# generators(Ideal) -- the generator matrix of an ideal

## Synopsis

• Function: generators
• Usage:
generators I
gens I
• Inputs:
• Optional inputs:
• Outputs:
• , the one-row matrix whose entries are the generators of I

## Description

Each ideal in Macaulay2 comes equipped with a one-row matrix with the generators of the ideal. It is this matrix that is returned.
 i1 : R = ZZ/101[a,b,c]; i2 : I = ideal(a^2,a*b-2,c^4,a*c-1,a*c-1) 2 4 o2 = ideal (a , a*b - 2, c , a*c - 1, a*c - 1) o2 : Ideal of R i3 : generators I o3 = | a2 ab-2 c4 ac-1 ac-1 | 1 5 o3 : Matrix R <--- R
To obtain a list of generators, rather than a matrix, use
 i4 : first entries generators I 2 4 o4 = {a , a*b - 2, c , a*c - 1, a*c - 1} o4 : List
If you want to remove unnecessary generators, use trim.
 i5 : I = trim I 2 o5 = ideal (a*c - 1, a*b - 2, a ) o5 : Ideal of R i6 : gens I o6 = | ac-1 ab-2 a2 | 1 3 o6 : Matrix R <--- R