Product of Chain Complexes

(1) -> p1:List(List(NNI)) := [[1::NNI,2::NNI]]

   (1)  [[1, 2]]
                               Type: List(List(NonNegativeInteger))
(2) -> p2:List(List(NNI)) := [[1::NNI,2::NNI]]

   (2)  [[1, 2]]
                               Type: List(List(NonNegativeInteger))
(3) -> ASIMP := FiniteSimplicialComplex(Integer)

   (3)  FiniteSimplicialComplex(Integer)
                                                         Type: Type
(4) -> c1 := simplicialComplex([],2,p1)$ASIMP

   (4)  points 1..2
          (1, 2)
                             Type: FiniteSimplicialComplex(Integer)
(5) -> c2 := simplicialComplex([],2,p2)$ASIMP

   (5)  points 1..2
          (1, 2)
                             Type: FiniteSimplicialComplex(Integer)
(6) -> c3 := product(c1,c2)

   (6)  points 1..4
         (1, 2, 4)
         (1, 3, 4)
                             Type: FiniteSimplicialComplex(Integer)
(7) -> chain c1

                + 1 +
   (7)  [0  0], |   |, []
                +- 1+
                                                 Type: ChainComplex
(8) -> chain c2

                + 1 +
   (8)  [0  0], |   |, []
                +- 1+
                                                 Type: ChainComplex
(9) -> chain c3

                                                 + 1    0 +
                      + 1    1    1    0    0 +  |        |
                      |                       |  | 0    1 |
                      |- 1   0    0    1    0 |  |        |  ++
   (9)  [0  0  0  0], |                       |, |- 1  - 1|, ||
                      | 0   - 1   0    0    1 |  |        |  ++
                      |                       |  | 1    0 |
                      + 0    0   - 1  - 1  - 1+  |        |
                                                 + 0    1 +
                                                 Type: ChainComplex
(10) -> 

Installing and Running Code

To run this code on FriCAS goto github here and download the following files.

Then compile them in FriCAS as follows:

)co logic
)co graph
)boot $bootStrapMode := true
)co alg_top
)boot $bootStrapMode := false
)co alg_top
)co gpresent