Hello all,
Under friendly advice by Fidel Barrera, I have been trying to use Sage
for my research since about two monts ago. I work with graphs and posets
and simplicial complexes coming from them, and I had used GAP + GRAPE +
SimplicialHomology for that. With Sage, I like mostly the fact that one
can get pretty drawings of posets and graps "out of the box", and that
there seems to be active work on simplicial complexes.
Since before using Sage I knew no Python, I have been put off by all the
different types of objects when using simplicial complexes in Sage. I
have defined the following functions that seem to work, and I would
appreciate any comments you may have that would help me improve when
working with Sage.
Best regards,
Rafael
# a free face is one that is contained properly in exactly one maximal face
def is_free_face (S,s):
def f(x): return set(s)<=set(x)
return not (Simplex(s) in S.facets()) and len(filter(f,S.facets()))==1
# we find (if it exists) a free face of the smallest dimension, and remove it
def free_face_removed ( S ):
i = -1
S1 = deepcopy( S )
found = false
dim = S1.dimension()
faces = S1.faces()
while i < dim and not found:
j = 0
ifaces = list(faces[i])
while j < len(ifaces) and not found:
if is_free_face( S1 , ifaces[j] ):
found = True
print "removing ",ifaces[j]
S1.remove_face( ifaces[j] )
else:
j = j+1
i = i+1
return S1
# remove all free faces
def collapsed_complex ( S ):
S1 = S
S2 = free_face_removed( S )
while S1 <> S2:
S1 = S2
S2 = free_face_removed( S1 )
return S2
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