Let

and f=

The elements of W are none zero. I want a procedure that return "true" if f is none zero w.r.t. W and return

"false" otherwise.

Which of Maple commands is better for computing the radical of a polynomial f (less time of computation and less complexity)?

For example if f=x^3+3x^2y+3xy^2+y^3 then rad(f)=x+y.

Let B is a list of polynomial conditions such that  are none zero. Consider one polynomial f. How can I detect that f is none zero w.r.t. B? For example if B=[a-1,b+2,b-c,ac-1] and f=a^2c-ac-a+1. From B we can conclude that a<>1 and b<>2 and b<>c and ac<>1. How can I deduce that f<>0 w.r.t. B automatically?

Let A and B be two lists of monomials. I want a new list C contained that monomials of A where not divide by any monomial of B. For example if A=[x,y,x^2y,xy^2,y^2] and B=[x^2,y^3] then C=[x,y,xy^2,y^2].

I think that I found a bug in Maple! Please run the following command:

I need the Generators of above Ideal. What is your idea?!