Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Can anyone solve,

eqn := diff(x(t), t, t)+omega^2*x(t)-epsilon*mu*(diff(x(t), t))+epsilon*alpha*x(t)^2*(diff(x(t), t))+epsilon*Zeta*cos(Omega*t)*x(t)=0;

This equation using MMS (Method of Multiple Scales) in maple.

Pls use Polar transformation function as (1/2)*a(t)*exp(-I*beta(t))

Please reply.

I am trying to see the solution to a PDE that I am coding with initial and boundary conditions. I know with the ODE, it shows the solution, but with the PDE I cannot seem to see it. Any suggestions?

Dear all,

I would like to evaluate a double integral numerically. The integrand is a complicated function of the variables beta and s, with complex values. The computation lasts for decades without obtaining a result.

I was wondering whether there exists subroutines / methods / tricks that could be helpful to accelerate the integration process. I have attached a Maple script of the double integral of interest. Rough precision would be fine (4 or 5 digits).

Any help would be highly appreciated.

Thanks

Federiko

Question.mw

Hi Dears,

I'm have a code like this:

sum(-GAMMA(k+1, x), k = 0 .. -2) and Maple give me : Ei(1, x).

How to check that answer is correct?

 

Thank you in advance.

I am looking forward to hearing from you.

Hi, i try resolve this equations numerical for the boundary between the spinglass and ferromagnetic phases:

 

how?

Regards.

 

 

Sudoku is a well known Latin square type game, see https://en.wikipedia.org/wiki/Sudoku

Here is a Sudoku game and its (unique) solution:

A,Sol:=  # A = Sudoku matrix, 0 for each empty cell
Matrix(9, [
[0,0,3,0,9,0,1,0,0],
[0,5,0,3,0,0,7,0,0],
[1,0,2,0,0,5,0,6,4],
[0,1,0,0,2,0,9,0,0],
[2,0,0,6,0,3,0,0,1],
[0,0,7,0,8,0,0,3,0],
[7,6,0,9,0,0,8,0,5],
[0,0,8,0,0,7,0,9,0],
[0,0,4,0,6,0,2,0,0]]),
Matrix(9, [
[4,7,3,2,9,6,1,5,8],
[8,5,6,3,4,1,7,2,9],
[1,9,2,8,7,5,3,6,4],
[3,1,5,7,2,4,9,8,6],
[2,8,9,6,5,3,4,7,1],
[6,4,7,1,8,9,5,3,2],
[7,6,1,9,3,2,8,4,5],
[5,2,8,4,1,7,6,9,3],
[9,3,4,5,6,8,2,1,7]]);


The procedure which follows is a very compact Sudoku solver. It uses Groebner bases. I hope that you will like it.
The input is the Sudoku matrix and the solution matrix is returned.
Note that the Sudoku matrix must be valid and must have a unique solution.
(Otherwise, theoretically, the error "Invalid Sudoku matrix" should appear.)
Note also that the procedure may be very slow for some games or Maple may crash. This happened to me once with a very "hard" matrix.

I was impressed that Maple's implementation for Groebner bases works now so well for this problem!

A few years ago on this site: http://www.mapleprimes.com/questions/131939-Calculating-Groebner-Basis-For-Sudoku
it was an attempt to solve the problem with this method but it failed (due to wrong number of polynomials).

sudoku:=proc(A::'Matrix'(9,integer))
local x_A,x,Q,R,r, i,j,u,v,G;
Q:=proc(X,Y) normal((mul(X-i,i=1..9)-mul(Y-i,i=1..9))/(X-Y)) end;
x_A:=seq(seq( `if`(A[i,j]>0,x[i,j]-A[i,j],NULL),i=1..9),j=1..9);
R:={seq({seq(x[i,j],j=1..9)},i=1..9), seq({seq(x[i,j],i=1..9)},j=1..9),
    seq(seq({seq(seq(x[3*u+i,3*v+j],i=1..3),j=1..3)},u=0..2),v=0..2)};
G:=Groebner:-Basis({seq(seq(seq(Q(u,v),u=r minus {v}),v=r),r=R),x_A},'_vv');
if nops(G)<>81 then error "Invalid Sudoku matrix" fi;
eval(Matrix(9,symbol=x), `union`(map(u->solve({u}), G)[]));
end:

sudoku(A) < A; # Solving the previous game

# Let's solve another one:
A:=Matrix(9,9,[[0,0,0,4,0,0,0,8,0],[0,5,2,7,0,0,4,0,0],[3,0,0,0,0,0,0,0,0],[5,1,0,8,0,0,0,0,0],[0,0,0,5,0,0,6,7,0],[0,9,0,0,7,0,0,0,3],[2,4,0,0,0,5,0,0,0],[9,0,0,0,0,0,0,3,8],[0,0,0,0,0,0,9,4,0]]):
sudoku(A) < A;

Matrix   # A Sudoku matrix which crashes Maple!
(9,[[8,0,0,0,0,0,0,0,0],[0,0,3,6,0,0,0,0,0],[0,7,0,0,9,0,2,0,0],[0,5,0,0,0,7,0,0,0],[0,0,0,0,4,5,7,0,0],[0,0,0,1,0,0,0,3,0],[0,0,1,0,0,0,0,6,8],[0,0,8,5,0,0,0,1,0],[0,9,0,0,0,0,4,0,0]]):

 

 

Hi

I have the ODEs: x'=x

ode:=diff(x(t),t)-x(t);

 

sketch the phase space and extended phase space of previous ode.

 

theta := a-(1/2)*beta*a*y^2+(1/24)*beta^2*a*y^4-(1/720)*beta^3*a*y^6+(1/40320)*beta^4*a*y^8-(1/3628800)*beta^5*a*y^10+(1/479001600)*beta^6*a*y^12-(1/87178291200)*beta^7*a*y^14+(1/20922789888000)*beta^8*a*y^16-(1/6402373705728000)*beta^9*a*y^18+(1/2432902008176640000)*beta^10*a*y^20-(1/1124000727777607680000)*beta^11*a*y^22+(1/620448401733239439360000)*beta^12*a*y^24

Pls, anyone with useful informations on how to convert a series just like the one above to trigonometry or hyperbolic form. Need response as soon as possible. Thankin you in anticipation for your favorable response. 

hello,I want to solve a quesstion about heat equation,that the quesstion like this:

I use the code like this

but the results is wrong obviously and what's wrong with this code?

anxious for your help,thanks.

 

 

hi

how can i plot a 3d polygonal cylinder for example a hexagonal?

Hi

Any help will be appreciated

I have a continuous time dynamical system

x in R ( set of real number)

t  a positive real time

and the function f_t(x)=x-t

How can we plot or sketch their behaviour in the phase space and in the extended phase space

 

Many thanks

 

 

Hello Guys,

I am having a problem plotting a graph from some sets of point. Please how do I plot a graph having some set of point.

Thanks. 

Dear friends:

I am facing to search the command which zoom a sactor of graph, I know it can be done by using maple tools whose present tool bar but I need a command for zooming please help me to fix this problem (attached) I want to see th sactor eta=0.8 to eta=1.2.

graph_phi_varies.mw

Please see the problem and correct as soon as possible. I am waiting your positive respone.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

 

The distance from the point to the surface easily calculated using the NLPSolve of Optimization package. If the point is not special, we will find for it a point on the surface, the distance between these two points is the shortest between the selected point and the surface.
Two examples:  the implicit surface and the parametric surface.
To test, we restore the normals from the  calculated  points (red) by using analytical equations.
DISTANCE_TO_SURFACE.mw

 

Find x  for which the path (on the real line):
        b -->  x -->  a --> x --> d --> b

has a minimal length.
Perhaps through the Repetition Statement (for...while...do)

 

 

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