Singular

LIB "matrix.lib";
ring r=0,(s,t,u,x(0..5)),dp;
varstr(r);
ideal I=x(0)-s2,x(1)-t2,x(2)-u2,x(3)-st,x(4)-su,x(5)-tu;
std(I);
vector v=[x(3)*x(4)-x(0)*x(5),x(1)*x(4)-x(3)*x(5),x(2)*x(3)-x(4)*x(5),x(1 )*x(2)-x(5)^2,x(0)*x(2)-x(4)^2,x(0)*x(1)-x(3)^2];
matrix A[4][6]=1,1,1,1,1,0,0,0,0,0,1,2,2,2,1,1,1,0,0,0,-1,-2,1,0,1;
print(A);
matrix B=A*v;
print(B);
ideal F=flatten(B);
print(F);
ideal J=eliminate(F,x(4)*x(5));
print(J);
poly f=J[1];
print(f);
poly g=J[2];
print(g);
poly h=resultant(f,g,x(3));
the resultat gives me 0.
Instead if I change the ring and try it with the same polynomials as above, it works
like this
ring r=0, (x,y,z,w),dp;
poly f=14xy2+xyz+14xyw-14xw2-zw2-14w3;
poly g=4x2y+6xy2+xyz+10xyw-4xw2-6yw2-yw2-10w3;
resultant(f,g,x);
thank you in advance!

The results are correct (resultant is 0 in the first case).
But the polynomials in the second ring are not the same.
This can be checked by defining a map