Hello to whomever this may concern. I am curently trying to estimate parameters and initial conditions for a system of ODEs. I have taken inspiration from the code given by Robert J. Lopez. I am having issues with minimizing the SSE (sum of squared errors) which I named as a procedure using the NLPSolve command from the Optimization package. It returns an error saying there are too many levels of recursion, which I do not understand where it is coming from or how to solve the issue and I was hoping to get an explination on how to solve it.

Below is the code up until the error. Any help or guidance would be greatly appreciated.

Parameter_estimation.mw

Hi, I am searching for an exercise in MapleLearn, which I would like to give to my students in the second year of a mathematics degree. The aim is to make them work only with Maple Learn during 15-20 minutes. So the exercise should be rather short. The original idea that I had was to give them the Fibonacci sequence equation to solve : F(n+2)=F(n+1)+F(n). I would like to transform the sequence using a 2x2 matrix, which is classical. Diagonalize the matrix, compute the powers and so on. This is very easy with Maple, but how can I do that with MapleLearn? I could enter the corresponding  2x2 matrix, compute its eigenvalues but that's it. I could not diagonalize it, compute its powers and so on. Maybe someone knows how to do that with MapleLearn? Else I would be happy to discover other exercises with MapleLearn. 

Apart from introducing the software to french universities, the aim is also to make a research experiment (it is an official collaboration with Maplesoft)

when i replace mu=0 in my equation mu[3] and mu[4] also become zero why ?

Download tester.mw

The local command is really horribly treated in the manual. Very difficult to figure out heads from tails.

What follows is Maple code to unprotect the metric tensor g_[], and alter the components. that part I figured out by trial and error where the manual fails to clearly describe how.

But, the problem I now have, is that the unprotected metric does not show the tensor "visual matrix" form anymore if I execute  g_[] . So it makes it all unusable.

How do I enter the unprotected and altered g_[] back into maple so it can be used to calculate the Ricci tensor, Einstein tensor and such ? I guess it will have to be protected again etc. ?

Here is the code

restart;
with(Physics);
g_[sc];
g_[];
_local(g_[]);
g_[1, 2] := 1;
g_[3, 3];
Physics:-g_[1, 1];
g_[1, 2];
Physics:-g_[1, 1];
g_[];
for x to 4 do
    for y to 4 do g_[x, y] := Physics:-g_[x, y]; end do;
end do;
g_[];

So the question is. How do you reverse a localalized metric back to being protected after you altered the metric ?

I am sure that this question must be answered. But when I do a search in the "Search" box, I always receive a page where it  is mentioned that there is an error of generating the page.  So this has been the case for more than a month, or maybe more. I don't know why this is happening.  So that is the reason why I ask a question here.

I would like to put an entry in the file maple.ini so that each time I do the command "plot", the size of the plot in the document will be a size=[300,300] in pixels.  That is supposed to give a plot of 8 cm by 8 cm.  So when I print the document, which will be the size of the plot on the printed page.  I want to do that because if I do not modify the size of the plot by default in the document, it takes up too much space in the page.  I want to do it in maple.ini so I don't have to do it manually each time I plot a function.

Thank you in advance for your help.

How we can calculate solution of this ODE by give assumption to the equation , we have otehr case too, like lambda>0&mu<0

I have a lot of questions about using evalf/Int with Monte-Carlo like methods.
They are red written in the attached file and concern several different points.
I would like you to answer each of them and not to focus on a specific one.
Thanks in advance.

method=_MonteCarlo uses the Fortran procedure d01gbc (maybe Maple rewritten?): the original NAG procedure is described here d01gbc

Download Numerical_integration_Using_MC_methods.mw

On considère un cercle fixe O et un point fixe A extérieur. Une sécante variable BC à ce cercle passe par un point fixe J.
Démontrer que le cercle ABC passe par un second point fixe P.
restart;
Proc := proc(m)
local xA, yA, xB, yB, xC, yC, xJ, yJ, tx, dr, Oo, c1, r, eqBJ, eq1, sol;
_EnvHorizontalName := 'x'; _EnvVerticalName := 'y';
xJ := 5; yJ := 1; geometry:-point(A, 2, 4); geometry:-point(J, xJ, yJ); geometry:-point(Oo, 0, 0);
r := 3; c1 := plottools[geometry:-circle]([0, 0], r, color = blue);
eqBJ := y = m*(x - xJ) + yJ; geometry:-line(BJ, eqBJ, [x, y]);
eq1 := x^2 + y^2 = r^2; sol := solve({eqBJ, eq1}, {x, y}, explicit);
xB := subs(sol[1], x); yB := subs(sol[1], y);
geometry:-point(B, xB, yB); xC := subs(sol[2], x); yC := subs(sol[2], y);
geometry:-point(C, xC, yC); geometry:-circle(c2, [A, B, C]); geometry:-line(AB, [A, B]); geometry:-line(AC, [A, C]);
eqBJ := y = m*(x - xJ) + yJ; geometry:-line(BJ, eqBJ, [x, y]);
eq1 := x^2 + y^2 = r^2; sol := solve({eqBJ, eq1}, {x, y},explicit);
xB := subs(sol[1], x); yB := subs(sol[1], y); geometry:-point(B, xB, yB);
xC := subs(sol[2], x); yC := subs(sol[2], y); geometry:-point(C, xC, yC);
geometry:-circle(c2, [A, B, C]); geometry:-line(AB, [A, B]); geometry:-line(AC, [A, C]);
tx := plots:-textplot([[geometry:-coordinates(A)[], "A"], [geometry:-coordinates(B)[], "B"], [geometry:-coordinates(C)[], "C"], [geometry:-coordinates(J)[], "J"]], font = [times, bold, 16], align = [above, right]);
dr := geometry:-draw([AB(color = black), c2(color = magenta), A(color = blue, symbol = solidcircle, symbolsize = 16),
B(color = red, symbol = solidcircle, symbolsize = 16), C(color = red, symbol = solidcircle, symbolsize = 16),
J(color = red, symbol = solidcircle, symbolsize = 16)]); plots:-display([dr, c1, tx], axes = normal, view = [-5 .. 6, -4 .. 6], scaling = constrained);
end proc;
plots:-animate(Proc, [m], m = -0.9 .. 0.2*Pi, frames = 50);
Error, (in plots/animate) two lists or Vectors of numerical values expected
NULL;
I am trying to find out point P; Thank you for your help.

From time to time Maple output containts brackets that are nor needed. Example:

int(f(x),x=a..c)-int(f(x),x=a..b);
simplify(%) assuming c>b

Why is that? Is there a way not to have these brackets printed?

Is there a way to force Maple to use basic linear algebra results?
Here is a result you can find in any linear algebra book (this one comes from Harville's Matrix Algebra From a Statistician's Perspective)
I'm using Maple to check my work and it would be helpful if some basic linear algebra results would be injected in Maple's algorithm.

Download Using_basic_linear_algebra.mw

Hello! I need to write some text (a string) and some data in a file on the hard drive. Something like

"Hello, it is me"

3.1415

These two things written in two different consecutives lines in a file called /home/PNL/test_file.txt

I have tried WriteString, WriteFile but I failed miserably. Thank you very much!

How to specify the number of digits shown in the output of CrossProduct?  I've tried specifying the number of digits with Digits:=5: but CrossProduct seems to ignore that. I thought maybe setting the CrossProduct datatype to float might help, but it didn't.

What do I need to do?

I don't know if this is a false memory, but I think that I saw once a command in Maple that make a list of all the assumptions that have been done i the output space. A command that could be named "ListAssumption()" and you would get that list. In fact, I was wondering if this list could be shown in the palettes "Variables." There could be, below the variables, another table with the first row the name of the letter that you made an assume on, and the second row (the value) would show the assumption.  Like this maybe:

Just to get an idea.  Do you think it would be a great idea?

Hello Everyone,

I am wondring if I can  find the StandardRepresentation of a subalgebra of simple Lie algebra?

For example I have this code:

with(DifferentialGeometry);
with(LieAlgebras);
with(Library);
with(LinearAlgebra);

G := SimpleLieAlgebraData("sl(6)", sl6);
DGsetup(G);
StandardRepresentation(sl6);
M3 := MinimalSubalgebra([e30, e35, e20]);
B3 := LieAlgebraData(M3, p62);
Query("Jacobi");
DGsetup(B3);
StandardRepresentation(p62);
Error, (in DifferentialGeometry:-LieAlgebras:-StandardRepresentation) expected a Lie algebra constructed by the procedure SimpleLieAlgebraData
 

For the first StandardRepresentation(sl6); it works becouse of the definition. Now what I want the same idea for the subalgebra. How can I do that?

Any idea why Maple returns empty string when asked for the latex of the Laplace of x(t)?  Am I doing anything wrong here? I do not see it

Download latex_of_laplace_nov_21_2024.mw

I was expecting something like this using another software

Did Maple always behave this way for Laplace? I do not have earlier version now to check.  Any workaround?