@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

@Carl Love 

Thanks, No I need a function or procedure for computing in polynomial quotient rings. Let I  be a homogeneous polynomial ideal of degree d (e.g. I=<x-y>) and R=K[x,y,z]. So R/I = K[x,y,z] / I ------> K[y,z] or K[x,z]. Also the polynomial ideal [x^2+y^2+z^2] changes into [2y^2+z^2] in R/I. I dont know how do automatically this in Maple.

Thanks again.

@Christian Wolinski 

Thank you so much for your answer.

@Carl Love 

Thank you so much for your efficient method.

Sincerely yours

@acer 

Thank you so much. So, using your comparison performance you suggest rtable_scanblock. Is this true?

You have to compute a Grobner basis w.r.t. a lex ordering not tdeg. Also, you could use the solve command for this.

@acer Thank you so much. I am trying to do it.

@Kitonum Oh my God!! this is excellent. Thank you so much.

@Kitonum Thank you so much. This is perfect!