Hi!

There is a (relatively) known software code (written in C), called ." GKLS-generator" or "GKLS" to generate, according to certain user paramenters, optimization test functions. The code is available for free at the web

http://wwwinfo.deis.unical.it/%7Eyaro/GKLS.html

The download with the files of the GKLS is the following:  download

I would like to write this code in Maple. In the attached zip there is a PDF explaining how to build these functions. For now, I tried the follwoing Maple code GKLS_v4.mw

I think I'm doing something wrong, since the drawing generated by the attached Maple does not look much like the PDF in the attached zip (Fig. 1 of page 8).

Please, Can you help me with this?

Many thanks in advance for your comments.

Hi!

Assume that we have, in the cube C:=[-1,1]^N, for a fixed integer N>=2, a point X1  and   cosider the (closed) ball centered at X1 and radius R1:=0.6. Fixed an integer m>2, Somebody can indicate me how to compute the centers (belonging to C) and the radius of m disjoint balls with the above ball?

That is to say, compute points X2,...,Xm (in C) and positive numbers R2,...,Rm such that the intersection of the (closed) balls B(Xj,Rj) for j=1,...,m be empty. 

Some suggestion?

Many thanks in advance for your comments.

Hi!

I am very interested in using the "phc.module", which is a module to work with "polynomial homotopy continuation" method. Please, see this paper      

I have downloaded the following files: [copied without permission, deleted by moderator]

Then, I open (as an "ordinary" maple worksheet) the file "phc_savelib.maple" and execute it, but it seems that I can not use their functions and procedures because it returns errors. 

For instance, follwing the attached PDF,  in the phc_savelib.maple file, define the polynomial system:

T := makeSystem([x, y], [], [x^2+y^2-1, x^3+y^3-1])

and try to solve the above system 

sols := solve(T)

but returns the error 

Error, (in fopen) file or directory does not exist
 

Many thanks in advance for your help!

Hi!

Let F(z) (with z complex) a given function. I want to compute F^n(z0), i.e. the composition of F with itself n-times, where z0 is a given point (complex).

Is correct the following procedure to compute F^k(z0)?

App := proc (k, z0) local z1, z2, j; z1 := z0; z2 := NULL; for j to k do z2 := F(z1); z1 := z2 end do; return z2 end proc

Many thanks in advance for your comments.

Hi!

I want to plot the approximation of a surface by polynomials. The surface is given by (x,y,f(x,y)) where f(x,y) is given by the following expression

proc (x) options operator, arrow; (sum(i*cos((i+1)*(-2+4*x[1])+i), i = 1 .. 5))*(sum(i*cos((i+1)*(-2+4*x[2])+i), i = 1 .. 5)) end proc

with both variables varying in the interval [0,1]. Then, by using the Bernstein polynomials of two variables (see, for instance, this paper for details  https://www.sciencedirect.com/science/article/pii/0021904589900956), the graph of the resulting (plot3d) surface (x,y,p(x,y))  it is not even like to the original surfaces.

Please, see this PDF of what I have done:  plots.pdf

Some idea or suggestion?

Thanks!