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Wolfram Language
SimplicialHomology
Guides
SimplicialHomology
Symbols
BettiNumber
HomologyGroup
SimplicialAutomorphismGroup
SimplicialComplex
SimplicialCone
SimplicialIsomorphicQ
SimplicialJoin
SimplicialLink
SimplicialProduct
SimplicialStar
SimplicialSuspension
SubComplexQ
Taggar`SimplicialHomology`
S
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S
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[
s
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m
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]
r
e
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s
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k
o
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s
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O
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i
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n
s
▪
s
c
must be a
S
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p
l
i
c
i
a
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C
o
m
p
l
e
x
and
s
i
g
m
a
must be a simplex in
s
c
.
▪
Link of
s
i
g
m
a
is the complex formed by all simplices that are disjoint from
s
i
g
m
a
and whose union with
s
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m
a
is a simplex of the complex.
Examples
(
4
)
Basic Examples
(
3
)
Link of a point of given square:
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[
1
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:
=
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[
{
{
1
,
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}
,
{
2
,
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}
,
{
3
,
4
}
,
{
1
,
4
}
}
]
,
{
1
}
O
u
t
[
1
]
=
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p
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c
i
a
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C
o
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p
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x
D
i
m
e
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s
i
o
n
:
0
V
e
r
t
i
c
e
s
:
2
Link of an interior vertex in a 2-Manifold:
I
n
[
1
]
:
=
S
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S
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p
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x
[
{
{
1
,
2
,
3
}
,
{
1
,
3
,
4
}
,
{
1
,
4
,
5
}
,
{
1
,
5
,
6
}
,
{
1
,
6
,
7
}
,
{
1
,
7
,
2
}
}
]
,
{
1
}
O
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t
[
1
]
=
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p
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c
i
a
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C
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p
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x
D
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s
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:
1
V
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s
:
6
I
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[
1
]
:
=
s
c
=
S
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m
p
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i
c
i
a
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C
o
m
p
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e
x
[
{
{
1
,
2
,
3
}
,
{
2
,
3
,
4
}
}
]
O
u
t
[
1
]
=
S
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m
p
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c
i
a
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C
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p
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x
D
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s
i
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:
2
V
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r
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s
:
4
Link of various simplices:
I
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[
2
]
:
=
S
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p
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i
a
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L
i
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k
[
s
c
,
{
1
}
]
O
u
t
[
2
]
=
S
i
m
p
l
i
c
i
a
l
C
o
m
p
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x
D
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s
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o
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:
1
V
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:
2
I
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[
3
]
:
=
S
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p
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c
i
a
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L
i
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k
[
s
c
,
{
2
}
]
O
u
t
[
3
]
=
S
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m
p
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c
i
a
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C
o
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p
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x
D
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s
i
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:
1
V
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:
3
I
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[
4
]
:
=
S
i
m
p
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i
c
i
a
l
L
i
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k
[
s
c
,
{
2
,
3
}
]
O
u
t
[
4
]
=
S
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m
p
l
i
c
i
a
l
C
o
m
p
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e
x
D
i
m
e
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s
i
o
n
:
0
V
e
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t
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c
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s
:
2
P
r
o
p
e
r
t
i
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s
&
R
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l
a
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i
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n
s
(
1
)
S
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A
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s
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▪
S
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"
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