1. Download the polynomial system of {6,22,17} and the check polynomial.
6-22-17_poly_17_txt.gz
6-22-17_chkpoly_txt.gz

2. Expand these files.
gzip -d 6-22-17_poly_17_txt.gz
gzip -d 6-22-17_chkpoly_txt.gz

3. Start Singular

4. Execute the following commands on Singular:
system("--min-time", "0.01");
system("--ticks-per-sec", 100);
timer = 1; // Display setting of cpu time
ring r=0,(w,u,q,o,k,e,d,c,b,f,a),(Wp(20,18,14,12,8,6,5,4,3,2,2)); // Setting the weights
< "./6-22-17_chkpoly_txt"; // load of the check polynomial h of {6,22,17}
< "./6-22-17_poly_17_txt"; // load of the polynomial system i of {6,22,17}
option(prot); // Display setting of the progress
option(redSB); // Setting for reduced Groebner basis computation
option(prot); // Display setting of the progress
ideal g=groebner(i); // Groebner basis computation
poly j=reduce(h,g); // Computation of normal form of h w.r.t g
poly h=cleardenom(j); // Converts the polynomial j with rational coefficients into the integral polynomial such that GCD of all its coefficients is 1.
poly t=h^3;
reduce(t,g); // Computation of normal form of h^3 w.r.t g

5. We get 0 by the above command. This shows that h in radical sqrt(Id(i)).