gb => DegreeLimit

DegreeLimit => n -- keyword for an optional argument used with gb which specifies that the computation should halt after dealing with degree n.

This option is relevant only for homogeneous matrices.

i1 : R = ZZ/101[x,y,z,w];
i2 : I = ideal(x*y-z^2,y^2-w^2)

                   2   2    2
o2 = ideal (x*y - z , y  - w )

o2 : Ideal of R
i3 : gb(I,DegreeLimit => 2)

o3 = {0} | y2-w2 xy-z2 |

o3 : GroebnerBasis
i4 : gb(I,DegreeLimit => 3)

o4 = {0} | y2-w2 xy-z2 yz2-xw2 |

o4 : GroebnerBasis

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