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 SimplicialHomology

compute the simplicial homology of a top simplices list

 Syntax
 ```SimplicialHomology(A: LIST): RECORD SimplicialHomology(A: LIST, B: LIST): RECORD```

 Description
This function computes the simplicial homology of a simplicial complex described by a list of top faces. With 2nd argument only with the second list of vertices.

Package GeomModelling, by Elisa Palezzato.

 Example
 ```/**/ Use QQ[x[1..5]], DegLex; --> DegLex ? /**/ L := [x[1]*x[2]*x[3], x[2]*x[3]*x[4], x[3]*x[4]*x[5]]; -- list top faces /**/ indent(SimplicialHomology(L)); record[ H_0 := record[betti := 1, lambda := []], H_i := [record[betti := 0, lambda := []]], H_max := record[betti := 0, lambda := []] ] -- 1 connected component (betti in H_0) /**/ L := [x[1]*x[2]*x[3], x[2]*x[3]*x[4]]; -- list top faces /**/ -- indent(SimplicialHomology(L)); --> Error: missing x[5] /**/ L := [x[1]*x[2]*x[3], x[2]*x[3]*x[4], x[5]]; /**/ indent(SimplicialHomology(L)); record[ H_0 := record[betti := 2, lambda := []], H_i := [record[betti := 0, lambda := []]], H_max := record[betti := 0, lambda := []] ] -- 2 connected components /**/ L := [x[1]*x[2]*x[3], x[2]*x[3]*x[4]]; /**/ indent( SimplicialHomology(L, [x[1], x[2], x[3], x[4]]) ); record[ H_0 := record[betti := 1, lambda := []], H_i := [record[betti := 0, lambda := []]], H_max := record[betti := 0, lambda := []] ] ```