We used Maple to illustrate how the Fourier series approximates a given function as more terms are added. We explored this through both static plots and interactive animations.

To help the student understand the behavior of different types of functions, we defined piecewise functions using Maple's piecewise command. This allowed us to model functions that behave differently over various intervals, such as the following cubic function exercise

Maple's Explore command was an effective tool for creating an interactive learning environment. We used it to create sliders that allowed the student to vary parameters, such as the number of terms in a Fourier series, and see the immediate impact on the plot.

Download Fourier_Series.mw

The first time they are evaluated, some aborts can occur; the second time they are evaluated, no exception is thrown: 
 

Download run__twice.mw

Why does (the outer) RootOf have to be evaluated twice? 
Note. There are other similar examples, but they are less concise (so they are omitted here).

If you draw a chord in any curve, when the latter becomes infinitely small, the ratio of the surface segment to the triangle formed by the chord and the associated tangents is 2:3.

(Source: Archive of Mathematics and Physics, editor Johann August Grunert, 31st part of 1858, pp. 449-453, "On a remarkable general theorem on curves",
Author: Andreas Völler)

(The curve may be assumed to be sufficiently differentiable.)

I have a quite complex expression (where and are real numbers): 

According to coulditbe, is satisfiable: 

_EnvTry := 'hard':
coulditbe(expr) assuming real;
 = 
                              true

But according to SMTLIB:-Satisfiable, is not satisfiable: 

SMTLIB:-Satisfiable(expr) assuming real;
 = 
                             false

Why are the two results opposite? 

For reference, below is the output from RealDomain:-solve: 

RealDomain:-solve(expr);
 = 
               /           1  2\                 
              { p = p, q = - p  }, {p = p, q = 0}
               \           4   /                 

I also tried using RealDomain:-simplify, yet the output remains almost unchanged (Why?). 

Bernoulli first order ode has form as show in wikipedia  and also on Maple own site as

Notice that it is P(x)*y above and not P(x)* y^(-1) so the y(x) must be linear in that term.   But when I give Maple this ode

ode:=diff(y(x),x) + x*y(x)^(-1)= y(x)^(-1);

Which is clearly not of the form above, it solves it as Bernoulli.  In the above ode, P(x) is x and Q(x) is 1 and n is -1.

The ode advisor correctly said it is separable. But trace shows it used Bernoulli. Also when asking it to solve it as Bernoulli, it does.

What Am I missing here?  Is it not wrong for Maple to use Bernoulli method on this ode which is not Bernoulli?

Worksheet below

Download why_this_ode_bernullli_sept_15_2024.mw

Dear Maple community,

I was going to export my math assignment about vector functions as an PDF, when I noticed that it butchered every column vector printed out in blue in the document as math-output. I only have this issue when exporting my work.

How do I make Maple display both coordinates of vector in the blue output field?

I produced the below image as an illustration of my problem:

Thank you in advance.