isMonomialIdeal -- whether something is a monomial ideal

i1 : QQ[w,x,y,z];

i2 : I = minors(2, matrix{{w,x,y},{x,y,z}})

               2                        2
o2 = ideal (- x  + w*y, - x*y + w*z, - y  + x*z)

o2 : Ideal of QQ[w, x, y, z]

i3 : isMonomialIdeal I

o3 = false

i4 : J = ideal leadTerm I

             2        2
o4 = ideal (y , x*y, x )

o4 : Ideal of QQ[w, x, y, z]

i5 : isMonomialIdeal J

o5 = true

i6 : K = monomialIdeal I

                     2        2
o6 = monomialIdeal (x , x*y, y )

o6 : MonomialIdeal of QQ[w, x, y, z]

i7 : isMonomialIdeal K

o7 = true