Now we turn to an example of the usage of the Dragilev method with Maple. Let us consider the curve
from
http://www.mapleprimes.com/questions/143454-How-To-Produce-Such-Animation .

Its points can be found by the Dragilev method as follows.

This is an effective method of solving systems of  N nonlinear and nonalgebraic equations in N+1 real-valued variables:
F(x)=0, where F=(f1,f2,..., fN) and x=(x1,x2,...,xN+1). (1)               
                                                                  
All the functions fj(x) are assumed to be continuously differentiable in some domain D in R^(N+1).
In general, such systems have an infinite set of the solutions which form a space curve in R^(N+1).
 The Optimization and DirectSearch solvers have difficulties with it.
The idea of the Dragilev method consists in the following. Let us assume that the space curve (1) can be parametrized through the  parameter t
which can be taken as the  length of the arc (for example, see http://en.wikipedia.org/wiki/Curve ).
That presentation provides to avoid the difficulties associated with self-intersections and singularities.
We will obtain the coordinates of the points of the space curve under consideration as the solution
of the Cauchy problem for certain system of ODEs. We put the coordinates of a known point of (1) as the initial conditions.
The system of ODEs is obtained by the differentiation  with respect to t:

We treat (2) as a linear system in the derivatives diff(xj(t),t),j=1..N+1. In general, its solutions form an infinite set.
We choose the  solution of (2) as follows. We put diff(xN+1)= -Determinant(Matrix(n, (i,j)->diff(fi(x),xj))).
This is one of the key points of the method under consideration.
Next, we find diff(xj,t), j=1..N. At last, we numerically solve that system of ODEs, obtaining an array of points.
 The general case of a system of N nonlinear  equations in N variables
G(y)=0, where y=(y1, y2, ..., yN), G=(g1,g2,..., gN) (3),
is reduced to the previous one by homotopy. We choose a point y0= (y01, ..., y0N) and consider the system
G(y)- v*G(y0)=0 (4)
of N equations in N+1 variables (v is taken as  a dummy variable). Changing v from 1 to 0, we arrive to (3).
We don't consider any mathematical justification of the above pattern here as that does not deal with Maple.
I would like to point out the sites

http://forum.exponenta.ru/viewtopic.php?t=3892 and
http://forum.exponenta.ru/viewtopic.php?t=11284 , where the Dragilev method is discussed. Unfortunately, in Russian.
The googling of "Dragilev" and "Draghilev" does not produce many info.
A short biographical sketch: Dr. Anatoliy Vladimirovich Dragilev (1923 - 1997) was a professor at  Rostov State University in Russia.
See his articles here: http://www.mathnet.ru/php/person.phtml?&personid=32359&option_lang=eng and
http://www.zentralblatt-math.org/zmath/en/search/?q=au%3A%22dragilev%2C%20a*%20v*%22 .
 

I am very grateful to Professor Alexey B. Ivanov, who is an enthusiast of the Dragilev method, for the very useful discussions.

hi,

I have created a large matrix (31  times 4) using Maple 15. some of the columns of the matrix contains a long list.

I would like to save the contents of the matrix to either MS-Word or Excel. I tried right-click>Browse>export and saved it as an excel file. But the data in the columns consisting the long lists is lost in the saved file.

1)Is there any other way I can save the contents of the matrix.

2) the matrix seems too large...

Hi,

I meet a problem when I want to find the derivative of an integral with parameters when th eintegral has an option for numerical evaluatio.  For example

>  S := Int(sin(a*x)/x,x=0..infinity,method=_DEFAULT);

> diff(S,a);

Error, (in diff/Int) invalid Int(...) format

What is the correct syntax ?

Thanks, 

 Dan

Thank you for the suggestions. Float command helped me a lot for real matrices but when I have imaginary numbers in my matrix it gives me error.  

 after I construct the matrix A I do = implies  Af:= Matrix(A, datatype= float):

That gives me error message ' Unable to store 0.-18844.3412345686*I ' when datatype=sfloat'    is there a solution for that like complex_float "? I  looked at Maple help but I could not find...

Hi

I have created a figure in Maple 15 using Plots:-display() command.  I want to save the combined figure (given by display) as a .eps format. I can do this by right-click on the image>export>Encapsulated Postcript. I need to run the code several times so that it produces a different image each time(by changing variables). I have to then click on the image and drag it so that it becomes the appropriate size I wanned.

My problem is that it is difficult...

Mrs Bopha, used phone that had 7 numbers. Som didn't clear her phone number.Som remember 4 numbers in the first that had 9 ,8 , 7 and 7 Som didn't clear serial number 5 about 1 or 2.For serial number 6 didn't remember. But Som remember that serial number7 equal 5 minus serial number 6.How many time that Som  should be chose right phone 's number to Mrs Bopha?

I intend to calculate the eigenvalues and eigenvectors, but for the same matrix when i executed the Eigenvectors command in mapple twice the eigenvalues generated are same both the times but the values of eigenvector are infinite at one instance whereas they are in numeric domain in the second instance.

Can anyone please tell me why this is occuring?

Hi.

I want to solve two varibles from a vector crossproduct equation, but receives a failure massage no matter what i do.
The equation is the one below and i want to solve for Gx and Gy.

Really hope you can help.. THANKS!

with(LinearAlgebra);
F1:=<Fr1,-Ft1,-Fa1>;
Sug :=<0,0,-Duzg>;
Su1:=<Dux1,0,-Duz1>;
Mmotor:=<0,0,-Mind>;
G:=<Gx,Gy,Gz>;
OO:=<0,0,0>;
        
U:=(Su1 &x F1) + (Sug &x G) - Mmotor = OO;...

The sine wave in Maple 16 is shown as following

The sine wave in Mathematica is shown as following

It's obvious that the second one is smoother than the first one,I want to know how to make curves smoother in Maple 16.

Hi,

  I have a .txt file created from maple. I want to read some data using maple. The content of that .txt file is

....

some word,                     -7
                    -0.25333 10

...

some word,

The second graph is incorrect. The reason?

plots[polarplot]([3+cos(4*t), 2-cos(4*t)], t = 0 .. 2*Pi)

Hi,

I would like to know if it is possible to make Maple do the following:

Suppose you have a function dx:=1/((x1-x3)^2+(x2-x4)^2) and we want  diff(dx,x1), is there a way to obtain: *-(2*x1-2*x3)/((x1-x3)^2+(x2-x4)^2)^2 instead of -1/(x1^2-2*x1*x3+x3^2+x2^2-2*x2*x4+x4^2)^2*(2*x1-2*x3)?

Basically how to keep the denominator in a fatorized form and not expanded?

Thanks.

Dear Sir,  I want to know why the procedure  appear the error : (in U1) unable to execute add.

My procedure:

restart:
>
> h0:=0.156;
> d:=0.32*h0;
> l:=1;
> h1:=h0-d;
> h2:=h0+d;
> h5:=evalf(2/3*h0);
> h7:=h0;
> s1:=evalf(2/3);
> s2:=evalf(2/3);
> g:=9.8;
> d1:=1;
> Term:=10;
> Num:=5:
> n:=1:
>
>
> for N from 1 to Num do
> k0:=evalf(0.5*Pi+2*(N-1)*Pi/(Num-1)):...

Can anyone tell me how i can compute the correct partial derivatis of this function? I need to compute the partial derivative with respect to P_j,k but since I am summing over 'j', it does not compute the chain rule properly.