finite simplicial complexes, projective spaces, facets, giving strange output
The code
n=2; x=simplicial_complexes.RealProjectiveSpace(n);
fcts=x.facets(); out=file('P'+str(n)+'.txt','w');
for a in fcts: out.write(str(a)+'\n')
out.close();
writes a nice result in the file P2.txt:
(0, 2, 3)
(0, 3, 4)
(0, 1, 5)
(0, 4, 5)
(2, 3, 5)
(1, 2, 4)
(0, 1, 2)
(1, 3, 4)
(1, 3, 5)
(2, 4, 5)
This works for $n=1,\ldots,4$. However, for $n=5$, the file contains
((1, 5, 6), (1, 6), (1, 3, 5, 6), (6,), (2,), (2, 4))
((1, 2, 4, 6), (5,), (1, 4), (3, 5), (4,), (1, 4, 6))
((3, 4, 6), (1, 3, 4, 5, 6), (4, 6), (1, 3, 4, 6), (6,), (2,))
((1, 5, 6), (1, 2, 3, 4, 5, 6), (1, 3, 5, 6), (1,), (1, 5), (1, 3, 4, 5, 6))
((1, 6), (1, 3, 5, 6), (1,), (1, 2, 3, 5, 6), (1, 3, 6), (4,))
((1, 2), (3,), (3, 5, 6), (1, 2, 4), (3, 5), (2,))
((1, 2), (1,), (3,), (3, 6), (1, 2, 4), (1, 2, 4, 5))
((1, 2), (1,), (1, 2, 3, 6), (4, 5), (1, 2, 6), (4,))
((2, 3, 4), (2, 3, 4, 5), (1, 2, 3, 4, 5), (2, 3), (6,), (2,))
((1, 3, 4, 5), (1, 3, 4, 5, 6), (5,), (3, 5), (2,), (3, 4, 5))
...
What am I doing wrong here? Why don't I get a list of 5-dimensional simplices? I would like to obtain only the facets of the first 10 projective spaces.
That's because the vertices are no longer integers, but rather tuples of integers.
@FrédéricC Not even that, since some tuples end in a comma, not an integer. Anyway, how can I get maximal simplices which have integers for vertices?
Tuples with only one element have a final comma in python :
"I would like to obtain only the facets of the first 10 projective spaces." Please look at the documentation. When
nis at least 5, there will be(n+2)!/2facets in Sage's triangulation of n-dimensional real projective space. Whenn=10, this will produce over 200 million facets.