# ideal(MonomialIdeal) -- converts a monomial ideal to an ideal

## Synopsis

• Function: ideal
• Usage:
ideal I
• Inputs:
• I,
• Outputs:
• an ideal, which is generated by the monomials in I

## Description

 i1 : R = QQ[x,y,z]; i2 : I = monomialIdeal(x*y^2, x^2*z, y^2*z) 2 2 2 o2 = monomialIdeal (x*y , x z, y z) o2 : MonomialIdeal of R i3 : ideal I 2 2 2 o3 = ideal (x*y , x z, y z) o3 : Ideal of R

Most operations between ideals and monomial ideals automatically perform the necessary conversions, so one rarely needs to apply the function ideal to a monomial ideal.

 i4 : I * ideal I 2 4 3 2 4 3 2 4 2 2 2 2 4 2 2 2 4 2 o4 = ideal (x y , x y z, x*y z, x y z, x z , x y z , x*y z, x y z , y z ) o4 : Ideal of R i5 : I + ideal(x*y+y*z) 2 2 2 o5 = ideal (x*y , x z, y z, x*y + y*z) o5 : Ideal of R