# monomialIdeal(Ideal) -- monomial ideal of lead monomials of a Gröbner basis

## Synopsis

• Function: monomialIdeal
• Usage:
monomialIdeal J
• Inputs:
• Outputs:
• , the monomial ideal generated by the lead monomials of a Gröbner basis of J

## Description

J may also be a submodule of R^1, for R the ring of J.
 i1 : R = ZZ/101[a,b,c]; i2 : I = ideal(a^3,b^3,c^3, a^2-b^2) 3 3 3 2 2 o2 = ideal (a , b , c , a - b ) o2 : Ideal of R i3 : monomialIdeal I 2 2 3 3 o3 = monomialIdeal (a , a*b , b , c ) o3 : MonomialIdeal of R i4 : monomialSubideal I 3 2 2 3 3 o4 = monomialIdeal (a , a b, a*b , b , c ) o4 : MonomialIdeal of R
If the coefficient ring is ZZ, lead coefficients of the monomials are ignored.
 i5 : R = ZZ[x,y] o5 = R o5 : PolynomialRing i6 : monomialIdeal ideal(2*x,3*y) o6 = monomialIdeal (x, y) o6 : MonomialIdeal of R