randomMonomialIdeal -- random monomial ideal with given degree generators

Synopsis

Usage:

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

Description

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

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..e]

o2 = S

o2 : PolynomialRing

i3 : L={3,5,7}

o3 = {3, 5, 7}

o3 : List

i4 : randomMonomialIdeal(L, S)

               2       3   6
o4 = ideal (a*b , a*c*d , c e)

o4 : Ideal of S

i5 : randomMonomialIdeal(5:2, S)

                                 2
o5 = ideal (a*c, a*d, a*b, c*e, c )

o5 : 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 randomMonomialIdeal :

randomMonomialIdeal(List,Ring)
randomMonomialIdeal(Sequence,Ring)

For the programmer