inducedMap(FilteredComplex,ZZ) -- the i th inclusion map in a filtered complex

Synopsis

Function: inducedMap
Usage:

f = inducedMap(K,i)
Inputs:
- K, a filtered chain complex,
- i, an integer,
Optional inputs:
- Degree => ..., default value null,
- Verify => ..., default value true,
Outputs:
- f, a chain complex map,

Description

Returns the chain complex map specifying the inclusion of the i piece of the filtered complex to the ambient chain complex.

i1 : A = QQ[x,y];

i2 : C = koszul vars A;

i3 : K = filteredComplex C

o3 = -1 : image 0 <-- image 0 <-- image 0
                                   
          0           1           2

     0 : image | 1 | <-- image 0 <-- image 0
                                      
         0               1           2

     1 : image | 1 | <-- image {1} | 1 0 | <-- image 0
                               {1} | 0 1 |      
         0                                     2
                         1

          1      2      1
     2 : A  <-- A  <-- A
                        
         0      1      2

o3 : FilteredComplex

i4 : inducedMap(K,1)

          1
o4 = 0 : A  <--------- image | 1 | : 0
               | 1 |

          2
     1 : A  <--------------- image {1} | 1 0 | : 1
               {1} | 1 0 |         {1} | 0 1 |
               {1} | 0 1 |

          1
     2 : A  <----- image 0 : 2
               0

o4 : ChainComplexMap

Ways to use this method: