Hom(FilteredComplex,Complex) -- the filtered Hom complex

Function: Hom
Usage:

f = Hom(K,C)
Inputs:
- K, a filtered chain complex,
- C, a complex,
Optional inputs:
- DegreeLimit => ..., default value null,
- MinimalGenerators => ..., default value true,
- Strategy => ..., default value null,
Outputs:
- f, a filtered chain complex,

Description

Returns the filtrations of the Hom complex determined by the double complex. Here is an example which illustrates the syntax.

i1 : A = QQ[x,y,z,w];

i2 : B = freeResolution monomialCurveIdeal(A, {1,2,3});

i3 : C = freeResolution monomialCurveIdeal(A, {1,3,4});

i4 : F' = Hom(filteredComplex B, C)

o4 = -3 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0
                                                                       
          -2          -1          0           1           2           3

     -2 : image {-3} | 1 0 | <-- image {-2} | 0 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0
                {-3} | 0 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 0 0 0 |           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  
                                       {-2} | 0 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 |           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3
          -2                           {-1} | 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 0 0 0 0 0 |           {3} | 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 0 0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 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 |           {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 1 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 |           {2} | 0 0 0 0 0 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 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 0 0 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 0 |           {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 |           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                 -1                                             {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 1 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 1 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 1 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 1 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                                                                {1} | 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                                                           
                                                                          0

     -1 : image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 0 0 0 0 0 0 0 | <-- image 0
                {-3} | 0 1 |           {-2} | 0 1 0 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 |           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |      
                                       {-2} | 0 0 1 0 0 0 0 0 0 0 0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |     3
          -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 0 0 0 0 |
                                       {0}  | 0 0 0 0 1 0 0 0 0 0 0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 1 0 0 |
                                       {0}  | 0 0 0 0 0 1 0 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 |           {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 1 0 |
                                       {0}  | 0 0 0 0 0 0 1 0 0 0 0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 1 |
                                       {-1} | 0 0 0 0 0 0 0 1 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 |           {2} | 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 1 0 0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2
                                       {0}  | 0 0 0 0 0 0 0 0 0 1 0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 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 1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {2} | 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 0 0 1 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                                 -1                                             {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {2} | 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 0 0 0 1 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                                                                {1} | 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1
                                                                                {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                                                           
                                                                          0

          2      11      21      18      7      1
     0 : A  <-- A   <-- A   <-- A   <-- A  <-- A
                                                
         -2     -1      0       1       2      3

o4 : FilteredComplex

i5 : F'' = Hom(B,filteredComplex C)

o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0
                                                                       
          -2          -1          0           1           2           3

     0 : image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0 <-- image 0
               {-3} | 0 1 |           {-2} | 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 0 |                              
                                      {-2} | 0 0 1 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 |     1           2           3
         -2                           {-1} | 0 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 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 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 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 |
                                      {-1} | 0 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 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 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 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 |
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                -1                                             {1} | 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 0 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 0 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 |
                                                                               {1} | 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 0 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 0 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 |
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                          
                                                                         0

     1 : image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image 0 <-- image 0
               {-3} | 0 1 |           {-2} | 0 1 0 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 |           {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |                  
                                      {-2} | 0 0 1 0 0 0 0 0 0 0 0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |     2           3
         -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                      {0}  | 0 0 0 0 1 0 0 0 0 0 0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 0 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 |           {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 1 0 0 0 0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 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 |           {1} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 0 0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {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 1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 1 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                -1                                             {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 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 0 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 |     1
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                          
                                                                         0

     2 : image {-3} | 1 0 | <-- image {-2} | 1 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {2} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {4} | 1 0 0 0 0 0 0 | <-- image 0
               {-3} | 0 1 |           {-2} | 0 1 0 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 |           {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 1 0 0 0 0 0 |      
                                      {-2} | 0 0 1 0 0 0 0 0 0 0 0 |           {1} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 1 0 0 0 0 |     3
         -2                           {-1} | 0 0 0 1 0 0 0 0 0 0 0 |           {1} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {4} | 0 0 0 1 0 0 0 |
                                      {0}  | 0 0 0 0 1 0 0 0 0 0 0 |           {1} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 0 |
                                      {0}  | 0 0 0 0 0 1 0 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 |           {2} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 0 |
                                      {0}  | 0 0 0 0 0 0 1 0 0 0 0 |           {1} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {3} | 0 0 0 0 0 0 0 |
                                      {-1} | 0 0 0 0 0 0 0 1 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 |           {2} | 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 1 0 0 |           {1} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |     2
                                      {0}  | 0 0 0 0 0 0 0 0 0 1 0 |           {0} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |           {2} | 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 1 |           {1} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |           {2} | 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 0 0 1 0 0 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                                -1                                             {1} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {2} | 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 0 0 0 1 0 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |           {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 1 0 0 0 |           {2} | 0 0 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 0 0 0 0 0 0 0 0 1 0 0 |      
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |     1
                                                                               {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                                                          
                                                                         0

          2      11      21      18      7      1
     3 : A  <-- A   <-- A   <-- A   <-- A  <-- A
                                                
         -2     -1      0       1       2      3

o5 : FilteredComplex

Ways to use this method:

Hom(Complex,FilteredComplex)
Hom(FilteredComplex,Complex) -- the filtered Hom complex

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SpectralSequences.m2:3129:0.

Hom(FilteredComplex,Complex) -- the filtered Hom complex

Description

See also

Ways to use this method: