def test_2d(self):
# one triangle
s = [[[0, 1, 2]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2]])
assert_equal(asc.simplices[1], [[0, 1], [0, 2], [1, 2]])
assert_equal(asc.simplices[2], [[0, 1, 2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0, 0, 0]])
assert_equal(B1, [[-1, -1, 0], [1, 0, -1], [0, 1, 1]])
assert_equal(B2, [[1], [-1], [1]])
# one triangle, one redundant edge
s = [[[0, 2]], [[0, 1, 2]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2]])
assert_equal(asc.simplices[1], [[0, 1], [0, 2], [1, 2]])
assert_equal(asc.simplices[2], [[0, 1, 2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0, 0, 0]])
assert_equal(B1, [[-1, -1, 0], [1, 0, -1], [0, 1, 1]])
assert_equal(B2, [[1], [-1], [1]])
# one triangle, two maximal edges
s = [[[0, 3], [4, 5]], [[0, 1, 2]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2], [3], [4], [5]])
assert_equal(asc.simplices[1],
[[0, 1], [0, 2], [0, 3], [1, 2], [4, 5]])
assert_equal(asc.simplices[2], [[0, 1, 2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0, 0, 0, 0, 0, 0]])
assert_equal(B1,
[[-1, -1, -1, 0, 0], [1, 0, 0, -1, 0], [0, 1, 0, 1, 0],
[0, 0, 1, 0, 0], [0, 0, 0, 0, -1], [0, 0, 0, 0, 1]])
assert_equal(B2, [[1], [-1], [0], [1], [0]])
def test_1d(self):
# two edges
s = [ [[0,1],[2,3]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2],[3]])
assert_equal(asc.simplices[1], [[0,1],[2,3]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0,0,0,0]])
assert_equal(B1, [[-1, 0],
[ 1, 0],
[ 0,-1],
[ 0, 1]])
# two edges, two redundant vertices
s = [ [[0],[2]], [[0,1],[2,3]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2],[3]])
assert_equal(asc.simplices[1], [[0,1],[2,3]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0,0,0,0]])
assert_equal(B1, [[-1, 0],
[ 1, 0],
[ 0,-1],
[ 0, 1]])
# two edges, two maximal vertices
s = [ [[2],[5]], [[0,1],[3,4]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2],[3],[4],[5]])
assert_equal(asc.simplices[1], [[0,1],[3,4]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0,0,0,0,0,0]])
assert_equal(B1, [[-1, 0],
[ 1, 0],
[ 0, 0],
[ 0,-1],
[ 0, 1],
[ 0, 0]])
def test_1d(self):
# two edges
s = [[[0, 1], [2, 3]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2], [3]])
assert_equal(asc.simplices[1], [[0, 1], [2, 3]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0, 0, 0, 0]])
assert_equal(B1, [[-1, 0], [1, 0], [0, -1], [0, 1]])
# two edges, two redundant vertices
s = [[[0], [2]], [[0, 1], [2, 3]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2], [3]])
assert_equal(asc.simplices[1], [[0, 1], [2, 3]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0, 0, 0, 0]])
assert_equal(B1, [[-1, 0], [1, 0], [0, -1], [0, 1]])
# two edges, two maximal vertices
s = [[[2], [5]], [[0, 1], [3, 4]]]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0], [1], [2], [3], [4], [5]])
assert_equal(asc.simplices[1], [[0, 1], [3, 4]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
assert_equal(B0, [[0, 0, 0, 0, 0, 0]])
assert_equal(B1, [[-1, 0], [1, 0], [0, 0], [0, -1], [0, 1], [0, 0]])
def test_2d(self):
# one triangle
s = [ [[0,1,2]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2]])
assert_equal(asc.simplices[1], [[0,1],[0,2],[1,2]])
assert_equal(asc.simplices[2], [[0,1,2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0,0,0]])
assert_equal(B1, [[-1,-1, 0],
[ 1, 0,-1],
[ 0, 1, 1]])
assert_equal(B2, [[ 1],
[-1],
[ 1]])
# one triangle, one redundant edge
s = [ [[0,2]], [[0,1,2]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2]])
assert_equal(asc.simplices[1], [[0,1],[0,2],[1,2]])
assert_equal(asc.simplices[2], [[0,1,2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0,0,0]])
assert_equal(B1, [[-1,-1, 0],
[ 1, 0,-1],
[ 0, 1, 1]])
assert_equal(B2, [[ 1],
[-1],
[ 1]])
# one triangle, two maximal edges
s = [ [[0,3],[4,5]], [[0,1,2]] ]
asc = abstract_simplicial_complex(s)
assert_equal(asc.simplices[0], [[0],[1],[2],[3],[4],[5]])
assert_equal(asc.simplices[1], [[0,1],[0,2],[0,3],[1,2],[4,5]])
assert_equal(asc.simplices[2], [[0,1,2]])
B0 = asc.chain_complex()[0].todense()
B1 = asc.chain_complex()[1].todense()
B2 = asc.chain_complex()[2].todense()
assert_equal(B0, [[0,0,0,0,0,0]])
assert_equal(B1, [[-1,-1,-1, 0, 0],
[ 1, 0, 0,-1, 0],
[ 0, 1, 0, 1, 0],
[ 0, 0, 1, 0, 0],
[ 0, 0, 0, 0,-1],
[ 0, 0, 0, 0, 1]])
assert_equal(B2, [[ 1],
[-1],
[ 0],
[ 1],
[ 0]])
