What is the correct idiom in Maple to check that one number is greater than another or not?

For example if n=sqrt(3) and m=3 ?

Maple does not like to compare sqrt(3) with other number. It says 

   Error, cannot determine if this expression is true or false: 3 <= 3^(1/2)

I am doing this in code, so solution has to be such that it works for all cases of n and m, without the ability to look at screen and decide.

I found that using is works without the need to convert to float.  Should one then use is(n>=m) instead of evalb(n>=m) always?  

I can also always apply evalf() on each side before. But this seems like an overkill to me.

Download checking_one_number_larger_than_another.mw

For reference, another software does compare these two numbers as is without the need to convert them to floating point;

But it looks the design of Maple in this aspect is different. Since the principal root of sqrt(3) is always the positive one, I did not think it will cause a problem.

A task that was famous at the time is worth remembering:

If for whole numbers x and y the number N = (x^2+y^2)/(1+x*y) is a positive whole number, then it is also a square number.

It can be proven that the converse is also true. Therefore, here is the task:

If N is a square number, then the Diophantine equation has solutions. Solutions must be calculated for N = 9, 49 and 729.

I’m currently working on a Maple project involving the symbolic differentiation of a user-defined potential energy function, which I then use in a system of differential equations. To implement this, I've been using placeholders like 'Un' when taking derivatives to substitute later during numerical calculations.

While this approach using placeholders works, I find it cumbersome and would prefer a more straightforward way to handle this symbolic differentiation without having to rely on intermediate placeholders like 'Un'.

Does anyone know if there is a more elegant way in Maple to achieve this functionality?

Specific Requirements:

• I want to symbolically differentiate the user-defined function W directly.
• The goal is to use this derivative in a system of differential equations for numerical solving.

Any suggestions on simplifying this process would be much appreciated!

Thanks in advance.

Download proteins.mw

What on earth am I doing wrong here? I am trying to check if two vectors are equal for parallelism.Yes, thinking about it I could use CrossProduct but that is the same problem because I would be checking if that new vector =<0,0,0>

l1:=<a,b,c>:l2:=<a,b,c>:
if l1 = l2 then 
print("Equal Vectors");
end if;

While cleaning up old documents, I found the following Diophantine equation and its solution. I tried to solve it using Maple´s "isolve" but it didn't work. Please give me some advice.
Equation:
x^2 - 12*x*y + 6*y^2 + 4*x + 12*y - 3=0

Why Maple gives

           improper op or subscript selector

On this ode? I was not expecting to see steps for this, but was just trying to see what it will show.

Download internal_error_ODEsteps_sept_26_2024.mw

I recently encountered an interesting issue when solving for the domain of a function in Maple using two different approaches, and I am curious about the differences in results between the following commands:

1. domain := solve(0 < x and x <> 2, x);
2. domain := solve({0 < x, x <> 2}, x);

I wonder if anyone could explain why Maple might treat these two syntaxes differently.

Download domain.mw

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, `&alpha;L`, 

   `&alpha;R`, delta, eqn, x; `&alpha;L` := 3+beta-6*beta^(1/2);\

   `&alpha;R` := 1-beta; delta := (`&alpha;R`-`&alpha;L`)/n; 

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

   print(`&alpha;L = `, evalf(`&alpha;L`, 5), ` &alpha;R = `, 

   evalf(`&alpha;R`, 5), `&delta; = `, evalf(delta, 5)); 

   print(``); for k from 0 to n+1 do alpha := `&alpha;L`+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);
                    &beta; = , 0.2, n = , 4.

 &alpha;L = , 0.51672,  &alpha;R = , 0.8, &delta; = , 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.

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

Update OCT 10, 2024

This is another example showing hang in Maple 2024.1 using timelimit. So adding it to this collection. I had large collection of such problems but not able to find it now.

I was trying to verify this solution (which could very well be wrong) on ode with IC. timelimit hangs when I added assumptions as shown. Used 10,20,30 seconds, and so on. all hang. Waited and waited. 

Does it hang on other systems? I am using Windows 10 and Maple 2024.1 with 128 GB RAM on fast CPU.

Download time_limit_hang_example_oct_10_2024.mw

I would like to officially offer $1,000 prize for any one who can solve the timelimit hanging problem in Maple. Will send you personal check of this amount if you find why it hangs and provide fix to use that I can verify works.

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