inducedMap(SimplicialModule,SimplicialModule) -- make the map of simplicial modules induced at each term by the identity map

Function: inducedMap
Usage:

f = inducedMap(D, C)
Inputs:
- C, a Simplicial Module,
- D, a Simplicial Module,
Optional inputs:
- Degree => ..., default value null, specify the degree of an induced map of simplicial modules
- Verify => ..., default value true,
Outputs:
- f, a Map of Simplicial Modules,

Description

Let $d$ be the value of the optional argument Degree, or zero, if not given. For each $i$, the terms $D_{i+d}$ and $C_i$ must be subquotients of the same ambient free module. This method returns the simplicial module map induced by the identity on each of these free modules.

If Verify => true is given, then this method also checks that these identity maps induce well-defined maps. This can be a relatively expensive computation.

We illustrate this method by truncating a free resolution at two distinct internal degrees. We check that the various induced maps compose to give another induced map.

i1 : needsPackage "Truncations"

o1 = Truncations

o1 : Package

i2 : kk = ZZ/32003

o2 = kk

o2 : QuotientRing

i3 : R = kk[a,b,c]

o3 = R

o3 : PolynomialRing

i4 : F = simplicialModule(freeResolution (ideal gens R)^2, 2, Degeneracy => true)

      1      7      21
o4 = R  <-- R  <-- R  <-- ...
                    
     0      1      2

o4 : SimplicialModule

i5 : C1 = truncate(3, F);

i6 : prune normalize C1

                                                                                                                                                   8      3
o6 = cokernel {3} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  | <-- cokernel {3} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | <-- R  <-- R
              {3} | -c 0  b  a  0  0  0  0  0  0  0  0  0  0  0  |              {3} | -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |             
              {3} | 0  -c 0  0  b  a  0  0  0  0  0  0  0  0  0  |              {3} | 0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |     2      3
              {3} | 0  0  -c 0  0  0  b  a  0  0  0  0  0  0  0  |              {3} | 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  -c -c 0  0  0  b  0  a  0  0  0  0  |              {3} | 0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  0  0  -c 0  0  0  0  0  b  0  a  0  |              {3} | 0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  0  0  0  -c 0  0  a  0  0  0  0  0  |              {3} | 0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  0  0  0  0  -c -c -b 0  0  a  0  0  |              {3} | 0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  0  0  0  0  0  0  0  -c -c -b 0  a  |              {3} | 0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  |
              {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |              {3} | 0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  |
     0                                                                          {3} | 0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  |
                                                                                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |
                                                                        
                                                                       1

o6 : Complex

i7 : C2 = truncate(4, F);

i8 : prune normalize C2

                                                                                                                                                                                                                                                                                                                                                                     3
o8 = cokernel {4} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | <-- cokernel {4} | 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | <-- cokernel {4} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | <-- R
              {4} | -c 0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | -c 0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |      
              {4} | 0  -c 0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  -c 0  0  b  0  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  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |     3
              {4} | 0  0  -c 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  -c 0  0  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  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
              {4} | 0  0  0  -c -c 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  -c -c -b 0  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  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
              {4} | 0  0  0  0  0  -c 0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  -c -b 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  -c 0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
              {4} | 0  0  0  0  0  0  0  -c -c 0  0  0  0  0  b  0  a  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  -c 0  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  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  -c 0  a  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  -c -c 0  0  0  0  0  0  b  0  a  0  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  0  -c 0  0  b  0  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  0  0  |              {4} | 0  0  0  0  0  0  0  -c -b 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  -c 0  0  0  0  0  0  0  0  b  0  a  0  |              {4} | 0  0  0  0  0  0  0  0  0  0  -c 0  0  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  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  0  b  a  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  -c 0  0  a  0  0  0  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  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  0  |              {4} | 0  0  0  0  0  0  0  0  0  -c 0  a  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  0  -c -c -b 0  0  a  0  0  0  0  0  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  -c -b 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  0  0  0  0  -c -c -b 0  0  a  0  0  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  |
              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  a  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  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  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  |
              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  b  0  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  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  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  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  |
     0                                                                                                     {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  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  |              {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  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  0  0  0  0  -c -b 0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  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  0  0  0  0  0  0  b  a  0  0  0  0  |
                                                                                                           {4} | 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 0  b  a  0  0  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  0  0  0  0  0  0  -c 0  a  0  0  0  |
                                                                                                           {4} | 0  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 0  0  b  0  a  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  0  0  0  0  0  0  0  -c -b 0  0  0  |
                                                                                                           {4} | 0  0  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 0  0  a  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  0  0  0  0  0  0  0  0  0  b  a  0  |
                                                                                                           {4} | 0  0  0  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 -c -b 0  a  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  0  0  0  0  0  0  0  0  0  -c 0  a  |
                                                                                                           {4} | 0  0  0  0  0  0  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 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  0  0  0  0  0  0  0  0  0  0  -c -b |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  |     2
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  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 0  0  b  0  a  0  0  0  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  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 0  0  a  0  0  0  0  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  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 -c -b 0  a  0  0  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  b  a  0  0  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  b  0  a  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  a  0  0  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 -c -b 0  a  |
                                                                                                           {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |
                                                                                                   
                                                                                                  1

o8 : Complex

i9 : assert isWellDefined C1

i10 : assert isWellDefined C2

i11 : f = inducedMap(C1, C2);

i12 : prune normalize f

o12 = 0 : cokernel {3} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  | <----------------------------------------- cokernel {4} | 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
                   {3} | -c 0  b  a  0  0  0  0  0  0  0  0  0  0  0  |    {3} | c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | -c 0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  -c 0  0  b  a  0  0  0  0  0  0  0  0  0  |    {3} | 0 c 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  -c 0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  -c 0  0  0  b  a  0  0  0  0  0  0  0  |    {3} | 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  -c 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  -c -c 0  0  0  b  0  a  0  0  0  0  |    {3} | 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  -c -c 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  -c 0  0  0  0  0  b  0  a  0  |    {3} | 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  -c 0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  -c 0  0  a  0  0  0  0  0  |    {3} | 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  -c 0  0  0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  0  -c -c -b 0  0  a  0  0  |    {3} | 0 0 0 0 0 0 c 0 0 0 b 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  -c -c 0  0  0  0  0  b  0  a  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  -c -c -b 0  a  |    {3} | 0 0 0 0 0 0 0 c 0 0 0 b 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  -c -c 0  0  0  0  0  0  b  0  a  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |    {3} | 0 0 0 0 0 0 0 0 c 0 0 0 b 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  -c 0  0  0  0  0  0  0  0  b  0  a  0  |
                                                                           {3} | 0 0 0 0 0 0 0 0 0 c 0 0 0 b a |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  a  0  0  0  0  0  0  0  0  |
                                                                                                                            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  0  a  0  0  0  0  0  |
                                                                                                                            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  0  a  0  0  |
                                                                                                                            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  a  |
                                                                                                                            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |

      1 : cokernel {3} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | <----------------------------------------------------------------------------------- cokernel {4} | 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | : 1
                   {3} | -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |    {3} | c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | -c 0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  |    {3} | 0 c 0 b 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  -c 0  0  b  0  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  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  |    {3} | 0 0 c 0 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 |            {4} | 0  0  -c 0  0  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  0  0  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  -c -c -b 0  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  0  0  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 0 c 0 b 0 0 0 0 0 0 0 0 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  -c -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  b  a  0  0  0  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 0 0 c 0 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 |            {4} | 0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 0 0 0 0 0 0 c 0 0 0 0 0 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  -c 0  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  0  0  0  0  0  |
                   {3} | 0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 b 0 0 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  -c 0  0  b  0  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  0  0  |
                   {3} | 0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  |    {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 b a 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  -c 0  0  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  0  0  0  |
                   {3} | 0  0  0  0  0  0  0  0  0  -c 0  a  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 c 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  -c -c -b 0  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  0  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  -c -b 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 c 0 b 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  0  0  -c -b 0  0  0  0  0  0  0  0  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  b  a  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 c 0 b a 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  0  0  0  0  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  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  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 c 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  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  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 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 c 0 b 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  b  0  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  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  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 c 0 b a 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  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  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  |    {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 c 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  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  |
                   {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |    {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 c 0 b 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 b a |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  b  a  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  b  0  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -c -b 0  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  b  a  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  0  b  0  a  0  0  0  0  0  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  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 0  0  a  0  0  0  0  0  0  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  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 -c -b 0  a  0  0  0  0  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  0  0  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  b  a  0  0  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  b  0  a  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 0  0  a  0  0  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 -c -b 0  a  |
                                                                                                                                                                               {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |

           8
      2 : R  <----------------------------------------------------------- cokernel {4} | b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  | : 2
                {3} | c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | -c 0  a  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 c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  -c -b 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 c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  b  a  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 c b a 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  -c 0  a  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 c b a 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  -c -b 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 c b a 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  b  a  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 c b a 0 0 0 |            {4} | 0  0  0  0  0  0  -c 0  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 c b a |            {4} | 0  0  0  0  0  0  0  -c -b 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  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  -c -b 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  b  a  0  0  0  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b 0  0  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  b  a  0  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c 0  a  |
                                                                                   {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -c -b |

o12 : ComplexMap

i13 : assert isWellDefined f

i14 : f1 = inducedMap(F, C1)

           1
o14 = 0 : R  <-------------------------------------------- image | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 | : 0
                | c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 |

           7
      1 : R  <------------------------------------------------------------------------------------ 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 | : 1
                {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 |         {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 |
                {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 |         {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 |
                {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 |         {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 |
                {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 |         {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 |
                {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 |         {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 |
                {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 |         {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 |
                {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 |

           21
      2 : R   <---------------------------------------------------------------------------------------------------------------------------------------- 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 0 0 0 0 0 0 0 0 0 0 0 | : 2
                 {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 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 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 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 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 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 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 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 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 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 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 |
                 {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 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 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 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 |         {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 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 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 |         {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 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 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 |         {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 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 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  0 0 0 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 |
                 {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 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 0 0 0 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 |
                 {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 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 0 0 0 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 |
                 {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 c b a 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 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 |
                 {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 1 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 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 |
                 {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 1 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 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 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 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 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 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 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 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 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 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 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 0 0 0 0 0 0 0 0 0 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 0 0 1 |

o14 : SimplicialModuleMap

i15 : f2 = inducedMap(F, C2)

           1
o15 = 0 : R  <---------------------------------------------------------------------- image | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 | : 0
                | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 |

           7
      1 : R  <-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- image {0} | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 0  0  0  0  0  0  0  0  0  0  0  0  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} | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 0  0  0  0  0  0  0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  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  c2 bc ac b2 ab a2 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  c2 bc ac b2 ab a2 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  0  0  c2 bc ac b2 ab a2 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  c2 bc ac b2 ab a2 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  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 |
                {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  c2 bc ac b2 ab a2 |

           21
      2 : R   <-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- image {0} | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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} | c4 bc3 ac3 b2c2 abc2 a2c2 b3c ab2c a2bc a3c b4 ab3 a2b2 a3b a4 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2 bc ac b2 ab a2 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |
                 {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |         {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |
                 {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |         {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |
                 {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |         {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |
                 {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  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 |

o15 : SimplicialModuleMap

i16 : assert isWellDefined f1

i17 : assert isWellDefined f2

i18 : assert(f2 == f1 * f)

Ways to use this method:

inducedMap(SimplicialModule,SimplicialModule) -- make the map of simplicial modules induced at each term by the identity map

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:2507:0.

inducedMap(SimplicialModule,SimplicialModule) -- make the map of simplicial modules induced at each term by the identity map

Description

See also

Ways to use this method: