This triangulation of the real projective plane has 6 vertices, 15 edges and 10 triangles.
i1 : R = ZZ[a..f] o1 = R o1 : PolynomialRing |
i2 : 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)
o2 = | def aef bdf bcf acf cde bce abe acd abd |
o2 : SimplicialComplex
|
i3 : faces(-1,D)
o3 = | 1 |
1 1
o3 : Matrix R <--- R
|
i4 : faces(0,D)
o4 = | a b c d e f |
1 6
o4 : Matrix R <--- R
|
i5 : faces(1,D)
o5 = | ab ac ad ae af bc bd be bf cd ce cf de df ef |
1 15
o5 : Matrix R <--- R
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i6 : faces(2,D)
o6 = | abd abe acd acf aef bce bcf bdf cde def |
1 10
o6 : Matrix R <--- R
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i7 : fVector D
o7 = HashTable{-1 => 1}
0 => 6
1 => 15
2 => 10
o7 : HashTable
|