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RandomIdeals :: randomSparseIdeal

randomSparseIdeal -- randomSparseIdeal made from a given set of monomials

Synopsis

Description

Each generator of I is formed by randomly choosing s (the sparsity) entries of the matrix B and taking a random linear combinations with coefficients in the (ultimate) coefficient ring of S, the ring in which the monomials lie.

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing
i2 : S=kk[a..e]

o2 = S

o2 : PolynomialRing
i3 : L={3,3,4,6}

o3 = {3, 3, 4, 6}

o3 : List
i4 : B = matrix{{a^3,b^4,d^5,a*b*c,e}}

o4 = | a3 b4 d5 abc e |

             1       5
o4 : Matrix S  <--- S
i5 : I=randomSparseIdeal(B,3,2)

             3             4
o5 = ideal (a  + 35a*b*c, b  - 32a*b*c + 5e)

o5 : Ideal of S

See also

Ways to use randomSparseIdeal :