squareFree -- ideal of all square-free monomials of given degree

• Usage:

  I = squareFree(d,S)

• Inputs:
  • d, an integer, positive
  • S, a ring, Polynomial ring
• Outputs:
  • I, an ideal, all square-free monomials of degree d

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..e]

o2 = S

o2 : PolynomialRing

i3 : squareFree(3, S)

o3 = ideal (a*b*c, a*b*d, a*b*e, a*c*d, a*c*e, a*d*e, b*c*d, b*c*e, b*d*e,
     ------------------------------------------------------------------------
     c*d*e)

o3 : Ideal of S