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# randomSparseIdeal -- randomSparseIdeal made from a given set of monomials

## Synopsis

• Usage:
I = randomSparseIdeal(B,s,n)
• Inputs:
• B, , 1xn matrix of monomials
• s, an integer, positive integer, the number of terms in the generators of I
• n, an integer, positive integer, the number of generators of I
• Outputs:
• I, an ideal, generated by n polynomials, each a random linear combination of s monomials

## 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

## Ways to use randomSparseIdeal :

• "randomSparseIdeal(Matrix,ZZ,ZZ)"

## For the programmer

The object randomSparseIdeal is .