A map of complexes stores its component maps.
i1 : S = ZZ/101[a,b,c]; |
i2 : C = freeResolution coker vars S
1 3 3 1
o2 = S <-- S <-- S <-- S
0 1 2 3
o2 : Complex
|
i3 : g1 = id_C
1 1
o3 = 0 : S <--------- S : 0
| 1 |
3 3
1 : S <----------------- S : 1
{1} | 1 0 0 |
{1} | 0 1 0 |
{1} | 0 0 1 |
3 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o3 : ComplexMap
|
i4 : g2 = randomComplexMap(C[1], C[2], Boundary => true)
1
o4 = -2 : 0 <----- S : -2
0
1 3
-1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
3 3
0 : S <------------------------------------------------- S : 0
{1} | 19a+7b-24c -29a-16b-26c 5b |
{1} | 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 14a-34b 40a-21b+29c -19a+25b+10c |
3 1
1 : S <------------------------ S : 1
{2} | 34a+16b-29c |
{2} | 19a-39b-24c |
{2} | -47a-21b-38c |
o4 : ComplexMap
|
i5 : f = g1 ++ g2
1
o5 = -2 : 0 <----- S : -2
0
1 3
-1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
4 4
0 : S <--------------------------------------------------- S : 0
{0} | 1 0 0 0 |
{1} | 0 19a+7b-24c -29a-16b-26c 5b |
{1} | 0 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 0 14a-34b 40a-21b+29c -19a+25b+10c |
6 4
1 : S <------------------------------ S : 1
{1} | 1 0 0 0 |
{1} | 0 1 0 0 |
{1} | 0 0 1 0 |
{2} | 0 0 0 34a+16b-29c |
{2} | 0 0 0 19a-39b-24c |
{2} | 0 0 0 -47a-21b-38c |
4 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
{3} | 0 0 0 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o5 : ComplexMap
|
i6 : assert isWellDefined f |
i7 : L = components f
1 1
o7 = {0 : S <--------- S : 0 ,
| 1 |
3 3
1 : S <----------------- S : 1
{1} | 1 0 0 |
{1} | 0 1 0 |
{1} | 0 0 1 |
3 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : S <------------- S : 3
{3} | 1 |
------------------------------------------------------------------------
1
-2 : 0 <----- S : -2 }
0
1 3
-1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
3 3
0 : S <------------------------------------------------- S : 0
{1} | 19a+7b-24c -29a-16b-26c 5b |
{1} | 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 14a-34b 40a-21b+29c -19a+25b+10c |
3 1
1 : S <------------------------ S : 1
{2} | 34a+16b-29c |
{2} | 19a-39b-24c |
{2} | -47a-21b-38c |
o7 : List
|
i8 : L_0 === g1 o8 = true |
i9 : L_1 === g2 o9 = true |
i10 : indices f
o10 = {0, 1}
o10 : List
|
i11 : f' = (greg => g1) ++ (mike => g2)
1
o11 = -2 : 0 <----- S : -2
0
1 3
-1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
4 4
0 : S <--------------------------------------------------- S : 0
{0} | 1 0 0 0 |
{1} | 0 19a+7b-24c -29a-16b-26c 5b |
{1} | 0 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 0 14a-34b 40a-21b+29c -19a+25b+10c |
6 4
1 : S <------------------------------ S : 1
{1} | 1 0 0 0 |
{1} | 0 1 0 0 |
{1} | 0 0 1 0 |
{2} | 0 0 0 34a+16b-29c |
{2} | 0 0 0 19a-39b-24c |
{2} | 0 0 0 -47a-21b-38c |
4 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
{3} | 0 0 0 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o11 : ComplexMap
|
i12 : components f'
1 1
o12 = {0 : S <--------- S : 0 ,
| 1 |
3 3
1 : S <----------------- S : 1
{1} | 1 0 0 |
{1} | 0 1 0 |
{1} | 0 0 1 |
3 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : S <------------- S : 3
{3} | 1 |
-----------------------------------------------------------------------
1
-2 : 0 <----- S : -2 }
0
1 3
-1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
3 3
0 : S <------------------------------------------------- S : 0
{1} | 19a+7b-24c -29a-16b-26c 5b |
{1} | 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 14a-34b 40a-21b+29c -19a+25b+10c |
3 1
1 : S <------------------------ S : 1
{2} | 34a+16b-29c |
{2} | 19a-39b-24c |
{2} | -47a-21b-38c |
o12 : List
|
i13 : indices f'
o13 = {greg, mike}
o13 : List
|
The names of the components are called indices, and are used to access the relevant inclusion and projection maps.
i14 : f'_[mike]
1 3
o14 = -1 : S <------------------------------------------- S : -1
| -41a+30b+29c -19a+5b+10c 29a+8b+46c |
4 3
0 : S <------------------------------------------------- S : 0
{0} | 0 0 0 |
{1} | 19a+7b-24c -29a-16b-26c 5b |
{1} | 48a+30b-38c 8a-50c -34a-8b+35c |
{1} | 14a-34b 40a-21b+29c -19a+25b+10c |
6 1
1 : S <------------------------ S : 1
{1} | 0 |
{1} | 0 |
{1} | 0 |
{2} | 34a+16b-29c |
{2} | 19a-39b-24c |
{2} | -47a-21b-38c |
o14 : ComplexMap
|
i15 : f'^[greg]
1 4
o15 = 0 : S <--------------- S : 0
| 1 0 0 0 |
3 4
1 : S <------------------- S : 1
{1} | 1 0 0 0 |
{1} | 0 1 0 0 |
{1} | 0 0 1 0 |
3 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o15 : ComplexMap
|
i16 : f^[0]
1 4
o16 = 0 : S <--------------- S : 0
| 1 0 0 0 |
3 4
1 : S <------------------- S : 1
{1} | 1 0 0 0 |
{1} | 0 1 0 0 |
{1} | 0 0 1 0 |
3 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o16 : ComplexMap
|
i17 : f_[0]
4 1
o17 = 0 : S <------------- S : 0
{0} | 1 |
{1} | 0 |
{1} | 0 |
{1} | 0 |
6 3
1 : S <----------------- S : 1
{1} | 1 0 0 |
{1} | 0 1 0 |
{1} | 0 0 1 |
{2} | 0 0 0 |
{2} | 0 0 0 |
{2} | 0 0 0 |
4 3
2 : S <----------------- S : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
{3} | 0 0 0 |
1 1
3 : S <------------- S : 3
{3} | 1 |
o17 : ComplexMap
|