Choose a random square-free monomial ideal whose generators have the degrees specified by the list or squence L.

i1 : setRandomSeed(currentTime()) o1 = 1594135600 |

i2 : kk=ZZ/101 o2 = kk o2 : QuotientRing |

i3 : S=kk[a..e] o3 = S o3 : PolynomialRing |

i4 : L={3,5,7} o4 = {3, 5, 7} o4 : List |

i5 : randomSquareFreeMonomialIdeal(L, S) low degree gens generated everything o5 = ideal(b*c*d) o5 : Ideal of S |

i6 : randomSquareFreeMonomialIdeal(5:2, S) o6 = ideal (c*d, a*d, b*c, b*d, a*e) o6 : Ideal of S |

The ideal is constructed degree by degree, starting from the lowest degree specified. If there are not enough monomials of the next specified degree that are not already in the ideal, the function prints a warning and returns an ideal containing all the generators of that degree.

- randomMonomial -- Choose a random monomial of given degree in a given ring
- randomMonomialIdeal -- random monomial ideal with given degree generators

- randomSquareFreeMonomialIdeal(List,Ring)
- randomSquareFreeMonomialIdeal(Sequence,Ring)