linearSystemOnRationalSurface -- compute a linear system on a rational surface

• Usage:

  H=linearSystemOnRationalSurface(P2,d,L)

  H=linearSystemOnRationalSurface(points,d,L)

• Inputs:
  • P2, a ring, homogeneous coordinate ring of P2
  • points, a list, a list of ideals defining points in P2
  • d, an integer, degree of the desired forms
  • L, a list, {r_1,...,r_s} of multiplicities
• Outputs:
  • H, a matrix, a 1xn matrix whose entries are a bases of L(d;r_1p_1,...,r_sp_s)

i1 : kk=ZZ/nextPrime(10^3)

o1 = kk

o1 : QuotientRing

i2 : t=symbol t

o2 = t

o2 : Symbol

i3 : P2=kk[t_0..t_2]

o3 = P2

o3 : PolynomialRing

i4 : d=8

o4 = 8

i5 : L=toList(3:3)|toList(2:4)|{1}

o5 = {3, 3, 3, 4, 4, 1}

o5 : List

i6 : expectedDimension(d,L)

o6 = 6

i7 : betti(H=linearSystemOnRationalSurface(P2,d,L))

            0 1
o7 = total: 1 6
         0: 1 .
         1: . .
         2: . .
         3: . .
         4: . .
         5: . .
         6: . .
         7: . 6

o7 : BettiTally