-- -*- M2-comint -*- {* hash: -1656762422 *}

i1 : loadPackage "SimplicialComplexes";

i2 : R = ZZ[a..d];

i3 : D = simplicialComplex {a*b*c*d}

o3 = | abcd |

o3 : SimplicialComplex

i4 : boundary(0,D)

o4 = | 1 1 1 1 |

              1        4
o4 : Matrix ZZ  <--- ZZ

i5 : faces(0,D)

o5 = | a b c d |

             1       4
o5 : Matrix R  <--- R

i6 : boundary(1,D)

o6 = | -1 -1 -1 0  0  0  |
     | 1  0  0  -1 -1 0  |
     | 0  1  0  1  0  -1 |
     | 0  0  1  0  1  1  |

              4        6
o6 : Matrix ZZ  <--- ZZ

i7 : faces(1,D)

o7 = | ab ac ad bc bd cd |

             1       6
o7 : Matrix R  <--- R

i8 : boundary(2,D)

o8 = | 1  1  0  0  |
     | -1 0  1  0  |
     | 0  -1 -1 0  |
     | 1  0  0  1  |
     | 0  1  0  -1 |
     | 0  0  1  1  |

              6        4
o8 : Matrix ZZ  <--- ZZ

i9 : faces(2,D)

o9 = | abc abd acd bcd |

             1       4
o9 : Matrix R  <--- R

i10 : boundary(3,D)

o10 = | -1 |
      | 1  |
      | -1 |
      | 1  |

               4        1
o10 : Matrix ZZ  <--- ZZ

i11 : faces(3,D)

o11 = | abcd |

              1       1
o11 : Matrix R  <--- R

i12 : boundary(4,D)

o12 = 0

               1
o12 : Matrix ZZ  <--- 0

i13 : R = QQ[a..f];

i14 : D = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f,b*c*d,b*d*e,b*e*f,c*d*f,c*e*f);

i15 : boundary(1,D)

o15 = | -1 -1 -1 -1 -1 0  0  0  0  0  0  0  0  0  0  |
      | 1  0  0  0  0  -1 -1 -1 -1 0  0  0  0  0  0  |
      | 0  1  0  0  0  1  0  0  0  -1 -1 -1 0  0  0  |
      | 0  0  1  0  0  0  1  0  0  1  0  0  -1 -1 0  |
      | 0  0  0  1  0  0  0  1  0  0  1  0  1  0  -1 |
      | 0  0  0  0  1  0  0  0  1  0  0  1  0  1  1  |

               6        15
o15 : Matrix QQ  <--- QQ

i16 : R' = ZZ/2[a..f];

i17 : D' = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f,b*c*d,b*d*e,b*e*f,c*d*f,c*e*f);

i18 : boundary(1,D')

o18 = | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 |
      | 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 |
      | 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 |
      | 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 |
      | 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 |
      | 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 |

              ZZ 6       ZZ 15
o18 : Matrix (--)  <--- (--)
               2          2

i19 :