# Revision history [back]

### homology of simplicial complexes

I am building a simplicial complex as follows:

sage:S=range(1,7) sage:Z=SimplicialComplex([S]) sage:T=Z.n_skeleton(1) sage:T.faces() {0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6), (5, 6), (2, 6), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2), (1, 3), (4, 5), (1, 5), (1, 6)]), -1: set([()])} sage:T.homology() {0: 0, 1: Z^10}

So far everything seems good. Then I try adding a face to T. sage:T.add_face([1,2,6]) sage:T.faces()
{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6), (5, 6), (1, 5), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2), (1, 3), (1, 6), (2, 6), (4, 5)]), 2: set([(1, 2, 6)]), -1: set([()])}

So the face seems to have been added.

But then:

sage:T.homology()

results in:

{0: 0, 1: Z^10, 2: 0}

But this doesn't make any sense --- clearly it should say 0:0, 1:Z^9, 2:0, since adding a 2-face kills a class in $H_1(T)$.

Can anyone tell what I'm doing wrong?

### homology of simplicial complexes

I am building a simplicial complex as follows:

sage:S=range(1,7) sage:Z=SimplicialComplex([S]) sage:T=Z.n_skeleton(1) sage:T.faces() sage:S=range(1,7)

sage:Z=SimplicialComplex([S])

sage:T=Z.n_skeleton(1)

sage:T.faces()

{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6), (5, 6), (2, 6), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2), (1, 3), (4, 5), (1, 5), (1, 6)]), -1: set([()])} sage:T.homology() set([()])}

sage:T.homology()

{0: 0, 1: Z^10}

So far everything seems good. Then I try adding a face to T. sage:T.add_face([1,2,6]) T.

sage:T.faces()

{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6), (5, 6), (1, 5), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2), (1, 3), (1, 6), (2, 6), (4, 5)]), 2: set([(1, 2, 6)]), -1: set([()])}

So the face seems to have been added.

But then:

sage:T.homology()

results in:

{0: 0, 1: Z^10, 2: 0}

But this doesn't make any sense --- clearly it should say 0:0, 1:Z^9, 2:0, since adding a 2-face kills a class in $H_1(T)$.

Can anyone tell what I'm doing wrong?

 3 No.3 Revision slelievre 15579 ●19 ●144 ●307 http://carva.org/samue...

### homology of simplicial complexes

I am building a simplicial complex as follows:

sage:S=range(1,7)

sage:Z=SimplicialComplex([S])

sage:T=Z.n_skeleton(1)

sage:T.faces()

sage: S = range(1,7)
sage: Z = SimplicialComplex([S])
sage: T = Z.n_skeleton(1)
sage: T.faces()
{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6),
(5, 6), (2, 6), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2),
(1, 3), (4, 5), (1, 5), (1, 6)]), -1: set([()])} sage:T.homology() set([()])}
sage: T.homology()
{0: 0, 1: Z^10}Z^10}


So far everything seems good. Then I try adding a face to T.

sage:T.faces()

sage: T.add_face([1,2,6])
sage: T.faces()
{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6),
(5, 6), (1, 5), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2),
(1, 3), (1, 6), (2, 6), (4, 5)]), 2: set([(1, 2, 6)]), -1: set([()])}set([()])}


So the face seems to have been added.

But then:

sage:T.homology()

sage: T.homology()


results in:

{0: 0, 1: Z^10, 2: 0}0}


But this doesn't make any sense --- it should say 0:0, 1:Z^9, 2:0, 2:0, since adding a 2-face kills a class in $H_1(T)$.

Can anyone tell what I'm doing wrong?

 4 retagged tmonteil 25703 ●30 ●184 ●477 http://wiki.sagemath.o...

### homology of simplicial complexes

I am building a simplicial complex as follows:

sage: S = range(1,7)
sage: Z = SimplicialComplex([S])
sage: T = Z.n_skeleton(1)
sage: T.faces()
{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6),
(5, 6), (2, 6), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2),
(1, 3), (4, 5), (1, 5), (1, 6)]), -1: set([()])}
sage: T.homology()
{0: 0, 1: Z^10}


So far everything seems good. Then I try adding a face to T.

sage: T.add_face([1,2,6])
sage: T.faces()
{0: set([(4,), (5,), (3,), (1,), (6,), (2,)]), 1: set([(2, 4), (3, 6),
(5, 6), (1, 5), (1, 4), (3, 5), (3, 4), (2, 3), (4, 6), (2, 5), (1, 2),
(1, 3), (1, 6), (2, 6), (4, 5)]), 2: set([(1, 2, 6)]), -1: set([()])}


So the face seems to have been added.

But then:

sage: T.homology()


results in:

{0: 0, 1: Z^10, 2: 0}


But this doesn't make any sense --- it should say 0:0, 1:Z^9, 2:0, since adding a 2-face kills a class in $H_1(T)$.

Can anyone tell what I'm doing wrong?