For comparison with other CAS choose from: Axiom Derive Macsyma Mathematica Reduce
with( grobner, gbasis );
[gbasis]
polys := [ 45*p + 35*s - 165*b - 36, 35*p + 40*z + 25*t - 27*s, \
15*w + 25*p*s + 30*z - 18*t - 165*b^2, \
-9*w + 15*p*t + 20*z*s, w*p + 2*z*t - 11*b^3, \
99*w - 11*s*b + 3*b^2, b^2 + 33/50*b + 2673/10000 ] ;
polys := [45 p + 35 s - 165 b - 36, 35 p + 40 z + 25 t - 27 s,
2
15 w + 25 p s + 30 z - 18 t - 165 b , - 9 w + 15 p t + 20 z s,
3 2 2 33 2673
w p + 2 z t - 11 b , 99 w - 11 s b + 3 b , b + ---- b + -----]
50 10000
vars := [ w, p, z, t, s, b ];
vars := [w, p, z, t, s, b]
gbasis( polys, vars, tdeg );
[1800 p - 3100 b - 1377, 18000 z + 24500 b + 10287,
2
60000 w + 9500 b + 3969, 10000 b + 6600 b + 2673,
750 t - 1850 b + 81, - 500 b - 9 + 200 s]