The graded module of reduced homologies of C with coefficients in R.
i1 : R=ZZ[x_0..x_5]; |
i2 : D=simplicialComplex apply({{x_0, x_1, x_2}, {x_1, x_2, x_3}, {x_0, x_1, x_4}, {x_0, x_3, x_4}, {x_2, x_3, x_4}, {x_0, x_2, x_5}, {x_0, x_3, x_5}, {x_1, x_3, x_5}, {x_1, x_4, x_5}, {x_2, x_4, x_5}},face)
o2 = | x_2x_4x_5 x_1x_4x_5 x_1x_3x_5 x_0x_3x_5 x_0x_2x_5 x_2x_3x_4 x_0x_3x_4 x_0x_1x_4 x_1x_2x_3 x_0x_1x_2 |
o2 : SimplicialComplex
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i3 : homology(D)
o3 = -1 : cokernel | -1 -1 -1 -1 -1 -1 |
0 : subquotient (| 1 0 0 0 0 |, | 1 1 1 1 1 0 0 0 0 0 0
| 0 0 1 0 0 | | -1 0 0 0 0 1 1 1 1 0 0
| 0 1 0 0 0 | | 0 -1 0 0 0 -1 0 0 0 1 1
| 0 0 0 1 0 | | 0 0 -1 0 0 0 -1 0 0 -1 0
| -1 -1 0 0 1 | | 0 0 0 -1 0 0 0 -1 0 0 -1
| 0 0 -1 -1 -1 | | 0 0 0 0 -1 0 0 0 -1 0 0
0 0 0 0 |)
0 0 0 0 |
1 0 0 0 |
0 1 1 0 |
0 -1 0 1 |
-1 0 -1 -1 |
1 : subquotient (| 0 1 0 0 0 0 0 0 0 0 |, | -1 -1 0 0 0 0
| 1 0 0 0 0 0 0 0 0 0 | | 1 0 -1 0 0 0
| 0 -1 1 0 -1 0 1 0 1 0 | | 0 0 0 -1 -1 0
| 0 0 0 0 0 1 0 0 0 0 | | 0 1 0 1 0 0
| -1 0 -1 0 1 -1 -1 0 -1 0 | | 0 0 1 0 1 0
| 0 0 0 0 1 0 0 0 0 0 | | -1 0 0 0 0 -1
| 0 0 0 1 0 0 0 0 1 1 | | 0 0 0 0 0 1
| 0 1 -1 0 0 0 0 0 -1 0 | | 0 -1 0 0 0 0
| 0 0 1 -1 -1 0 0 0 0 -1 | | 0 0 0 0 0 0
| 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 -1
| 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0
| 1 0 0 0 1 0 0 -1 0 -1 | | 0 0 -1 0 0 0
| 0 -1 1 0 -1 0 1 1 2 1 | | 0 0 0 -1 0 0
| 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 -1 0
| 0 0 0 0 -1 1 1 1 1 2 | | 0 0 0 0 0 0
0 0 0 0 |)
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
-1 0 0 0 |
0 -1 0 0 |
1 1 0 0 |
0 0 -1 0 |
0 0 1 -1 |
0 0 0 1 |
0 0 -1 0 |
-1 0 0 0 |
0 -1 0 -1 |
2 : image 0
o3 : GradedModule
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i4 : homology(D,QQ)
o4 = -1 : cokernel | -1 -1 -1 -1 -1 -1 |
0 : subquotient (| -1 -1 -1 -1 -1 |, | 1 1 1 1 1 0 0 0 0 0 0
| 1 0 0 0 0 | | -1 0 0 0 0 1 1 1 1 0 0
| 0 1 0 0 0 | | 0 -1 0 0 0 -1 0 0 0 1 1
| 0 0 1 0 0 | | 0 0 -1 0 0 0 -1 0 0 -1 0
| 0 0 0 1 0 | | 0 0 0 -1 0 0 0 -1 0 0 -1
| 0 0 0 0 1 | | 0 0 0 0 -1 0 0 0 -1 0 0
0 0 0 0 |)
0 0 0 0 |
1 0 0 0 |
0 1 1 0 |
0 -1 0 1 |
-1 0 -1 -1 |
1 : subquotient (| 1 1 1 1 0 0 0 0 0 0 |, | -1 -1 0 0 0 0
| -1 0 0 0 1 1 1 0 0 0 | | 1 0 -1 0 0 0
| 0 -1 0 0 -1 0 0 1 1 0 | | 0 0 0 -1 -1 0
| 0 0 -1 0 0 -1 0 -1 0 1 | | 0 1 0 1 0 0
| 0 0 0 -1 0 0 -1 0 -1 -1 | | 0 0 1 0 1 0
| 1 0 0 0 0 0 0 0 0 0 | | -1 0 0 0 0 -1
| 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1
| 0 0 1 0 0 0 0 0 0 0 | | 0 -1 0 0 0 0
| 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0
| 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 -1
| 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0
| 0 0 0 0 0 0 1 0 0 0 | | 0 0 -1 0 0 0
| 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 -1 0 0
| 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 -1 0
| 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0
0 0 0 0 |)
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
0 0 0 0 |
-1 0 0 0 |
0 -1 0 0 |
1 1 0 0 |
0 0 -1 0 |
0 0 1 -1 |
0 0 0 1 |
0 0 -1 0 |
-1 0 0 0 |
0 -1 0 -1 |
2 : image 0
o4 : GradedModule
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i5 : homology(D,ZZ/2)
o5 = -1 : cokernel | 1 1 1 1 1 1 |
0 : subquotient (| 1 1 1 1 1 |, | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 |)
| 1 0 0 0 0 | | 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 |
| 0 1 0 0 0 | | 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 |
| 0 0 1 0 0 | | 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 |
| 0 0 0 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 0 1 0 0 0 1 0 0 1 0 1 1 |
1 : subquotient (| 1 1 1 1 0 0 0 0 0 0 |, | 1 1 0 0 0 0 0 0 0 0 |)
| 1 0 0 0 1 1 1 0 0 0 | | 1 0 1 0 0 0 0 0 0 0 |
| 0 1 0 0 1 0 0 1 1 0 | | 0 0 0 1 1 0 0 0 0 0 |
| 0 0 1 0 0 1 0 1 0 1 | | 0 1 0 1 0 0 0 0 0 0 |
| 0 0 0 1 0 0 1 0 1 1 | | 0 0 1 0 1 0 0 0 0 0 |
| 1 0 0 0 0 0 0 0 0 0 | | 1 0 0 0 0 1 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 1 0 0 0 |
| 0 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 0 0 |
| 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 1 0 0 |
| 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 1 0 |
| 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 1 |
| 0 0 0 0 0 0 1 0 0 0 | | 0 0 1 0 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 1 0 0 0 0 1 0 |
| 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 1 0 1 0 0 0 |
| 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 1 0 1 |
2 : image | 1 |
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o5 : GradedModule
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