def betti(index: int, xs: Complex, subspace: Optional[Complex] = None) -> int:
def lists_from_complex(immutable: Complex) -> List[List[int]]:
return list([list(y for y in x) for x in immutable])
if subspace is not None:
return simplicialHomology(index,
lists_from_complex(xs),
lists_from_complex(subspace),
rankOnly=True)
else:
return simplicialHomology(index, lists_from_complex(xs), rankOnly=True)
H1=sh.localHomology(1,toplexes,[[1]])
H2=sh.localHomology(2,toplexes,[[1]])
if H0.shape[1] != 0 or H1.shape[1] != 0 or H2.shape[1] != 0:
print "Test 2b failed"
print "H0="+ H0.__repr__()
print "H1="+ H1.__repr__()
print "H2="+ H2.__repr__()
else:
print "Test 2b passed"
# Test 3: line segment localized to the star over a vertex
# (using relative homology, "by hand")
toplexes=[[1,2]]
H0=sh.simplicialHomology(0,toplexes,[[1]],True)
H1=sh.simplicialHomology(1,toplexes,[[1]],True)
H2=sh.simplicialHomology(2,toplexes,[[1]],True)
if H0 != 0 or H1 != 0 or H2 != 0:
print "Test 3a failed"
print "H0="+ str(H0)
print "H1="+ str(H1)
print "H2="+ str(H2)
else:
print "Test 3a passed"
H0=sh.simplicialHomology(0,toplexes,[[1]])
H1=sh.simplicialHomology(1,toplexes,[[1]])
H2=sh.simplicialHomology(2,toplexes,[[1]])
H1 = sh.localHomology(1, toplexes, [[1]])
H2 = sh.localHomology(2, toplexes, [[1]])
if H0.shape[1] != 0 or H1.shape[1] != 0 or H2.shape[1] != 0:
print "Test 2b failed"
print "H0=" + H0.__repr__()
print "H1=" + H1.__repr__()
print "H2=" + H2.__repr__()
else:
print "Test 2b passed"
# Test 3: line segment localized to the star over a vertex
# (using relative homology, "by hand")
toplexes = [[1, 2]]
H0 = sh.simplicialHomology(0, toplexes, [[1]], True)
H1 = sh.simplicialHomology(1, toplexes, [[1]], True)
H2 = sh.simplicialHomology(2, toplexes, [[1]], True)
if H0 != 0 or H1 != 0 or H2 != 0:
print "Test 3a failed"
print "H0=" + str(H0)
print "H1=" + str(H1)
print "H2=" + str(H2)
else:
print "Test 3a passed"
H0 = sh.simplicialHomology(0, toplexes, [[1]])
H1 = sh.simplicialHomology(1, toplexes, [[1]])
H2 = sh.simplicialHomology(2, toplexes, [[1]])
H1=sh.localHomology(toplexes,1,[[1]])
H2=sh.localHomology(toplexes,2,[[1]])
if H0.shape[1] != 0 or H1.shape[1] != 0 or H2.shape[1] != 0:
print "Test 2 failed"
print "H0="+ H0.__repr__()
print "H1="+ H1.__repr__()
print "H2="+ H2.__repr__()
else:
print "Test 2 passed"
# Test 3: line segment localized to the star over a vertex
# (using relative homology, "by hand")
toplexes=[[1,2]]
H0=sh.simplicialHomology(toplexes,0,[[1]])
H1=sh.simplicialHomology(toplexes,1,[[1]])
H2=sh.simplicialHomology(toplexes,2,[[1]])
if H0.shape[1] != 0 or H1.shape[1] != 0 or H2.shape[1] != 0:
print "Test 3 failed"
print "H0="+ H0.__repr__()
print "H1="+ H1.__repr__()
print "H2="+ H2.__repr__()
else:
print "Test 3 passed"
# Test 4: empty triangle localized to an edge
toplexes=[[1,2],[1,3],[2,3]]
H0=sh.localHomology(toplexes,0,[[1,2]])
