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

## Synopsis

• Usage:
I = randomIdeal(L,m)
• Inputs:
• L, a list, or sequence of positive integers
• m, , 1xn matrix of homogeneous polynomials in a ring S
• Outputs:
• I, an ideal, generated by random linear combinations of degrees given by L of the given polynomials

## Description

This function composes m with a random map from a free module with degrees specified by L to the source of m.

 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 : m = matrix{{a^3,b^4+c^4,d^5}} o4 = | a3 b4+c4 d5 | 1 3 o4 : Matrix S <--- S i5 : I=randomIdeal(L,m) 3 4 4 5 5 5 6 5 o5 = ideal (a , b + c , a*d + 42b*d - 27c*d + 41d - 2d e) o5 : Ideal of S

## Ways to use randomIdeal :

• "randomIdeal(List,Matrix)"
• "randomIdeal(Sequence,Matrix)"

## For the programmer

The object randomIdeal is .