i1 : A = QQ[a,b,c,d];
|
i2 : D = simplicialComplex {a*d*c, a*b, a*c, b*c};
|
i3 : F2D = D
o3 = simplicialComplex | bc ab acd |
o3 : SimplicialComplex
|
i4 : F1D = simplicialComplex {a*c, d}
o4 = simplicialComplex | d ac |
o4 : SimplicialComplex
|
i5 : F0D = simplicialComplex {a,d}
o5 = simplicialComplex | d a |
o5 : SimplicialComplex
|
i6 : K= filteredComplex({F2D, F1D, F0D},ReducedHomology => false)
o6 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0
-1 0 1 2
0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0
| 0 0 |
-1 | 0 0 | 1 2
| 0 1 |
0
1 : image 0 <-- image | 1 0 0 | <-- image | 0 | <-- image 0
| 0 0 0 | | 1 |
-1 | 0 1 0 | | 0 | 2
| 0 0 1 | | 0 |
| 0 |
0
1
4 5 1
2 : image 0 <-- QQ <-- QQ <-- QQ
-1 0 1 2
o6 : FilteredComplex
|
i7 : E = prune spectralSequence(K)
o7 = E
o7 : SpectralSequence
|
i8 : E^0
+-------+-------+-------+
| 2 | 1 | 1 |
o8 = |QQ |QQ |QQ |
| | | |
|{0, 0} |{1, 0} |{2, 0} |
+-------+-------+-------+
| | 1 | 4 |
|0 |QQ |QQ |
| | | |
|{0, -1}|{1, -1}|{2, -1}|
+-------+-------+-------+
| | | 1 |
|0 |0 |QQ |
| | | |
|{0, -2}|{1, -2}|{2, -2}|
+-------+-------+-------+
o8 : SpectralSequencePage
|
i9 : E^1
+-------+-------+-------+
| 2 | | |
o9 = |QQ |0 |0 |
| | | |
|{0, 0} |{1, 0} |{2, 0} |
+-------+-------+-------+
| | | 2 |
|0 |0 |QQ |
| | | |
|{0, -1}|{1, -1}|{2, -1}|
+-------+-------+-------+
o9 : SpectralSequencePage
|
i10 : E^2
+-------+-------+-------+
| 2 | | |
o10 = |QQ |0 |0 |
| | | |
|{0, 0} |{1, 0} |{2, 0} |
+-------+-------+-------+
| | | 2 |
|0 |0 |QQ |
| | | |
|{0, -1}|{1, -1}|{2, -1}|
+-------+-------+-------+
o10 : SpectralSequencePage
|
i11 : E^3
+-------+-------+-------+
| 1 | | |
o11 = |QQ |0 |0 |
| | | |
|{0, 0} |{1, 0} |{2, 0} |
+-------+-------+-------+
| | | 1 |
|0 |0 |QQ |
| | | |
|{0, -1}|{1, -1}|{2, -1}|
+-------+-------+-------+
o11 : SpectralSequencePage
|
i12 : E^infinity
+-------+-------+-------+
| 1 | | |
o12 = |QQ |0 |0 |
| | | |
|{0, 0} |{1, 0} |{2, 0} |
+-------+-------+-------+
| | | 1 |
|0 |0 |QQ |
| | | |
|{0, -1}|{1, -1}|{2, -1}|
+-------+-------+-------+
o12 : Page
|
i13 : C = K_infinity
4 5 1
o13 = image 0 <-- QQ <-- QQ <-- QQ
-1 0 1 2
o13 : ChainComplex
|
i14 : prune HH C
o14 = -1 : 0
1
0 : QQ
1
1 : QQ
2 : 0
o14 : GradedModule
|
i15 : E^2 .dd
o15 = {-3, 2} : 0 <----- 0 : {-1, 1}
0
{-3, 3} : 0 <----- 0 : {-1, 2}
0
{-3, 4} : 0 <----- 0 : {-1, 3}
0
{0, -2} : 0 <----- 0 : {2, -3}
0
{0, -1} : 0 <----- 0 : {2, -2}
0
2 2
{0, 0} : QQ <------------ QQ : {2, -1}
| 0 1 |
| 0 -1 |
{0, 1} : 0 <----- 0 : {2, 0}
0
{-1, -1} : 0 <----- 0 : {1, -2}
0
{-1, 0} : 0 <----- 0 : {1, -1}
0
{-1, 1} : 0 <----- 0 : {1, 0}
0
{-1, 2} : 0 <----- 0 : {1, 1}
0
{-2, 0} : 0 <----- 0 : {0, -1}
0
2
{-2, 1} : 0 <----- QQ : {0, 0}
0
{-2, 2} : 0 <----- 0 : {0, 1}
0
{-2, 3} : 0 <----- 0 : {0, 2}
0
{-3, 1} : 0 <----- 0 : {-1, 0}
0
o15 : SpectralSequencePageMap
|