lowerShadow -- the lower shadow of a subset of a poset

• Usage:

  lowerShadow(P,S)

• Inputs:
  • P, an instance of the type Poset,
  • S, a list, a subset of the ground set of the poset
• Outputs:
  • a list,

i1 : lowerShadow(divisorPoset 12, {12})

o1 = {4, 6}

o1 : List

i2 : S = QQ[x,y]/(x^4, y^4)

o2 = S

o2 : QuotientRing

i3 : x = S_0

o3 = x

o3 : S

i4 : y = S_1

o4 = y

o4 : S

i5 : lowerShadow(getPoset S, {x^3, x^2*y})

       2
o5 = {x , x*y}

o5 : List