Linearly Independent Quadratics in a 7variable polynomial Ideal
I'm just beginning to learn about polynomial Ideals and groebner basis. I've got a system of polynomials in seven variables and groebner basis using lex order for several orderings of the variables. The number of quadratics in the basis varies depending on the order. This is because several of the original polynomials are of the form
x_{i} + y_{j}^{2} + y_{k}y_{n} ...
so it makes a big difference if the x's or the y's come first in the variable ordering.
I'd like to get a maximal set of linearly independent quadratics for the Ideal. How should I proceed? Would gradlex or gradrevlex automatically do this? Is there some cookbook procedure like the ones used for saturation or intersection of ideals? Is there a book for applied algebraic topology that covers topics like this?
