I want to solve n nonlinear equations in n unknowns named lambda[1], lambda[2], ..., lambda[n]. For simplicity, I assume n=3. Each of the three equations includes matrices and dot products.

Running solve() takes forever...I assume this is because Maple is trying to find the explicit form. I am not sure, but I have reasons to believe that a solution exists.

Questions:

1. Did I set up the three equations correctly? Is there a simpler or smarter way to set up my problem?
2. Is it okay for Maple that lambda[i] sometimes appears isolated and sometimes as a component of a vector?  
3. Is there a way to keep my quantities (except the lambda vector I guess, since it containts the lambda[i] component I need to solve for) undefined/implicit while making sure Maple correctly deals with matrices and dot products?
   e.g., the solution should display terms like p^%T.R.w as such, rather than the corresponding explicit computation...

Worksheet:

Download dot_products.mw

I'm having some trouble finding how to do this: given some field with spacetime indices, say h[mu,nu] and a Lagrangian L of that field, I want to do a n+1 split to find the canonical momentum pi[~mu,~nu]. I can do the splitting fine, but it's calculating the canonical momentum that is the problem. I've tried a couple of different methods using diff and SubstituteTensorIndices but I can't get it to work: I either get the wrong answer or zero (also wrong). Anyone with any ideas or a working example of this, I'd appreciate to hear from!

The XMLTools:-Validate function can be called with a reference to a schema.

I am a bit unsure where the schema location should be, especially if I can have the .xsd file in a library location.

Have done some tests, and as far as I can see, Maple does not give any error messages if the schema is not found at all. So I'm a bit unsure how to check if the schema defintion actually is read at all.

Something has changed in the past weeks (not sure for how long) and I have not figured out what exactly.

Probably it is me doing something differently while editing an input line. Below is an example where the name data is not italic any more

Anybody else experiencing the same?

My interface seetings:

how do i replace equation in maple for istance i want to replace u_t , u_xx, and u_x in the equation "u_t=-au_xx+bu_x"

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

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.

An example of solving a system of nonlinear equations, when all (real) solutions are found for one initial approximation. To make it easier to understand the program text, a description of the solution method is provided separately in PDF format.

Draghilev’s_method_pdf.pdf

3_EQUATIONS.mw

Using the curve, the projection of which from the space R^4 to R^3 we see in the figure, we find good approximations to the solution. For each solution, the program prints out the norm of the discrepancy of the entire system of equations and shows a simple graph when the additional variable intersects R^3 . At this moment of intersection, the solution of our system is fixed.
System of equations and initial approximation.
 

f1 := x1^2+x2^2-x3^2; 
f2 := (x1-1)^4+x2^4+(x3-2)^4-81; 
f3 := x3-3*tan(.4*x2); 
x01, x02, x03 := 1, 1, 1

Old link to a similar example, where the dimension of the system of equations is 2, and we can see the auxiliary curve completely in R^3.

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