i1 : S = QQ[a..f]; |

i2 : I = ideal(a^5, b^5, c^5, d^5, e^5); o2 : Ideal of S |

i3 : degree I o3 = 3125 |

i4 : degree(S^1/I) o4 = 3125 |

i5 : I = intersect(ideal(a-1,b-1,c-1),ideal(a-2,b-1,c+1),ideal(a-4,b+7,c-3/4)); o5 : Ideal of S |

i6 : degree I o6 = 3 |

- dim -- compute the Krull dimension
- codim -- compute the codimension
- genus -- arithmetic genus
- genera -- list of the successive linear sectional arithmetic genera
- hilbertSeries -- compute the Hilbert series
- reduceHilbert -- reduce a Hilbert series expression
- poincare -- assemble degrees into polynomial
- hilbertPolynomial -- compute the Hilbert polynomial