Created
November 16, 2016 16:07
-
-
Save pbelmans/46f0250073aadcebca254c00238a96b1 to your computer and use it in GitHub Desktop.
Understanding normalisation and basic properties of weighted projective spaces
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import itertools | |
def reduce(Q): | |
return tuple([qi / gcd(Q) for qi in Q]) | |
def normalise(Q): | |
Q = reduce(Q) | |
D = [gcd(Q[:i] + Q[i+1:]) for i in range(len(Q))] | |
A = [lcm(D[:i] + D[i+1:]) for i in range(len(Q))] | |
a = lcm(A) | |
return tuple([qi / ai for (qi, ai) in zip(Q, A)]) | |
def isNormalised(Q): | |
return Q == normalise(Q) | |
def isGorenstein(Q): | |
return sum(Q) % lcm(Q) == 0 | |
bound = 20 | |
dimension = 2 | |
#bound = 25 | |
#dimension = 3 | |
weights = itertools.product(range(1, bound), repeat=dimension+1) | |
weights = filter(lambda Q: Q == tuple(sorted(Q)), weights) | |
normalised = filter(isNormalised, weights) | |
Gorenstein = filter(isGorenstein, normalised) | |
print len(normalised) | |
print len(Gorenstein), Gorenstein |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment