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Packages » SimplicialModules :: truncate(List,SimplicialModule)
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truncate(List,SimplicialModule) -- truncation of a simplicial module at a specified degree or set of degrees

Description

Truncation of homogeneous (graded) modules induces a natural operation on simplicial modules.

In the singly graded case, the truncation of a homogeneous module $M$ at degree $d$ is generated by all homogeneous elements of degree at least $d$ in $M$. This method applies this operation to each term in a simplicial module.

i1 : R = QQ[a,b,c];
 
i2 : I = ideal(a*b, a*c, b*c)

o2 = ideal (a*b, a*c, b*c)

o2 : Ideal of R
 
i3 : C = simplicialModule(freeResolution I, 3, Degeneracy => true)

      1      4      9      16
o3 = R  <-- R  <-- R  <-- R  <-- ...
                           
     0      1      2      3

o3 : SimplicialModule
 
i4 : D = truncate(3,C)

o4 = image | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 | <-- image {0} | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 0 0 0 0 0 0 0 0 0 | <-- image {0} | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {0} | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 0 0 0 0 0 0 0 0 0 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  c b a 0 0 0 0 0 0 |           {2} | 0  0   0   0   0   0   0  0   0   0  c b a 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  c b a 0 0 0 0 0 0 0 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 c b a 0 0 0 |           {2} | 0  0   0   0   0   0   0  0   0   0  0 0 0 c b a 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 c b a 0 0 0 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 c b a |           {2} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 0 0 c b a 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 c b a 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 c b a 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 c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 c b a 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 c b a 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 c b a 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 c b a 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 0 0 0 0 0 1 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 c b a 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 0 0 0 0 0 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 c b a 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 0 0 0 0 0 c b a 0 0 0 0 0 0 |
                                                                                                                                 2                                                                                                    {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 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 |
                                                                                                                                                                                                                                      {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 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 |
                                                                                                                                                                                                                                      {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 0 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 |
                                                                                                                                                                                                                                      {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 0 0 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 |
                                                                                                                                                                                                                                      {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 0 0 0 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 |
                                                                                                                                                                                                                                      {3} | 0  0   0   0   0   0   0  0   0   0  0 0 0 0 0 0 0 0 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 |
                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                3

o4 : SimplicialModule
 
i5 : assert isWellDefined D

Truncating at a degree less than the minimal generators is the identity operation.

i6 : assert(C == truncate(0, C))

In the multi-graded case, the truncation of a homogeneous module at a list of degrees is generated by all homogeneous elements of degree that are component-wise greater than or equal to at least one of the degrees.

i7 : A = ZZ/101[x_0, x_1, y_0, y_1, y_2, Degrees => {2:{1,0}, 3:{0,1}}];
 
i8 : I = intersect(ideal(x_0, x_1), ideal(y_0, y_1, y_2))

o8 = ideal (x y , x y , x y , x y , x y , x y )
             1 2   0 2   1 1   0 1   1 0   0 0

o8 : Ideal of A
 
i9 : C = simplicialModule(freeResolution I, 3, Degeneracy => true)

      1      7      22      51
o9 = A  <-- A  <-- A   <-- A  <-- ...
                            
     0      1      2       3

o9 : SimplicialModule
 
i10 : D1 = prune truncate({{1,1}}, C)

o10 = cokernel {1, 1} | x_0  y_1  0    0    y_0  0    0    0    0    | <-- cokernel {1, 1} | x_0  y_1  0    0    y_0  0    0    0    0    | <-- cokernel {1, 1} | x_0  y_1  0    0    y_0  0    0    0    0    | <-- cokernel {1, 1} | x_0  y_1  0    0    y_0  0    0    0    0    |<-- ...
               {1, 1} | -x_1 0    y_1  0    0    0    y_0  0    0    |              {1, 1} | -x_1 0    y_1  0    0    0    y_0  0    0    |              {1, 1} | -x_1 0    y_1  0    0    0    y_0  0    0    |              {1, 1} | -x_1 0    y_1  0    0    0    y_0  0    0    |
               {1, 1} | 0    -y_2 0    x_0  0    y_0  0    0    0    |              {1, 1} | 0    -y_2 0    x_0  0    y_0  0    0    0    |              {1, 1} | 0    -y_2 0    x_0  0    y_0  0    0    0    |              {1, 1} | 0    -y_2 0    x_0  0    y_0  0    0    0    |
               {1, 1} | 0    0    -y_2 -x_1 0    0    0    y_0  0    |              {1, 1} | 0    0    -y_2 -x_1 0    0    0    y_0  0    |              {1, 1} | 0    0    -y_2 -x_1 0    0    0    y_0  0    |              {1, 1} | 0    0    -y_2 -x_1 0    0    0    y_0  0    |
               {1, 1} | 0    0    0    0    -y_2 -y_1 0    0    x_0  |              {1, 1} | 0    0    0    0    -y_2 -y_1 0    0    x_0  |              {1, 1} | 0    0    0    0    -y_2 -y_1 0    0    x_0  |              {1, 1} | 0    0    0    0    -y_2 -y_1 0    0    x_0  |
               {1, 1} | 0    0    0    0    0    0    -y_2 -y_1 -x_1 |              {1, 1} | 0    0    0    0    0    0    -y_2 -y_1 -x_1 |              {1, 1} | 0    0    0    0    0    0    -y_2 -y_1 -x_1 |              {1, 1} | 0    0    0    0    0    0    -y_2 -y_1 -x_1 |
                                                                                    {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
      0                                                                             {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                    {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                    {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                    {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                    {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                           1                                                                             {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {2, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {2, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {2, 1} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {1, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                         {1, 2} | 0    0    0    0    0    0    0    0    0    |              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                2                                                                             {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 1} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {2, 2} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 3} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                              {1, 3} | 0    0    0    0    0    0    0    0    0    |
                                                                                                                                                                                                                      
                                                                                                                                                                                                                     3

o10 : SimplicialModule
 
i11 : D2 = truncate({{1,0}}, C)

o11 = image | x_1 x_0 | <-- image {0, 0} | x_1 x_0 0 0 0 0 0 0 | <-- image {0, 0} | x_1 x_0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {0, 0} | x_1 x_0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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   1 0 0 0 0 0 |           {1, 1} | 0   0   1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 0 0 0 0 0 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 1 0 0 0 0 |           {1, 1} | 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 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 |
                                  {1, 1} | 0   0   0 0 1 0 0 0 |           {1, 1} | 0   0   0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 0 0 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 1 0 0 |           {1, 1} | 0   0   0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 1} | 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 |
                                  {1, 1} | 0   0   0 0 0 0 1 0 |           {1, 1} | 0   0   0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 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 1 |           {1, 1} | 0   0   0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                            1                                              {1, 1} | 0   0   0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |           {1, 1} | 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 |
                                                                           {1, 1} | 0   0   0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 |           {1, 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 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 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 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 |           {1, 1} | 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 |
                                                                           {2, 1} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |           {1, 1} | 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 |
                                                                           {2, 1} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |           {1, 1} | 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 |
                                                                           {1, 2} | 0   0   0 0 0 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 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 |
                                                                           {1, 2} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |           {1, 1} | 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 |
                                                                           {2, 1} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 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, 2} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |           {1, 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 0 0 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, 2} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |           {2, 1} | 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 |
                                                                           {1, 2} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |           {2, 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 0 0 0 0 0 0 0 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 1 |           {1, 2} | 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 |
                                                                                                                                                  {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 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 |
                                                                     2                                                                            {2, 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 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 |
                                                                                                                                                  {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 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 |
                                                                                                                                                  {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 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 |
                                                                                                                                                  {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 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 |
                                                                                                                                                  {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 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, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                  {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                  {2, 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 |
                                                                                                                                                  {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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                  {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                  {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                  {2, 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 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                                                                                                                                                  {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                                                                                                                                                  {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                                                                                                                                                  {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                                                                                                                                                  {1, 3} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 |
                                                                                                                                                  {1, 3} | 0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 |
                                                                                                                                             
                                                                                                                                            3

o11 : SimplicialModule
 
i12 : D3 = truncate({{0,1}}, C)

o12 = image | y_2 y_1 y_0 | <-- image {0, 0} | y_2 y_1 y_0 0 0 0 0 0 0 | <-- image {0, 0} | y_2 y_1 y_0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | <-- image {0, 0} | y_2 y_1 y_0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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   1 0 0 0 0 0 |           {1, 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 |           {1, 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 0 0 0 0 0 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 1 0 0 0 0 |           {1, 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 |           {1, 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 0 0 0 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 1 0 0 0 |           {1, 1} | 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, 1} | 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 |
                                      {1, 1} | 0   0   0   0 0 0 1 0 0 |           {1, 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 |           {1, 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 0 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 1 0 |           {1, 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 |           {1, 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 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 1 |           {1, 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 |           {1, 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 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 1 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 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 |
                                1                                                  {1, 1} | 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, 1} | 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 |
                                                                                   {1, 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 |           {1, 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 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 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 0 0 0 0 0 0 0 0 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 1 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 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 |
                                                                                   {1, 1} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 1 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 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 |
                                                                                   {2, 1} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 |
                                                                                   {2, 1} | 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, 1} | 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 |
                                                                                   {1, 2} | 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, 1} | 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 |
                                                                                   {1, 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 |           {1, 1} | 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 |
                                                                                   {2, 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 |           {1, 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 0 0 0 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, 2} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 |
                                                                                   {1, 2} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |           {2, 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 0 0 0 0 0 0 0 0 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 1 0 |           {2, 1} | 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 |
                                                                                   {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 1 |           {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 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 |
                                                                                                                                                              {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 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 |
                                                                             2                                                                                {2, 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 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 |
                                                                                                                                                              {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 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 |
                                                                                                                                                              {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 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 |
                                                                                                                                                              {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 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 |
                                                                                                                                                              {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 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, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                              {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                              {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                              {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                              {2, 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 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                              {2, 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 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                                                                                                                                                              {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                                                                                                                                                              {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                                                                                                                                                              {2, 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                                                                                                                                                              {1, 3} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 |
                                                                                                                                                              {1, 3} | 0   0   0   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 |
                                                                                                                                                         
                                                                                                                                                        3

o12 : SimplicialModule
 
i13 : D4 = truncate({{1,0},{0,1}}, C);
 
i14 : D5 = truncate({{2,2}}, C);
 
i15 : assert all({D1,D2,D3,D4,D5}, isWellDefined)

See also

Ways to use this method:

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:1035:0.