isElement -- test whether a ring element lies in a monomial ideal

• Usage:

  isElement(f, I)

• Inputs:
  • f, a ring element,
  • I, a monomial ideal,
• Outputs:
  • a Boolean value, whether f lies in I

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = monomialIdeal(x*y, x^3*z)

                          3
o2 = monomialIdeal (x*y, x z)

o2 : MonomialIdeal of R

i3 : isElement(x^2*y + x*y*z + x^3*z^3, I)

o3 = true

i4 : isElement(x*y^2 + x^3*y*z + z^2, I)

o4 = false