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

Synopsis

Function: Hom
Usage:

f = Hom(K,C)
Inputs:
- K, a filtered chain complex,
- C, a chain 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 = res monomialCurveIdeal(A, {1,2,3});

i3 : C = res 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 <-- image 0 <-- image 0
                                                                                               
          -3          -2          -1          0           1           2           3           4

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

o4 : FilteredComplex

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

o5 = -1 : image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0 <-- image 0
                                                                                               
          -3          -2          -1          0           1           2           3           4

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

o5 : FilteredComplex

Ways to use this method: