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



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

i1 : setRandomSeed(currentTime())

o1 = 1695883741
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*b*c)

o5 : Ideal of S
i6 : randomSquareFreeMonomialIdeal(5:2, S)

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

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.

See also

Ways to use randomSquareFreeMonomialIdeal :

For the programmer

The object randomSquareFreeMonomialIdeal is a method function.