@Carl Love This is very good. Could you please explain your way? I dont know some command that you use in the above your implementation such as "C*" and "~" .

@Carl Love Could you please combine this way with your LinearCombo for checking whether a polynomial f is linear independent of some other polynomials F. Please note that f is a polynomial with parametric coefficients and F is a list of polynomials with parametric coefficients. I want the output is

1- true(f is linear dependent of F) and the coefficients vectors

or

2- false(f is linear independent of F)

@Carl Love Thanks for this good way. I have a suggestion: When its output is false (the polynomials are linearly independent) then the finding coefficients is meaningless. For saving memory and time it is better do not compute the coefficient, when it is false. What is your idea? 

@Markiyan Hirnyk I want a general procedeure to use it in my main algorithm some times, not for special example.

@Markiyan Hirnyk I want to the parameters specialize automatically means that the input of algorithm is a list of parametric polynomials only.

@Markiyan Hirnyk How can write a procedure that its input be a list of polynomial and its output be some true and false for all possible specialization of parameters?

@Markiyan Hirnyk {(a-1)x^2-by^2,cx-by,y-1+abx} where a,b,c are parameters and x,y are variables. I know that it is related to being zero or none zero a,b,c.

@Markiyan Hirnyk Is this command appropriate for checking Independence or dependence of some polynomials with parametric coefficients?

@Markiyan Hirnyk  This is derivative of the polynomials w.r.t. the variable x. What is results if we use
 Wronskian([x^2+y^2, x^2+y, y^2-y], y, 'determinant')?

@Carl Love Thank you very much. This is nice. Can I use this for polynomials with parametric coefficients?

This is the piccture from my Maple sheet:

@Carl Love But there is an error.

@Markiyan Hirnyk For example if f=x^3+y^3+xy-y  and g1=y+x^2 , g2=y^2-y then f=(x)g1+(y-1)g2 and this is obvious that x , y-1 are not in field R!!!

@Markiyan Hirnyk But this is nice for this example. for another example we can not decide whether a polynomial is a linear combination of some polynomials by Grobner basis. Since of, the coefficient must be in field K and in normalform command coefficient are polynomial!!

@Carl Love Thanks very much for this good help. Yes. ColumnDimension is better in my procedure.