LIB "olga.lib";
ring R = 0,(x,y,Dx,Dy),dp;
def S = Weyl();
setring S; S;
==> // coefficients: QQ considered as a field
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x y Dx Dy
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    Dxx=x*Dx+1
==> //    Dyy=y*Dy+1
// monoidal localization
poly g1 = x^2*y+x+2;
poly g2 = y^3+x*y;
list L = g1,g2;
poly g = g1^2*g2;
poly f = g-1;
isInS(g, 0, L); // g is in the denominator set
==> 1
isInS(f, 0, L); // f is NOT in the denominator set
==> 0
// geometric localization
ideal p = x-1, y-3;
g = x^2+y-3;
f = (x-1)*g;
isInS(g, 1, p); // g is in the denominator set
==> 1
isInS(f, 1, p); // f is NOT in the denominator set
==> 0
// rational localization
intvec v = 2;
g = y^5+17*y^2-4;
f = x*y;
isInS(g, 2, v); // g is in the denominator set
==> 1
isInS(f, 2, v); // f is NOT in the denominator set
==> 0