i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing
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i2 : addCokerGrading(R)
o2 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o2 : Matrix ZZ <-- ZZ
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i3 : C0=simplex(R)
o3 = 4: x x x x x
0 1 2 3 4
o3 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0
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i4 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o4 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o4 : Ideal of R
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i5 : C=idealToComplex(I)
o5 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o5 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1
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i6 : embeddingComplex C
o6 = 4: x x x x x
0 1 2 3 4
o6 : complex of dim 4 embedded in dim 4 (printing facets)
equidimensional, simplicial
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i7 : idealToComplex(I,C0)
o7 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o7 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1
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i8 : complexToIdeal(C)
o8 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 0 4 3 4
o8 : Ideal of R
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i9 : cC=idealToCoComplex(I,C0)
o9 = 2: x x x x x x x x x x x x x x x
0 1 3 0 2 3 0 2 4 1 2 4 1 3 4
o9 : co-complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {0, 0, 0, 5, 5, 1}, Euler = 1
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i10 : cC==complement C
o10 = true
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i11 : I==coComplexToIdeal(cC)
o11 = true
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i12 : dualize cC
o12 = 1: v v v v v v v v v v
0 2 0 3 1 3 1 4 2 4
o12 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1
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