testSplitting -- test a random Gorenstein set of points in P^3 for a factor

Synopsis

• Usage:

  testSplitting(S,hV,k)

• Inputs:

  • S, a ring, homogeneous coordinate ring of P³ over a finite field FF
  • hV, a list, the h-vector of the Gorenstein set of point
  • k, an integer, the degree of the desired subset defined over FF
• Outputs:

  • a Boolean value, true, if a (within the function) randomly choosen Gorenstein collection with h-vector hV in P³ splits of a subset of desired degree k ?

Description

i1 : S=ZZ/10009[x_0..x_3]

o1 = S

o1 : PolynomialRing

i2 : hV={1,3,6,10,6,3,1}

o2 = {1, 3, 6, 10, 6, 3, 1}

o2 : List

i3 : time tally apply(10,i->testSplitting(S,hV,10))
     -- used 0.214318 seconds

o3 = Tally{false => 6}
           true => 4

o3 : Tally