How can I compute F from G according to the following text? (I implemented this but I need a more efficient implementation.)

Given a set G of polynomials which are a subset of k[U, X] and a monomial order with U << X, we want to comput set F from G s.t.

1. F is subset of G and for any two distinct f1, f2 in F , neither lpp (f1) is a multiple of lpp (f2) nor lpp (f2) is a multiple of lpp (f1).

2. for every polynomial g in G, there is some polynomial f in F such that lpp (g) is a multiple of
lpp (f ), i.e. ⟨lpp (F )⟩ = ⟨lpp (G)⟩,

--------------------------------------------------------------------------------------

It is worth nothing that F is not unique.

Example:  Let us consider G = {ax^2 − y, ay^2 − 1, ax − 1, (a + 1)x − y, (a + 1)y − a} ⊂ Q[a, x, y], with the lexicographic order on terms with a < y < x.

Then F = {ax − 1, (a + 1)y − a} and F ′ = {(a + 1)x − y, (a + 1)y − a} are both considered set.

please not that K[U,X] is a parametric polynomial ring (U is e sequence of parameters and X is a sequence of variables).

lpp(f) is leading monomial of f w.r.t. variables X. For example lpp(a*x^2+b*y)= x^2.

Is there any Maple command for computing the product of two set A and B?

For example if A={a,b,c} and B={x,y} then we have A*B={ax,ay,bx,by,cx,cy}.

There is an error in my implementation as follow:

"Error, (in unknown) incorrect syntax in parse: `*` unexpected (near 1st character of parsed string)"

What I have to do to remove this error?

How can I generate some n-tuple random list of integers s.t. any component is between -30 and 50? For example if n=5 then four random of such 5-tuple are

[-1,2,8,7,9] , [0,-9,2,-3,-5] , [4,5,3,-8,-1] , [12, -5, 0, 6,8]

Let B=be a list.

How can I sort B as BB=?