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^2b^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
