@dharr 

I need a*A4+b*A5 +c. I deal with any variables but usually x is variable.

@dharr

Thank you again. This is okay, but I believe it is not working properly. Please see the attached file.draft2.mw

@dharr 

Thanks again, but I'm sorry, this also doesn't work in Maple 18!

@dharr 

Thank you so much for your answer. But, when I run your implementation an error appears. Please see the attached file.dcoeffs.mw

@sursumCorda 

Thanks, Yes, this is OK but I need an efficient implementation that receives a list of polynomials and returns as above. Also, it is possible that F contains subset F1,...Fm (Homogeneous polynomials ordered in ascending degrees and not necessarily in consecutive degrees). For example, the input is:
F=[F1={x-y}, F2={-x*y*z+z^3, x*y^2+y*z^2-z^3},F3={-x^2*y*z+z^4, x*y^3+y*z^3-z^4}].  We have to multiply F1 by all monomials in degree two in k[x,y,z] and add them to F2. Now, we must multiply F1 by all monomials in degree 4 multiply F2 by any monomials in degree 2, and add them to F3. 

@Joe Riel Thanks.
OK, I will use the homogeneous option to fix it. But, terms=1 means that a monomial, not -y-4!!

@Joe Riel A file attached namely bug.mw. Also, x^2-y-4 is not binomial while I used the following command in my procedure:

f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i)

@Axel Vogt Thank you so much. It is helpful almost. I am trying to implement a simple procedure too. Thanks again.

@Axel Vogt Thanks again. At first, I want to know how to create a zero-dimensional random binomial ideal for instance in K[x,y,z]. Then I think I could implement a simple algorithm.

@Axel Vogt I accept Epostma's answer but I mentioned that I need a simple procedure for doing it. You are right <x^2,y^2> is zero-dimensional but this is not an appropriate example for my purpose.

@epostma Thanks for your response, I need a simple procedure to receive an ideal with the above property and give another set of generators containing the binomials and non-binomials.

@vv Thank you so much for your answer.

@acer 

Thanks again for your helps and useful comments.

@acer 

What should I do If I want to generalize your procedure to any input F and any monomial ordering T?

@acer 

Thank you so much for your solution this is OK.

Sincerely yours