How  we can decide whether a polynomial f is a linear combination of some polynomials g1,...,gm?

For example if f=x^2+y^2 and g1=y+x^2 , g2=y^2-y then f=g1+g2.

Let M be the matrix [[]] means that a matrix without any array. If we call RowDimension(M) then it output is 1 and we know that it is zero. What I have to do? It is hilarious that the RowDimension([[1]])=RowDimension([[]])!!!

I know that the "Rank(M)" command of Maple computes the rank of matrix M and I know that the "RowDimension(M)" gives the number of rows of M. Is there any command to gives the number of nonzero rows or columns of M?

For example, Let M be the following matrix. I want [2,3] as the output  where the first component ( second component. resp) is the number of nonzero rows (nonzero columns. resp) of M.

                              [1  5  6]

                       M=   [0  0  0]

                              [2  3  5]

I have a question about "EliminationIdeal" command. When I call EliminationIdeal(<x>,{a,b,c}) appears error. I know that the output of this computation must be []. What I have to do?

Let I  be a polynomial in K[A][X] s.t. A is a sequence of parameters (coefficients of f in F) and X is a sequence of variables. I want to extract the variables from ideal I.

For example if I=[(a-1)x*y^2-b+x, x-y+x^2-c] s.t. a,b,c are parameters and x,y are variables. I want {x,y} as the output of algorithm.