lines through >=3 vertices: 9 ; vertices per line: [4, 4, 4, 4, 4, 4, 4, 4, 4]
lines per vertex: [3]
groups (triples, no two on a common line): [('d0', 'd1', 'dinf'), ('g0', 'g1', 'ginf'), ('h0', 'h1', 'hinf'), ('v0', 'v1', 'vinf')]
group ('d0', 'd1', 'dinf') : distinct member sets over the 6 labellings = 1
group ('g0', 'g1', 'ginf') : distinct member sets over the 6 labellings = 1
group ('h0', 'h1', 'hinf') : distinct member sets over the 6 labellings = 1
group ('v0', 'v1', 'vinf') : distinct member sets over the 6 labellings = 1
number of cubics: 8
my 8 cubics == BHRS p.7 list (up to scalars): True
all 8 cubics smooth (rank of partials x quadrics in degree 4 = 15)
each cubic through exactly the 9 vertices of its Lambda_t; at each vertex 6 cubics, 2 directions, 3 cubics (3 distinct pencils) per direction: True
pairs of cubics: sum of local intersection multiplicities at common vertices == 9 for all pairs: True
   histogram (same pencil?, multiplicities at common vertices): count
      (False, (1, 1, 1, 2, 2, 2)) 24
      (True, (1, 1, 1, 1, 1, 1, 1, 1, 1)) 4
time so far 1.0s
t =  7 : dim S_t =  36, exact rank of the 60 conditions = 36, h^1(I_Z(t)) = 24, dim I_t =   0
t =  8 : dim S_t =  45, exact rank of the 60 conditions = 45, h^1(I_Z(t)) = 15, dim I_t =   0
t =  9 : dim S_t =  55, exact rank of the 60 conditions = 52, h^1(I_Z(t)) =  8, dim I_t =   3
t = 10 : dim S_t =  66, exact rank of the 60 conditions = 57, h^1(I_Z(t)) =  3, dim I_t =   9
t = 11 : dim S_t =  78, exact rank of the 60 conditions = 60, h^1(I_Z(t)) =  0, dim I_t =  18
t = 12 : dim S_t =  91, exact rank of the 60 conditions = 60, h^1(I_Z(t)) =  0, dim I_t =  31
t = 13 : dim S_t = 105, exact rank of the 60 conditions = 60, h^1(I_Z(t)) =  0, dim I_t =  45
time so far 6.4s
primes used: [1000003, 1000033]
[p=1000003] Z-ranks mod p equal the exact ranks for t=7..13: True
[p=1000003] 3Z: t=20, #conditions=396, dim S_t=231, rank=231, dim I(3Z)_t (mod p) = 0
[p=1000003] 3Z: t=21, #conditions=396, dim S_t=253, rank=253, dim I(3Z)_t (mod p) = 0
[p=1000003] 3Z: t=22, #conditions=396, dim S_t=276, rank=276, dim I(3Z)_t (mod p) = 0
[p=1000003] 3Z: t=23, #conditions=396, dim S_t=300, rank=300, dim I(3Z)_t (mod p) = 0
[p=1000003] 3Z: t=24, #conditions=396, dim S_t=325, rank=324, dim I(3Z)_t (mod p) = 1
[p=1000003] 3Z: t=25, #conditions=396, dim S_t=351, rank=348, dim I(3Z)_t (mod p) = 3
[p=1000003] C_3 (product of the 8 cubics) satisfies all 3Z conditions: True
[p=1000003] t=24: #products=2539, rank (I^2)_t mod p = 133, dim I(2Z)_t mod p = 133, dim I(3Z)_t mod p = 1, I(3Z)_t inside span of products: True
[p=1000003] t=25: #products=3438, rank (I^2)_t mod p = 159, dim I(2Z)_t mod p = 159, dim I(3Z)_t mod p = 3, I(3Z)_t inside span of products: True
[p=1000003] t=26: #products=6423, rank (I^2)_t mod p = 186, dim I(2Z)_t mod p = 186, dim I(3Z)_t mod p = 6, I(3Z)_t inside span of products: True
[p=1000003] time 3.1s
[p=1000033] Z-ranks mod p equal the exact ranks for t=7..13: True
[p=1000033] 3Z: t=20, #conditions=396, dim S_t=231, rank=231, dim I(3Z)_t (mod p) = 0
[p=1000033] 3Z: t=21, #conditions=396, dim S_t=253, rank=253, dim I(3Z)_t (mod p) = 0
[p=1000033] 3Z: t=22, #conditions=396, dim S_t=276, rank=276, dim I(3Z)_t (mod p) = 0
[p=1000033] 3Z: t=23, #conditions=396, dim S_t=300, rank=300, dim I(3Z)_t (mod p) = 0
[p=1000033] 3Z: t=24, #conditions=396, dim S_t=325, rank=324, dim I(3Z)_t (mod p) = 1
[p=1000033] 3Z: t=25, #conditions=396, dim S_t=351, rank=348, dim I(3Z)_t (mod p) = 3
[p=1000033] C_3 (product of the 8 cubics) satisfies all 3Z conditions: True
[p=1000033] t=24: #products=2539, rank (I^2)_t mod p = 133, dim I(2Z)_t mod p = 133, dim I(3Z)_t mod p = 1, I(3Z)_t inside span of products: True
[p=1000033] t=25: #products=3438, rank (I^2)_t mod p = 159, dim I(2Z)_t mod p = 159, dim I(3Z)_t mod p = 3, I(3Z)_t inside span of products: True
[p=1000033] t=26: #products=6423, rank (I^2)_t mod p = 186, dim I(2Z)_t mod p = 186, dim I(3Z)_t mod p = 6, I(3Z)_t inside span of products: True
[p=1000033] time 2.5s
DST test: dim J_a mod p for a=3..6: [0, 3, 9, 16]
DST test: F in J^(3) (all 2nd-order Taylor coefficients vanish at the 12 vertices): True
DST test: rank (J^2)_9 = 18, with F added = 19  ->  F in J^2 (mod p): False  (expected False)
total time 12.0s
