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# monomialIdeal(Matrix) -- monomial ideal of lead monomials

## Synopsis

• Function: monomialIdeal
• Usage:
monomialIdeal L
• Inputs:
• Outputs:
• , the monomial ideal of lead monomials of the elements of L

## Description

If L is a matrix, then it must have only one row. For all of these types, the result is generated by only the lead monomials given: no Gröbner bases are computed. See monomialIdeal(Ideal) if the lead monomials of a Gröbner basis is desired.
 i1 : R = ZZ/101[a,b,c]; i2 : I = monomialIdeal(a^3,b^3,c^3, a^2-b^2) 2 3 3 o2 = monomialIdeal (a , b , c ) o2 : MonomialIdeal of R i3 : M = monomialIdeal vars R o3 = monomialIdeal (a, b, c) o3 : MonomialIdeal of R i4 : J = monomialIdeal 0_R o4 = monomialIdeal () 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(2*x,3*y) o6 = monomialIdeal (x, y) o6 : MonomialIdeal of R