@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.

@Carl Love Let I have an empty set [] and I want to convert [] to a matrix then it appears [[]] as the empty matrix in my procedure.

@tomleslie Could you please write without "with(ArrayTools)"?

Could you please explain what is Psi(-z)?

@Carl Love If I want to use from EliminationIdeal command, from this time, at the first I have to paste the code that Roman gave in my Maple sheet. Is this true?

@roman_pearce  In usage, how can I call this? Could you please give an example?

What is module bodies?