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RandomIdeals :: randomSquareFreeMonomialIdeal

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

Synopsis

Description

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

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.

See also

Ways to use randomSquareFreeMonomialIdeal :