Hello,
I recently ran into an issue when trying to determine the number of fine,
regular triangulations of a point configuration. Using different methods
for obtaining the number of triangulations gives differing results.
Explicitly, I constructed my PointConfiguration and set the restrictions via
lp = LatticePolytope([[1,0,0],[1,2,0],[0,0,1],[-8,-24,9]])
pc = PointConfiguration(lp.points())
pc =
pc.restrict_to_fine_triangulations().restrict_to_regular_triangulations()
For reference, the full set of points in the polytope is [[1, 0, 0], [1, 2,
0], [0, 0, 1], [-8, -24, 9], [-1, -3, 2], [-2, -6, 3], [-3, -9, 4], [-4,
-12, 5], [-5, -15, 6], [-6, -18, 7], [-7, -21, 8], [0, -1, 1], [-1, -4, 2],
[-2, -7, 3], [-3, -10, 4], [-4, -13, 5], [-5, -16, 6], [1, 1, 0], [0, -2,
1], [-1, -5, 2], [-2, -8, 3]].
I computed the number of fine, regular triangulations via three methods as
shown below. All three were run in Sage 8.2, on an Ubuntu 18.04.1 LTS
64-bit system.
Method 1:
ct1 = 0
tris = pc.triangulations()
for _ in tris:
ct1 += 1
with open("test1.txt",'w') as f:
f.write(str(ct1))
Method 2:
data2 = list(pc.triangulations())
ct2 = len(data2)
with open("test2.txt",'w') as f:
f.write(str(ct2))
Method 3:
data3 = pc.triangulations_list()
ct3 = len(data3)
with open("test3.txt",'w') as f:
f.write(str(ct3))
The outputs that I got (that is, the contents of the files test1.txt,
test2.txt, and test3.txt) were:
Method 1: 2,004,662
Method 2: 1,966,238
Method 3: 1,750,907
In theory, shouldn't all three of these give the same result? I'm inclined
to use with the result of Method 1, as it agrees with a direct call to
points2nfinetriangs, but I'd like to understand the source of the
discrepancy/report this if it's a bug.
I should note, for anyone going to test these, that all three of these took
me about 6 hours to run. I'd give a quicker example if I could, but I
haven't yet run across one with this issue.
Thanks,
Jon
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