Hilbert series in Singular

Question

I am new to singular.

I would like to compute some Hilbert series using singular.

I use the following code.

LIB "primdec.lib";

ring  r = 0,(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12),dp;

ideal i = (x3-x1)*(x3-x4), (x3-x2)*(x3-x5), (x4-x2)*(x4-x6), (x5-x1)*(x5-x6), (x7-x3)*(x7-x11), (x7-x4)*(x7-x9), (x7-x5)*(x7-x10), (x7-x6)*(x7-x8), (x8-x1)*(x8-x10), (x8-x2)*(x8-x9), (x8-x3)*(x8-x12), (x9-x1)*(x9-x11), (x9-x5)*(x9-x12), (x10-x2)*(x10-x11), (x10-x4)*(x10-x12), (x11-x6)*(x11-x12), -x1^2+x2^2, -x1^2+x3^2, -x1^2+x4^2, -x1^2+x5^2, -x1^2+x6^2,
 -x1^2+x7^2, -x1^2+x8^2, -x1^2+x9^2, -x1^2+x10^2, -x1^2+x11^2, -x1^2+x12^2;

ideal pr = radical(i);

hilb(pr);

The result should be $(45*t^3+39*t^2+11*t+1)/(1-t)$.

But I obtain the following.

// ** \text{ pr is no standard basis }
 \\
//         1 t^0 \\
//       -27 t^2 \\
//        56 t^3 \\
//       165 t^4 \\
//      -792 t^5 \\
//       825 t^6 \\
//      1584 t^7 \\
//     -6237 t^8 \\
//      9680 t^9 \\
//     -9009 t^10 \\
//      5400 t^11 \\
//     -2057 t^12 \\
//       456 t^13 \\
//       -45 t^14 \\
//         1 t^0 \\
//        11 t^1 \\
//        39 t^2 \\
//        45 t^3 \\
// dimension (proj.)  = 0 \\
// degree (proj.)   = 96

How could I obtain the Hilbert series: $(45*t^3+39*t^2+11*t+1)/(1-t)$ using Singular? Thank you very much.