/**/ 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 !!! as expected: 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 := []]
]
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