Boundary of Simplicial Complexes

FriCAS code

(1) -> FACTORY := SimplicialComplexFactory(Integer)

   (1)  SimplicialComplexFactory(Integer)
                                               Type: Type
(2) -> b1 := sphereSolid(2)$FACTORY

   (2)  points 1..3
          (1,2,3)
                   Type: FiniteSimplicialComplex(Integer)
(3) -> d1 := boundary(b1)

   (3)  points 1..3
           (1,2)
          -(1,3)
           (2,3)
                   Type: FiniteSimplicialComplex(Integer)
(4) -> z1 := boundary(d1)

   (4)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(5) -> b2 := sphereSolid(3)$FACTORY

   (5)  points 1..4
         (1,2,3,4)
                   Type: FiniteSimplicialComplex(Integer)
(6) -> d2 := boundary(b2)

   (6)  points 1..4
          (1,2,3)
         -(1,2,4)
          (1,3,4)
         -(2,3,4)
                    Type: FiniteSimplicialComplex(Integer)
(7) -> z2 := boundary(d2)

   (7)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(8) -> b3 := sphereSurface(2)$FACTORY

   (8)  points 1..3
           (1,2)
          -(1,3)
           (2,3)
                   Type: FiniteSimplicialComplex(Integer)
(9) -> d3 := boundary(b3)

   (9)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(10) -> z3 := boundary(d3)

   (10)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(11) -> b4 := sphereSurface(3)$FACTORY

   (11)  points 1..4
           (1,2,3)
          -(1,2,4)
           (1,3,4)
          -(2,3,4)
                    Type: FiniteSimplicialComplex(Integer)
(12) -> d4 := boundary(b4)

   (12)  [empty]
                    Type: FiniteSimplicialComplex(Integer)
(13) -> z4 := boundary(d4)

   (13)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(14) -> b5 := torusSurface()$FACTORY

   (14)  points 1..7
           (1,2,3)
           (2,3,5)
           (2,4,5)
           (2,4,7)
           (1,2,6)
           (2,6,7)
           (3,4,6)
           (3,5,6)
           (3,4,7)
           (1,3,7)
           (1,4,5)
           (1,4,6)
           (5,6,7)
           (1,5,7)
                   Type: FiniteSimplicialComplex(Integer)
(15) -> d5 := boundary(b5)

   (15)  points 1..7
           2*(1,2)
           2*(2,3)
          - 2*(2,5)
           2*(3,5)
           2*(2,4)
           2*(4,5)
          - 2*(2,7)
           2*(4,7)
          - 2*(1,6)
           2*(2,6)
           2*(6,7)
           2*(3,4)
          - 2*(3,6)
           2*(4,6)
           2*(5,6)
          - 2*(1,7)
           2*(1,4)
                  Type: FiniteSimplicialComplex(Integer)
(16) -> z5 := boundary(d5)

   (16)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(17) -> b6 := projectiveSpace(2)$FACTORY

   (17)  points 1..6
           (1,2,3)
           (1,3,4)
           (1,2,6)
           (1,5,6)
           (1,4,5)
           (2,3,5)
           (2,4,5)
           (2,4,6)
           (3,4,6)
           (3,5,6)
                   Type: FiniteSimplicialComplex(Integer)
(18) -> d6 := boundary(b6)

   (18)  points 1..6
           2*(1,2)
           2*(2,3)
           2*(3,4)
          - 2*(1,6)
           2*(5,6)
           2*(4,5)
          - 2*(2,5)
           2*(3,5)
           2*(2,4)
           2*(4,6)
          - 2*(3,6)
                   Type: FiniteSimplicialComplex(Integer)
(19) -> z6 := boundary(d6)

   (19)  [empty]
                   Type: FiniteSimplicialComplex(Integer)
(20) -> b7 := kleinBottle()$FACTORY

   (20)  points 1..8
           (3,4,8)
           (2,3,4)
           (2,4,6)
           (2,6,8)
           (2,5,8)
           (3,5,7)
           (2,3,7)
           (1,2,7)
           (1,2,5)
           (1,3,5)
           (4,5,8)
           (4,5,7)
           (4,6,7)
           (1,6,7)
           (1,3,6)
           (3,6,8)
                  Type: FiniteSimplicialComplex(Integer)
(21) -> d7 := boundary(b7)

   (21)  points 1..8
           2*(3,4)
          - 2*(3,8)
           2*(2,3)
           2*(4,6)
          - 2*(2,8)
           2*(6,8)
           2*(2,5)
           2*(5,8)
           2*(3,5)
           2*(5,7)
           2*(1,2)
          - 2*(1,7)
          - 2*(1,5)
           2*(1,3)
           2*(4,5)
          - 2*(4,7)
           2*(6,7)
           2*(3,6)
                   Type: FiniteSimplicialComplex(Integer)
(22) -> z7 := boundary(d7)

   (22)  [empty]
                   Type: FiniteSimplicialComplex(Integer)

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see also:
  • I have put the code here.
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