Grobner bases

 

In Mathematica

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Reduce

inputs outputs

    polys := 45p + 35s - 165b - 36,
              35p + 40z + 25t - 27s,
              15w + 25p s + 30z - 18t - 165b^2,
              -9w + 15p t + 20z s,
              w p + 2z t - 11b^3,
              99w - 11s b + 3b^2,
              b^2 + 33/50b + 2673/10000

    vars := w,p,z,t,s,b

    GroebnerBasis[ polys, vars ]

                            2
    {2673 + 6600 b + 10000 b , -9 - 500 b + 200 s,

     81 - 1850 b + 750 t, 10287 + 24500 b + 18000 z,

     -1377 - 3100 b + 1800 p, 3969 + 9500 b + 60000 w}