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SimplicialHomology

Guides

  • SimplicialHomology

Symbols

  • BettiNumber
  • HomologyGroup
  • SimplicialAutomorphismGroup
  • SimplicialComplex
  • SimplicialCone
  • SimplicialIsomorphicQ
  • SimplicialJoin
  • SimplicialSuspension
  • SubComplexQ
Taggar`SimplicialHomology`
BettiNumber
​
BettiNumber
[
SimplicialComplex
[…],n]
computes the
n
th
Betti number of the given
SimplicialComplex
.
​
​
BettiNumber
[
SimplicialComplex
[…]]
computes all Betti numbers of the given
SimplicialComplex
.
​
Details and Options
▪
The following options can be given:
"Reduced"
False
whether to calculate reduced homology
"Coefficients"
Integers
coefficients over which to calculate homology
▪
"Coefficients" option takes the following values:
Integers
integers
Rationals
rational numbers
p
elements of finite field
p
​
Examples  
(8)
Basic Examples  
(3)
Calculate betti numbers of a space:
In[1]:=
BettiNumber

SimplicialComplex
["Circle"],0
Out[1]=
1
In[2]:=
BettiNumber

SimplicialComplex
["Circle"],1
Out[2]=
1
​
th
0
Betti number of two disjoint points demonstrating the number of connected components:
In[1]:=
BettiNumber

SimplicialComplex
[{{1},{2}}],0
Out[1]=
2
​
Their reduced Betti number:
In[1]:=
BettiNumber

SimplicialComplex
[{{1},{2}}],0,"Reduced"True
Out[1]=
1
Scope  
(1)

Options  
(2)

Applications  
(1)

Neat Examples  
(1)

SeeAlso
SimplicialComplex
 
▪
HomologyGroup
RelatedGuides
▪
SimplicialHomology
""

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