randomSquareFreeMonomialIdeal -- random square-free monomial ideal with given degree generators

Synopsis

Usage:

I = randomSquareFreeMonomialIdeal(L,S)
Inputs:
- L, a list, or sequence of non-negative integers
- S, a ring, Polynomial ring
Outputs:
- I, an ideal, square-free monomial ideal with generators of specified degrees

Description

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

i1 : setRandomSeed(currentTime())

o1 = 1711041350

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(a*d*e)

o5 : Ideal of S

i6 : randomSquareFreeMonomialIdeal(5:2, S)

o6 = ideal (c*d, b*c, d*e, c*e, b*d)

o6 : Ideal of S

Caveat

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.

Ways to use randomSquareFreeMonomialIdeal :

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

For the programmer