As a Maple beginner, I am now interested in symbolic calculations in Maple. As before, I set a problem from a subject area that interests me in order to learn from professional answers.

Determine all regular square (n;n) matrices (determinant not equal to zero) that are commutable with every regular (n;n) matrix with respect to matrix multiplication.

(I know the solution from long ago.)

Example code

printlevel :=1     

for indx1 from 1 by 1 to  3  do  

f[indx1] :=indx1;  

 end do;

This prints
f₁:=1
f₂:=2
f₃:=3

How do I use the "save" command to save exactly the loop's results above to a file so that I can read the file later and execute it in another  maple worksheet.

The maple manual https://www.maplesoft.com/support/help/Maple/view.aspx? 

for "save"   contains no examples, and definately not how to save results of a loop using the save command. e.g. how do you append  with a file using the "save" command ?

Note: I dont need any help with reading the results, from the saved file, my question is only about writing the results with "save" command. The "save" command gives me the best results for reading files back into a speadsheet, and text file save routines just gives me ascii garbage and not the exact results in executable maple format as "save" does, saving exacltly what you see on screen. Therefore text save routines are useless to me.

I have a file TEST.m. How can I make it so that every time I start Maple, all the subprograms in the TEST.m file will run first? Then I just need to type the function with(TEST): sumpro(2,3,4) to get the result 9. I copied the TEST.m file into Maple's lib directory, but it doesn't run after starting Maple.

I just need to type sumvip(2, 3, 4) to get the result, but Maple doesn't understand it.

Please help.

Download TEST.mw

2024-12-20_Q_simplification_Question.mw
Solve the general cubic. Apply values and simplify. 

Could someone show how Maple simplifies to the value of X=3? I tried doing it manually and I could not figure it out. 

Also is there a Help assistant to see the setps?

Download 2024-12-20_Q_simplification_Question.mw

In the decimal system, we are looking for all natural numbers with at most six digits that only swap the order of the digits when multiplied by 2, 3, ..., 6.

In a plane, equilateral triangles D(i) with side lengths a(i)= 2*i−1, i = 1; 2; 3; ... are arranged along a straight line g in such a way that the "right" corner point of triangle D(k) coincides with the "left" corner point of triangle D(k+1) and that the third corner points all lie in the same half-plane generated by g. Determine the curve/function on which the third corner points lie!

Good afternoon.

I have a differential equation of non-integer degree and would like to know if it is possible to express a solution in terms of elementary or special-functions for certain values of the exponent, n>0.

For this equation, Maple provides an analytical solution for the exponent values n=0 and n=1, otherwise, there is no solution returned. I am particularly interested in the cases where n=1/2, 3/2, 2, 5/2, and 3

I am hoping that someone can help me resolve this - if a closed-form solution is not possible, then a numerical solution would also be welcome.

I have provided the details in the attached worksheet.

Thanks for reading!

MaplePrimes_Dec_19.mw

Given the center x1 of a circle in R^2 with radius d12, and a point p2 on the circle, so that d12=||p2-x1||, denote the points on the line segment from x1 to p2 as x1(t) = x1+t*v12, with t=0..d12, and v12 =( p2-x1)/d12.  I want to animate the points x1(t) moving along the line segment from x1 to p2 and the corresponding circles of decreasing radius, with center x(t) and radius d12-t, so that p2 remains on the circle.

I can animate the points along the line segment from x1 to p2 using ‘style=point, symbol=solidcircle’.

I would like to use plottools-circle, to plot the circles. I have also tried the following type commands for the circles of decreasing radius.

Plot([x1(1)+t*v12(1)+(d12-t)*cos(theta)*v12(1)+ (d12-t)*sin(theta)*u12(1), x1(2)+ +t*v12(2)+(d12-t)*d12*cos(theta)*v12(2)+(d12-t)*sin(theta)*u12(2), theta=0..2*PI]

where u12 is a unit vector orthogonal to v12.

I have not been able to combine the two plots into an animation. Thank you

On considère une ellipse x^2/a^2+y^2/b^2-1=0 et 2 sommets de cette ellipse A(a,0) et B(0,b). On imagine une hyperbole équilatère variable passant par les points O, A et B. Cette courbe rencontre l'ellipse en 2 autres points A1 et B1. Montrer que la droite A1B1 passe par un point fixe. Même avec l'intelligence artificielle, je ne parviens pas à résoudre ce problème. Pourriez-vous d'aider. Merci.

Machine translation by moderator:

We consider an ellipse x^2/a^2+y^2/b^2-1=0 and 2 vertices of this ellipse A(a,0) and B(0,b). We imagine a variable equilateral hyperbola passing through the points O, A and B. This curve meets the ellipse at 2 other points A1 and B1. Show that the line A1B1 passes through a fixed point. Even with artificial intelligence, I can't solve this problem. Could you help. Thank you.

I have this system

eq1 := diff(x(t), t)-(1/6)*(6*x(t)^3*y(t)+(2*y(t)^2-2)*x(t)^2+3*y(t)*(z(t)-2)*x(t)-2*y(t)^2+2)*sqrt(3) = 0;
                         
eq2 := diff(y(t), t)-(1/6)*(y(t)-1)*sqrt(3)*(y(t)+1)*(6*x(t)^2+2*y(t)*x(t)+3*z(t)-2) = 0;
                                    
eq3 := diff(z(t), t)-(1/3)*z(t)*sqrt(3)*(6*y(t)*x(t)^2+2*x(t)*y(t)^2+3*z(t)*y(t)-2*x(t)-3*y(t)) = 0;

I solved it numerically using these ics

ics := x(0) = -0.01, y(0) = .99, z(0) = 0.01

sol1 := dsolve({ics, op(syst)}, {x(t), y(t), z(t)}, type = numeric, output = listprocedure)

I need to use the x(t), y(t), z(t) as follows
  X :=  eval(x(t), sol1)
  Y :=  eval(y(t), sol1)

Z :=  eval(z(t), sol1)

to solve the following system for P(t), Q(t), R(t) numerically 
eq4 := diff(R(t), t)-P(t)*Z-(-2*(-Y^2+2)*X/sqrt(3)+sqrt(3)*(-2*X^2+Z+4/3)*Y)*R(t) = 0;
eq5 := diff(Q(t), t)-(2/3)*R(t)+2*((1/3)*Y+X)*P(t)/sqrt(3)-(-2*(-Y^2+2)*X/sqrt(3)+2*sqrt(3)*(X^2-(1/2)*Z-2/3)*X)*Q(t) = 0;
eq6 := diff(P(t), t)+(1/2)*R(t)+2*sqrt(3)*X*Q(t)+(2*(-Y^2+2)*X/sqrt(3)+sqrt(3)*(-2*X^2+Z+1)*Y)*P(t) = 0;

Any help please? 

Hey Guys, 

I have to solve multiple system of equations under some restrictions given as inequalities. Sometimes solve is not able to find the result in houres so I tryd to break the problem in half. So in the first step I just want to solve my 8 polynomial equations with 8 variables and in a second step I want so take the solutions, bring them together with the set of inequalities and solve it again. Since also some sets of equations are to hard for the simple solve command I got the advice from people of this plattform to try PolynomialSystem with the diffrent engines. However I have the feeling they make misstakes and now Im not sure If I can trust my results. 

Attached you can find a file with an example. In the beginning I solve equations and restrictions together and there is a solutions. Then I tryd to solve only the equations with PolynomialSystem and the the four known engines and the eniges traditional and backsolve dont find the solution which as we saw before exist. When a soultions holds under restrictions it should always appear if I omit the restirctions. When I use the enige triade and groebner then the right solution is there. 
However in some other cases it feels the other way round.
So to me it looks like no matter which engine I take, I can never 100% trust my results. Did I something wrong? Whats the reason for those mistakes? Furthermore backsolve gives me 7 solutions, but solutions 2 and 7 are the same. I also recognized, that there is a diffrence between putting in the variable vars as a list or a set. What happens, if I dont specify which engine should be used?

I am happy about any advice. Thank you in advance.

Regards

Felix

Can_I_trust_the_diffrent_eniges_of_Polynomial_Systems.mw

I have a simple question, but don't find a neat solution for it. I have 4 3d Vectors that result in the resulting Vector V5. I now want the unit vector of V5. How do I do it the most efficient way? 

My attempt is in the file attached. I get the error message: "Error, (in rtable/Power) exponentiation operation not defined for Vectors"

Thanks a lot for your help.3d_vector.mw

Assuming I have a sumpro function written in Maple 2016. How can I implement it in C# and what is the process?

Please help me.

sumpro := proc (i) local a, b;

        a := (rand(1 .. 10))(); b := (rand(1 .. 10))();

        print("Sum of ", a, " and ", b, " is ", a+b)

end proc;

save sumpro, "D://Sumpro.m"

Download mapleprime_sumpro_to_c.mw

This text is typed directly into the browser. I can now change the font size to something bigger. I can also change the font from Default to something else.

This text in Calibri 11 was pasted from Word. What do I have to do to change it to MaplePrimes default font (which I have used above)? Selecting default from 

does not work because default is already selected when I put the cursor into the pasted text.

What is the default font type by the way? Can I change it permanetly?

All on Windows 10 and with Firefox.