i1 : A = QQ[a,b,c];
|
i2 : D = simplicialComplex({a*b*c})
o2 = simplicialComplex | abc |
o2 : SimplicialComplex
|
i3 : F3D = D;
|
i4 : F2D = simplicialComplex({a*b,a*c,b*c})
o4 = simplicialComplex | bc ac ab |
o4 : SimplicialComplex
|
i5 : F1D = simplicialComplex({a*b,c})
o5 = simplicialComplex | c ab |
o5 : SimplicialComplex
|
i6 : F0D = simplicialComplex({a,b})
o6 = simplicialComplex | b a |
o6 : SimplicialComplex
|
i7 : K = filteredComplex({F3D,F2D,F1D,F0D}, ReducedHomology => false)
o7 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0
-1 0 1 2
0 : image 0 <-- image | 1 0 | <-- image 0 <-- image 0
| 0 1 |
-1 | 0 0 | 1 2
0
1 : image 0 <-- image | 1 0 0 | <-- image | 1 | <-- image 0
| 0 1 0 | | 0 |
-1 | 0 0 1 | | 0 | 2
0 1
2 : image 0 <-- image | 1 0 0 | <-- image | 1 0 0 | <-- image 0
| 0 1 0 | | 0 1 0 |
-1 | 0 0 1 | | 0 0 1 | 2
0 1
3 3 1
3 : image 0 <-- QQ <-- QQ <-- QQ
-1 0 1 2
o7 : FilteredComplex
|
i8 : E = prune spectralSequence K
o8 = E
o8 : SpectralSequence
|
i9 : E^0
+-------+-------+-------+-------+
| 2 | 1 | | |
o9 = |QQ |QQ |0 |0 |
| | | | |
|{0, 0} |{1, 0} |{2, 0} |{3, 0} |
+-------+-------+-------+-------+
| | 1 | 2 | 1 |
|0 |QQ |QQ |QQ |
| | | | |
|{0, -1}|{1, -1}|{2, -1}|{3, -1}|
+-------+-------+-------+-------+
o9 : SpectralSequencePage
|
i10 : E^0 .dd
o10 = {3, -4} : 0 <----- 0 : {3, -3}
0
{-1, 0} : 0 <----- 0 : {-1, 1}
0
{3, -3} : 0 <----- 0 : {3, -2}
0
{-1, 1} : 0 <----- 0 : {-1, 2}
0
1
{3, -2} : 0 <----- QQ : {3, -1}
0
{-1, 2} : 0 <----- 0 : {-1, 3}
0
{2, -4} : 0 <----- 0 : {2, -3}
0
{2, -3} : 0 <----- 0 : {2, -2}
0
2
{2, -2} : 0 <----- QQ : {2, -1}
0
2
{2, -1} : QQ <----- 0 : {2, 0}
0
{1, -3} : 0 <----- 0 : {1, -2}
0
1
{1, -2} : 0 <----- QQ : {1, -1}
0
1 1
{1, -1} : QQ <----- QQ : {1, 0}
0
1
{1, 0} : QQ <----- 0 : {1, 1}
0
{0, -2} : 0 <----- 0 : {0, -1}
0
2
{0, -1} : 0 <----- QQ : {0, 0}
0
2
{0, 0} : QQ <----- 0 : {0, 1}
0
{0, 1} : 0 <----- 0 : {0, 2}
0
{3, -5} : 0 <----- 0 : {3, -4}
0
{-1, -1} : 0 <----- 0 : {-1, 0}
0
o10 : SpectralSequencePageMap
|
i11 : E^0
+-------+-------+-------+-------+
| 2 | 1 | | |
o11 = |QQ |QQ |0 |0 |
| | | | |
|{0, 0} |{1, 0} |{2, 0} |{3, 0} |
+-------+-------+-------+-------+
| | 1 | 2 | 1 |
|0 |QQ |QQ |QQ |
| | | | |
|{0, -1}|{1, -1}|{2, -1}|{3, -1}|
+-------+-------+-------+-------+
o11 : SpectralSequencePage
|
i12 : E^1
+-------+-------+-------+-------+
| 2 | 1 | | |
o12 = |QQ |QQ |0 |0 |
| | | | |
|{0, 0} |{1, 0} |{2, 0} |{3, 0} |
+-------+-------+-------+-------+
| | 1 | 2 | 1 |
|0 |QQ |QQ |QQ |
| | | | |
|{0, -1}|{1, -1}|{2, -1}|{3, -1}|
+-------+-------+-------+-------+
o12 : SpectralSequencePage
|
i13 : E^0 .dd_{1,0}
o13 = 0
1 1
o13 : Matrix QQ <-- QQ
|
i14 : E^1 .dd
o14 = {2, -3} : 0 <----- 0 : {3, -3}
0
{-2, 1} : 0 <----- 0 : {-1, 1}
0
{2, -2} : 0 <----- 0 : {3, -2}
0
{-2, 2} : 0 <----- 0 : {-1, 2}
0
2 1
{2, -1} : QQ <---------- QQ : {3, -1}
| 1 |
| -1 |
{-2, 3} : 0 <----- 0 : {-1, 3}
0
{1, -3} : 0 <----- 0 : {2, -3}
0
{1, -2} : 0 <----- 0 : {2, -2}
0
1 2
{1, -1} : QQ <------------- QQ : {2, -1}
| -1 -1 |
1
{1, 0} : QQ <----- 0 : {2, 0}
0
{0, -2} : 0 <----- 0 : {1, -2}
0
1
{0, -1} : 0 <----- QQ : {1, -1}
0
2 1
{0, 0} : QQ <---------- QQ : {1, 0}
| 1 |
| -1 |
{0, 1} : 0 <----- 0 : {1, 1}
0
{-1, -1} : 0 <----- 0 : {0, -1}
0
2
{-1, 0} : 0 <----- QQ : {0, 0}
0
{-1, 1} : 0 <----- 0 : {0, 1}
0
{-1, 2} : 0 <----- 0 : {0, 2}
0
{2, -4} : 0 <----- 0 : {3, -4}
0
{-2, 0} : 0 <----- 0 : {-1, 0}
0
o14 : SpectralSequencePageMap
|
i15 : E^1
+-------+-------+-------+-------+
| 2 | 1 | | |
o15 = |QQ |QQ |0 |0 |
| | | | |
|{0, 0} |{1, 0} |{2, 0} |{3, 0} |
+-------+-------+-------+-------+
| | 1 | 2 | 1 |
|0 |QQ |QQ |QQ |
| | | | |
|{0, -1}|{1, -1}|{2, -1}|{3, -1}|
+-------+-------+-------+-------+
o15 : SpectralSequencePage
|
i16 : E^0
+-------+-------+-------+-------+
| 2 | 1 | | |
o16 = |QQ |QQ |0 |0 |
| | | | |
|{0, 0} |{1, 0} |{2, 0} |{3, 0} |
+-------+-------+-------+-------+
| | 1 | 2 | 1 |
|0 |QQ |QQ |QQ |
| | | | |
|{0, -1}|{1, -1}|{2, -1}|{3, -1}|
+-------+-------+-------+-------+
o16 : SpectralSequencePage
|
i17 : E^2
+------+
| 1 |
o17 = |QQ |
| |
|{0, 0}|
+------+
o17 : SpectralSequencePage
|
i18 : prune HH K_infinity
o18 = -1 : 0
1
0 : QQ
1 : 0
2 : 0
o18 : GradedModule
|
i19 : E^infinity
+------+
| 1 |
o19 = |QQ |
| |
|{0, 0}|
+------+
o19 : Page
|