minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module

Function: minimalPresentation
Usage:

D = minimalPresentation C

D = prune C

h = minimalPresentation f

h = prune f
Inputs:
- C, a Simplicial Module, or $f$ a Map of Simplicial Modules
Optional inputs:
- Exclude => ..., default value {}, unused
Outputs:
- D, a Simplicial Module, isomorphic to the input, where each term is replaced by a minimally presented model, or $h$ a Map of Simplicial Modules where the source and target are minimally presented
Consequences:
- The isomorphism $g : D \to C$ is available as g = D.cache.pruningMap. The inverse isomorphism can be obtained as g^-1

Description

This is frequently useful to make the output of certain operations readable or understandable. This operation is functorial, applying both to simplicial modules and simplicial module maps.

In particular, images/kernels/cokernels of maps need to be pruned to be understood. For instance, this is useful for recognizing when terms given by subquotient modules are actually zero.

i1 : S = ZZ/101[a,b,c,d,e];

i2 : I = ideal(a,b) * ideal(c,d,e)

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

o2 : Ideal of S

i3 : F = simplicialModule((dual freeResolution I)[-4], 2, Degeneracy => true)

      1      6      20
o3 = S  <-- S  <-- S  <-- ...
                    
     0      1      2

o3 : SimplicialModule

i4 : C = HH F

o4 = cokernel {-5} | -e d -c -b a | <-- subquotient ({-5} | 1 0 0  0 0  0 0  0 0  0 0 |, {-5} | -e d -c -b a 0 0  0  0 0  0  0  0  0 |) <-- subquotient ({-5} | 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 |, {-5} | -e d -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 |)<-- ...
                                                     {-4} | 0 d c  0 b  0 0  a 0  0 0 |  {-4} | 0  0 0  0  0 d -c -b a 0  0  0  0  0 |                   {-4} | 0 d c  0 b  0 0  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 d -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} | 0 e 0  c 0  b 0  0 a  0 0 |  {-4} | 0  0 0  0  0 e 0  0  0 -c -b a  0  0 |                   {-4} | 0 e 0  c 0  b 0  0 a  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 e 0  0  0 -c -b a  0  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |
                                                     {-4} | 0 0 -e d 0  0 b  0 0  a 0 |  {-4} | 0  0 0  0  0 0 e  0  0 -d 0  0  -b a |                   {-4} | 0 0 -e d 0  0 b  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 e  0  0 -d 0  0  -b a 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |
                                                     {-4} | 0 0 0  0 -e d -c 0 0  0 a |  {-4} | 0  0 0  0  0 0 0  e  0 0  -d 0  c  0 |                   {-4} | 0 0 0  0 -e d -c 0 0  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  e  0 0  -d 0  c  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |
                                                     {-4} | 0 0 0  0 0  0 0  e -d c b |  {-4} | 0  0 0  0  0 0 0  0  e 0  0  -d 0  c |                   {-4} | 0 0 0  0 0  0 0  e -d c b 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  e 0  0  -d 0  c 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 d c  0 b  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 d -c -b a 0  0  0  0  0 0  0  0  0  0  0 |
                                        1                                                                                                                {-4} | 0 0 0  0 0  0 0  0 0  0 0 e 0  c 0  b 0  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 e 0  0  0 -c -b a  0  0 0  0  0  0  0  0 |
                                                                                                                                                         {-4} | 0 0 0  0 0  0 0  0 0  0 0 0 -e d 0  0 b  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  0 0 e  0  0 -d 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 -e d -c 0 0  0 a 0 0 0  0  0  0  0 |  {-4} | 0  0 0  0  0 0 0  0  0 0  0  0  0  0 0 0  e  0 0  -d 0  c  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  e -d c b 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  e 0  0  -d 0  c 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  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 -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 0 d 0 0  b  0  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  -b a  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 d 0  -c 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 -d 0  c  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 -d 0  0  c  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  -d 0  c  0  0 |
                                                                                                                                                         {-3} | 0 0 0  0 0  0 0  0 0  0 0 0 0  0 0  0 0  0 0  0 0 e 0 0  0  b  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  -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 e 0  0  -c 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 -e 0  0  0  c  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 -e 0  0  0  c |  {-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  -e 0  0  0  c |
                                                                                                                                                         {-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  e  -d 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  -e 0  d  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  -e d |  {-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  -e 0  d |
                                                                                                                                             
                                                                                                                                            2

o4 : SimplicialModule

i5 : D = prune C

o5 = cokernel {-5} | e d c b a | <-- cokernel {-5} | e d c b a 0 0 0 | <-- cokernel {-5} | e d c b a 0 0 0 0 0 0 0 0 |<-- ...
                                              {-3} | 0 0 0 0 0 e d c |              {-3} | 0 0 0 0 0 e d c 0 0 0 0 0 |
     0                                                                              {-3} | 0 0 0 0 0 0 0 0 e d c 0 0 |
                                     1                                              {-2} | 0 0 0 0 0 0 0 0 0 0 0 b a |
                                                                            
                                                                           2

o5 : SimplicialModule

i6 : g = D.cache.pruningMap

o6 = 0 : cokernel {-5} | -e d -c -b a | <-------------- cokernel {-5} | e d c b a | : 0
                                           {-5} | 1 |

     1 : subquotient ({-5} | 1 0 0  0 0  0 0  0 0  0 0 |, {-5} | -e d -c -b a 0 0  0  0 0  0  0  0  0 |) <---------------- cokernel {-5} | e d c b a 0 0 0 | : 1
                      {-4} | 0 d c  0 b  0 0  a 0  0 0 |  {-4} | 0  0 0  0  0 d -c -b a 0  0  0  0  0 |     {-5} | 1 0 |            {-3} | 0 0 0 0 0 e d c |
                      {-4} | 0 e 0  c 0  b 0  0 a  0 0 |  {-4} | 0  0 0  0  0 e 0  0  0 -c -b a  0  0 |     {-3} | 0 0 |
                      {-4} | 0 0 -e d 0  0 b  0 0  a 0 |  {-4} | 0  0 0  0  0 0 e  0  0 -d 0  0  -b a |     {-3} | 0 0 |
                      {-4} | 0 0 0  0 -e d -c 0 0  0 a |  {-4} | 0  0 0  0  0 0 0  e  0 0  -d 0  c  0 |     {-3} | 0 0 |
                      {-4} | 0 0 0  0 0  0 0  e -d c b |  {-4} | 0  0 0  0  0 0 0  0  e 0  0  -d 0  c |     {-3} | 0 0 |
                                                                                                            {-3} | 0 0 |
                                                                                                            {-3} | 0 0 |
                                                                                                            {-3} | 0 0 |
                                                                                                            {-3} | 0 0 |
                                                                                                            {-3} | 0 0 |
                                                                                                            {-3} | 0 1 |

     2 : subquotient ({-5} | 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 |, {-5} | -e d -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 |) <-------------------- cokernel {-5} | e d c b a 0 0 0 0 0 0 0 0 | : 2
                      {-4} | 0 d c  0 b  0 0  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 d -c -b a 0  0  0  0  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |     {-5} | 1 0 0 0 |            {-3} | 0 0 0 0 0 e d c 0 0 0 0 0 |
                      {-4} | 0 e 0  c 0  b 0  0 a  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 e 0  0  0 -c -b a  0  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |            {-3} | 0 0 0 0 0 0 0 0 e d c 0 0 |
                      {-4} | 0 0 -e d 0  0 b  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 e  0  0 -d 0  0  -b a 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |            {-2} | 0 0 0 0 0 0 0 0 0 0 0 b a |
                      {-4} | 0 0 0  0 -e d -c 0 0  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  e  0 0  -d 0  c  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  e -d c b 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  e 0  0  -d 0  c 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  0 0  0 0 d c  0 b  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 d -c -b a 0  0  0  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  0 0  0 0 e 0  c 0  b 0  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 e 0  0  0 -c -b a  0  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  0 0  0 0 0 -e d 0  0 b  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  0 0 e  0  0 -d 0  0  -b a 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  0 0  0 0 0 0  0 -e d -c 0 0  0 a 0 0 0  0  0  0  0 |  {-4} | 0  0 0  0  0 0 0  0  0 0  0  0  0  0 0 0  e  0 0  -d 0  c  0 0  0  0  0  0  0 |     {-3} | 0 0 0 0 |
                      {-4} | 0 0 0  0 0  0 0  0 0  0 0 0 0  0 0  0 0  e -d c b 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  e 0  0  -d 0  c 0  0  0  0  0  0 |     {-3} | 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  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 -b a  0  0  0  0 |     {-3} | 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 d 0 0  b  0  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  -b a  0  0 |     {-3} | 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 d 0  -c 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 -d 0  c  0  0  0 |     {-3} | 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 -d 0  0  c  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  -d 0  c  0  0 |     {-3} | 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 e 0 0  0  b  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  -b a |     {-3} | 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 e 0  0  -c 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 -e 0  0  0  c  0 |     {-3} | 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 -e 0  0  0  c |  {-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  -e 0  0  0  c |     {-3} | 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  e  -d 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  -e 0  d  0 |     {-3} | 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  -e d |  {-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  -e 0  d |     {-3} | 0 0 0 0 |
                                                                                                                                                                                               {-3} | 0 0 0 0 |
                                                                                                                                                                                               {-3} | 0 0 1 0 |
                                                                                                                                                                                               {-2} | 0 0 0 1 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |
                                                                                                                                                                                               {-2} | 0 0 0 0 |

o6 : SimplicialModuleMap

i7 : assert isWellDefined g

i8 : assert isSimplicialMorphism g

i9 : assert (target g == C)

i10 : assert (source g == D)

i11 : g^-1

o11 = 0 : cokernel {-5} | e d c b a | <-------------- cokernel {-5} | -e d -c -b a | : 0
                                         {-5} | 1 |

      1 : cokernel {-5} | e d c b a 0 0 0 | <---------------------------------- subquotient ({-5} | 1 0 0  0 0  0 0  0 0  0 0 |, {-5} | -e d -c -b a 0 0  0  0 0  0  0  0  0 |) : 1
                   {-3} | 0 0 0 0 0 e d c |    {-5} | 1 0 0 0 0 0 0 0 0 0 0 |                {-4} | 0 d c  0 b  0 0  a 0  0 0 |  {-4} | 0  0 0  0  0 d -c -b a 0  0  0  0  0 |
                                               {-3} | 0 0 0 0 0 0 0 0 0 0 1 |                {-4} | 0 e 0  c 0  b 0  0 a  0 0 |  {-4} | 0  0 0  0  0 e 0  0  0 -c -b a  0  0 |
                                                                                             {-4} | 0 0 -e d 0  0 b  0 0  a 0 |  {-4} | 0  0 0  0  0 0 e  0  0 -d 0  0  -b a |
                                                                                             {-4} | 0 0 0  0 -e d -c 0 0  0 a |  {-4} | 0  0 0  0  0 0 0  e  0 0  -d 0  c  0 |
                                                                                             {-4} | 0 0 0  0 0  0 0  e -d c b |  {-4} | 0  0 0  0  0 0 0  0  e 0  0  -d 0  c |

      2 : cokernel {-5} | e d c b a 0 0 0 0 0 0 0 0 | <-------------------------------------------------------------------- subquotient ({-5} | 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 |, {-5} | -e d -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
                   {-3} | 0 0 0 0 0 e d c 0 0 0 0 0 |    {-5} | 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 |                {-4} | 0 d c  0 b  0 0  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 d -c -b a 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 e d c 0 0 |    {-3} | 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 |                {-4} | 0 e 0  c 0  b 0  0 a  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 e 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 b a |    {-3} | 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 |                {-4} | 0 0 -e d 0  0 b  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 e  0  0 -d 0  0  -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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |                {-4} | 0 0 0  0 -e d -c 0 0  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  e  0 0  -d 0  c  0 0 0  0  0 0  0  0  0  0 0  0  0  0  0  0 |
                                                                                                                                         {-4} | 0 0 0  0 0  0 0  e -d c b 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  e 0  0  -d 0  c 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 d c  0 b  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 d -c -b a 0  0  0  0  0 0  0  0  0  0  0 |
                                                                                                                                         {-4} | 0 0 0  0 0  0 0  0 0  0 0 e 0  c 0  b 0  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 e 0  0  0 -c -b a  0  0 0  0  0  0  0  0 |
                                                                                                                                         {-4} | 0 0 0  0 0  0 0  0 0  0 0 0 -e d 0  0 b  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  0 0 e  0  0 -d 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 -e d -c 0 0  0 a 0 0 0  0  0  0  0 |  {-4} | 0  0 0  0  0 0 0  0  0 0  0  0  0  0 0 0  e  0 0  -d 0  c  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  e -d c b 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  e 0  0  -d 0  c 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  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 -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 0 d 0 0  b  0  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  -b a  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 d 0  -c 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 -d 0  c  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 -d 0  0  c  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  -d 0  c  0  0 |
                                                                                                                                         {-3} | 0 0 0  0 0  0 0  0 0  0 0 0 0  0 0  0 0  0 0  0 0 e 0 0  0  b  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  -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 e 0  0  -c 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 -e 0  0  0  c  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 -e 0  0  0  c |  {-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  -e 0  0  0  c |
                                                                                                                                         {-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  e  -d 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  -e 0  d  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  -e d |  {-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  -e 0  d |

o11 : SimplicialModuleMap

i12 : assert(g*g^-1 == 1 and g^-1*g == 1)

The image of a map of simplicial modules also becomes more understandable via pruning.

i13 : S = ZZ/101[a,b,c];

i14 : I = ideal(a^2,b^2,c^2);

o14 : Ideal of S

i15 : J = I + ideal(a*b*c);

o15 : Ideal of S

i16 : FI = simplicialModule(freeResolution I, Degeneracy => true)

       1      4      10      20
o16 = S  <-- S  <-- S   <-- S  <-- ...
                             
      0      1      2       3

o16 : SimplicialModule

i17 : FJ = simplicialModule(freeResolution J, Degeneracy => true)

       1      5      15      34
o17 = S  <-- S  <-- S   <-- S  <-- ...
                             
      0      1      2       3

o17 : SimplicialModule

i18 : f = randomSimplicialMap(FJ, FI ** S^{-1}, Cycle => true)

           1                       1
o18 = 0 : S  <------------------- S  : 0
                | 32a-36b-30c |

           5
      1 : S  <----------------------------------------------------------- image {1} | 1 0 0 0 | : 1
                {0} | 32a-36b-30c 0           0           0           |         {1} | 0 0 0 0 |
                {2} | 0           32a-36b-30c 0           0           |         {3} | 0 1 0 0 |
                {2} | 0           0           32a-36b-30c 0           |         {3} | 0 0 1 0 |
                {2} | 0           0           0           32a-36b-30c |         {3} | 0 0 0 1 |
                {3} | 0           0           0           0           |

           15
      2 : S   <---------------------------------------------------------------------------------------------------------------------------------- image {1} | 1 0 0 0 0 0 0 0 0 0 | : 2
                 {0} | 32a-36b-30c 0           0           0           0           0           0           0           0          0           |         {1} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           32a-36b-30c 0           0           0           0           0           0           0          0           |         {3} | 0 1 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           32a-36b-30c 0           0           0           0           0           0          0           |         {3} | 0 0 1 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           32a-36b-30c 0           0           0           0           0          0           |         {3} | 0 0 0 1 0 0 0 0 0 0 |
                 {3} | 0           0           0           0           0           0           0           0           0          0           |         {1} | 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           0           32a-36b-30c 0           0           0           0          0           |         {3} | 0 0 0 0 1 0 0 0 0 0 |
                 {2} | 0           0           0           0           0           32a-36b-30c 0           0           0          0           |         {3} | 0 0 0 0 0 1 0 0 0 0 |
                 {2} | 0           0           0           0           0           0           32a-36b-30c 0           0          0           |         {3} | 0 0 0 0 0 0 1 0 0 0 |
                 {3} | 0           0           0           0           0           0           0           0           0          0           |         {1} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           32a-36b+42c -19c       19c         |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           -29a        24a        24a-36b-30c |         {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                        {5} | 0 0 0 0 0 0 0 1 0 0 |
                                                                                                                                                        {5} | 0 0 0 0 0 0 0 0 1 0 |
                                                                                                                                                        {5} | 0 0 0 0 0 0 0 0 0 1 |

           34
      3 : S   <--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- image {1} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : 3
                 {0} | 32a-36b-30c 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 |
                 {2} | 0           32a-36b-30c 0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           32a-36b-30c 0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           32a-36b-30c 0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 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 |
                 {2} | 0           0           0           0           32a-36b-30c 0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           0           0           32a-36b-30c 0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           0           0           0           32a-36b-30c 0           0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {3} | 0           0           0           0           0           0           0           0           0           0           0           0          0           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 |
                 {2} | 0           0           0           0           0           0           0           32a-36b-30c 0           0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           0           0           0           0           0           32a-36b-30c 0           0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                 {2} | 0           0           0           0           0           0           0           0           0           32a-36b-30c 0           0          0           0           0          0           0           0          0           0                        |         {3} | 0 0 0 0 0 0 0 0 0 1 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                        |         {1} | 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           32a-36b+42c -19c       19c         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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a        24a        24a-36b-30c 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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           32a-36b+42c -19c       19c         0           0          0           0                        |         {5} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           29b+10c     19b-29c    -19b+22c    0           0          0           0                        |         {5} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a+29c    -19a-24c   19a+8c      0           0          0           0                        |         {5} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10b        32a-7b-30c -22b        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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10a-29b    29a+24b    -22a-8b     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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a        24a        24a-36b-30c 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 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           32a-36b+42c -19c       19c         0                        |         {3} | 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           29b+10c     19b-29c    -19b+22c    0                        |         {3} | 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           -29a+29c    -19a-24c   19a+8c      0                        |         {3} | 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           -10b        32a-7b-30c -22b        0                        |         {3} | 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           -10a-29b    29a+24b    -22a-8b     0                        |         {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a        24a        24a-36b-30c 0                        |         {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           19a2+19b2+32ac-36bc+42c2 |         {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           -22a2-32ab+7b2+30bc-10c2 |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           24a2-36ab-24b2-30ac-29c2 |         {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                                                                                                                                                                                                                                                                                           {1} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 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 |
                                                                                                                                                                                                                                                                                           {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                           {7} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |

o18 : SimplicialModuleMap

i19 : C = image f

o19 = image | 32a-36b-30c | <-- image {0} | 32a-36b-30c 0           0           0           | <-- image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0          0           | <-- image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |<-- ...
                                      {2} | 0           32a-36b-30c 0           0           |           {2} | 0           32a-36b-30c 0           0           0           0           0           0           0          0           |           {2} | 0           32a-36b-30c 0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
      0                               {2} | 0           0           32a-36b-30c 0           |           {2} | 0           0           32a-36b-30c 0           0           0           0           0           0          0           |           {2} | 0           0           32a-36b-30c 0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                                      {2} | 0           0           0           32a-36b-30c |           {2} | 0           0           0           32a-36b-30c 0           0           0           0           0          0           |           {2} | 0           0           0           32a-36b-30c 0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                                      {3} | 0           0           0           0           |           {3} | 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                        |
                                                                                                        {2} | 0           0           0           0           32a-36b-30c 0           0           0           0          0           |           {2} | 0           0           0           0           32a-36b-30c 0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                                1                                                                       {2} | 0           0           0           0           0           32a-36b-30c 0           0           0          0           |           {2} | 0           0           0           0           0           32a-36b-30c 0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                                                                                                        {2} | 0           0           0           0           0           0           32a-36b-30c 0           0          0           |           {2} | 0           0           0           0           0           0           32a-36b-30c 0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                                                                                                        {3} | 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                        |
                                                                                                        {4} | 0           0           0           0           0           0           0           32a-36b+42c -19c       19c         |           {2} | 0           0           0           0           0           0           0           32a-36b-30c 0           0           0           0          0           0           0          0           0           0          0           0                        |
                                                                                                        {4} | 0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    |           {2} | 0           0           0           0           0           0           0           0           32a-36b-30c 0           0           0          0           0           0          0           0           0          0           0                        |
                                                                                                        {4} | 0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      |           {2} | 0           0           0           0           0           0           0           0           0           32a-36b-30c 0           0          0           0           0          0           0           0          0           0                        |
                                                                                                        {4} | 0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        |           {3} | 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           -10a-29b    29a+24b    -22a-8b     |           {4} | 0           0           0           0           0           0           0           0           0           0           32a-36b+42c -19c       19c         0           0          0           0           0          0           0                        |
                                                                                                        {4} | 0           0           0           0           0           0           0           -29a        24a        24a-36b-30c |           {4} | 0           0           0           0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    0           0          0           0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      0           0          0           0           0          0           0                        |
                                                                                                  2                                                                                                                                              {4} | 0           0           0           0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        0           0          0           0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     0           0          0           0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a        24a        24a-36b-30c 0           0          0           0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           32a-36b+42c -19c       19c         0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           29b+10c     19b-29c    -19b+22c    0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a+29c    -19a-24c   19a+8c      0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10b        32a-7b-30c -22b        0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10a-29b    29a+24b    -22a-8b     0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a        24a        24a-36b-30c 0           0          0           0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           32a-36b+42c -19c       19c         0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           29b+10c     19b-29c    -19b+22c    0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a+29c    -19a-24c   19a+8c      0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10b        32a-7b-30c -22b        0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10a-29b    29a+24b    -22a-8b     0                        |
                                                                                                                                                                                                                                                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a        24a        24a-36b-30c 0                        |
                                                                                                                                                                                                                                                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           19a2+19b2+32ac-36bc+42c2 |
                                                                                                                                                                                                                                                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           -22a2-32ab+7b2+30bc-10c2 |
                                                                                                                                                                                                                                                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           24a2-36ab-24b2-30ac-29c2 |
                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                           3

o19 : SimplicialModule

i20 : D = prune C

       1      4      10      20
o20 = S  <-- S  <-- S   <-- S  <-- ...
                             
      0      1      2       3

o20 : SimplicialModule

i21 : g = D.cache.pruningMap

                                                1
o21 = 0 : image | 32a-36b-30c | <------------- S  : 0
                                   {1} | 1 |

                                                                                              4
      1 : image {0} | 32a-36b-30c 0           0           0           | <------------------- S  : 1
                {2} | 0           32a-36b-30c 0           0           |    {1} | 1 0 0 0 |
                {2} | 0           0           32a-36b-30c 0           |    {3} | 0 1 0 0 |
                {2} | 0           0           0           32a-36b-30c |    {3} | 0 0 1 0 |
                {3} | 0           0           0           0           |    {3} | 0 0 0 1 |

                                                                                                                                                                                 10
      2 : image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0          0           | <------------------------------- S   : 2
                {2} | 0           32a-36b-30c 0           0           0           0           0           0           0          0           |    {1} | 1 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           32a-36b-30c 0           0           0           0           0           0          0           |    {3} | 0 1 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           32a-36b-30c 0           0           0           0           0          0           |    {3} | 0 0 1 0 0 0 0 0 0 0 |
                {3} | 0           0           0           0           0           0           0           0           0          0           |    {3} | 0 0 0 1 0 0 0 0 0 0 |
                {2} | 0           0           0           0           32a-36b-30c 0           0           0           0          0           |    {3} | 0 0 0 0 1 0 0 0 0 0 |
                {2} | 0           0           0           0           0           32a-36b-30c 0           0           0          0           |    {3} | 0 0 0 0 0 1 0 0 0 0 |
                {2} | 0           0           0           0           0           0           32a-36b-30c 0           0          0           |    {3} | 0 0 0 0 0 0 1 0 0 0 |
                {3} | 0           0           0           0           0           0           0           0           0          0           |    {5} | 0 0 0 0 0 0 0 1 0 0 |
                {4} | 0           0           0           0           0           0           0           32a-36b+42c -19c       19c         |    {5} | 0 0 0 0 0 0 0 0 1 0 |
                {4} | 0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    |    {5} | 0 0 0 0 0 0 0 0 0 1 |
                {4} | 0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      |
                {4} | 0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        |
                {4} | 0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     |
                {4} | 0           0           0           0           0           0           0           -29a        24a        24a-36b-30c |

                                                                                                                                                                                                                                                                                                                                        20
      3 : image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        | <--------------------------------------------------- S   : 3
                {2} | 0           32a-36b-30c 0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {1} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           32a-36b-30c 0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           32a-36b-30c 0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           32a-36b-30c 0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           0           32a-36b-30c 0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           0           0           32a-36b-30c 0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                {3} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           0           0           0           32a-36b-30c 0           0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           0           0           0           0           32a-36b-30c 0           0           0          0           0           0          0           0           0          0           0                        |    {3} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |
                {2} | 0           0           0           0           0           0           0           0           0           32a-36b-30c 0           0          0           0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 1 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                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           32a-36b+42c -19c       19c         0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           -29a        24a        24a-36b-30c 0           0          0           0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           32a-36b+42c -19c       19c         0           0          0           0                        |    {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           29b+10c     19b-29c    -19b+22c    0           0          0           0                        |    {7} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a+29c    -19a-24c   19a+8c      0           0          0           0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10b        32a-7b-30c -22b        0           0          0           0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10a-29b    29a+24b    -22a-8b     0           0          0           0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a        24a        24a-36b-30c 0           0          0           0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           32a-36b+42c -19c       19c         0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           29b+10c     19b-29c    -19b+22c    0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a+29c    -19a-24c   19a+8c      0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10b        32a-7b-30c -22b        0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10a-29b    29a+24b    -22a-8b     0                        |
                {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a        24a        24a-36b-30c 0                        |
                {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           19a2+19b2+32ac-36bc+42c2 |
                {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           -22a2-32ab+7b2+30bc-10c2 |
                {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           24a2-36ab-24b2-30ac-29c2 |

o21 : SimplicialModuleMap

i22 : assert isWellDefined g

i23 : assert isSimplicialMorphism g

i24 : assert (target g == C)

i25 : assert (source g == D)

i26 : g^-1

           1
o26 = 0 : S  <------------- image | 32a-36b-30c | : 0
                {1} | 1 |

           4
      1 : S  <------------------- image {0} | 32a-36b-30c 0           0           0           | : 1
                {1} | 1 0 0 0 |         {2} | 0           32a-36b-30c 0           0           |
                {3} | 0 1 0 0 |         {2} | 0           0           32a-36b-30c 0           |
                {3} | 0 0 1 0 |         {2} | 0           0           0           32a-36b-30c |
                {3} | 0 0 0 1 |         {3} | 0           0           0           0           |

           10
      2 : S   <------------------------------- image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0          0           | : 2
                 {1} | 1 0 0 0 0 0 0 0 0 0 |         {2} | 0           32a-36b-30c 0           0           0           0           0           0           0          0           |
                 {3} | 0 1 0 0 0 0 0 0 0 0 |         {2} | 0           0           32a-36b-30c 0           0           0           0           0           0          0           |
                 {3} | 0 0 1 0 0 0 0 0 0 0 |         {2} | 0           0           0           32a-36b-30c 0           0           0           0           0          0           |
                 {3} | 0 0 0 1 0 0 0 0 0 0 |         {3} | 0           0           0           0           0           0           0           0           0          0           |
                 {3} | 0 0 0 0 1 0 0 0 0 0 |         {2} | 0           0           0           0           32a-36b-30c 0           0           0           0          0           |
                 {3} | 0 0 0 0 0 1 0 0 0 0 |         {2} | 0           0           0           0           0           32a-36b-30c 0           0           0          0           |
                 {3} | 0 0 0 0 0 0 1 0 0 0 |         {2} | 0           0           0           0           0           0           32a-36b-30c 0           0          0           |
                 {5} | 0 0 0 0 0 0 0 1 0 0 |         {3} | 0           0           0           0           0           0           0           0           0          0           |
                 {5} | 0 0 0 0 0 0 0 0 1 0 |         {4} | 0           0           0           0           0           0           0           32a-36b+42c -19c       19c         |
                 {5} | 0 0 0 0 0 0 0 0 0 1 |         {4} | 0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    |
                                                     {4} | 0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      |
                                                     {4} | 0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        |
                                                     {4} | 0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     |
                                                     {4} | 0           0           0           0           0           0           0           -29a        24a        24a-36b-30c |

           20
      3 : S   <--------------------------------------------------- image {0} | 32a-36b-30c 0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        | : 3
                 {1} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           32a-36b-30c 0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           32a-36b-30c 0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           32a-36b-30c 0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {3} | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           32a-36b-30c 0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           0           32a-36b-30c 0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           0           0           32a-36b-30c 0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 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                        |
                 {3} | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           0           0           0           32a-36b-30c 0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {3} | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           0           0           0           0           32a-36b-30c 0           0           0          0           0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 |         {2} | 0           0           0           0           0           0           0           0           0           32a-36b-30c 0           0          0           0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 1 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                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           32a-36b+42c -19c       19c         0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           -29a        24a        24a-36b-30c 0           0          0           0           0          0           0                        |
                 {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 |         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           32a-36b+42c -19c       19c         0           0          0           0                        |
                 {7} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           29b+10c     19b-29c    -19b+22c    0           0          0           0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a+29c    -19a-24c   19a+8c      0           0          0           0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10b        32a-7b-30c -22b        0           0          0           0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10a-29b    29a+24b    -22a-8b     0           0          0           0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a        24a        24a-36b-30c 0           0          0           0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           32a-36b+42c -19c       19c         0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           29b+10c     19b-29c    -19b+22c    0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a+29c    -19a-24c   19a+8c      0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10b        32a-7b-30c -22b        0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10a-29b    29a+24b    -22a-8b     0                        |
                                                                         {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a        24a        24a-36b-30c 0                        |
                                                                         {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           19a2+19b2+32ac-36bc+42c2 |
                                                                         {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           -22a2-32ab+7b2+30bc-10c2 |
                                                                         {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           24a2-36ab-24b2-30ac-29c2 |

o26 : SimplicialModuleMap

i27 : assert(g*g^-1 == 1 and g^-1*g == 1)

One can directly prune the map of simplicial modules $f$.

i28 : h = prune f

           1                       1
o28 = 0 : S  <------------------- S  : 0
                | 32a-36b-30c |

           5                                                               4
      1 : S  <----------------------------------------------------------- S  : 1
                {0} | 32a-36b-30c 0           0           0           |
                {2} | 0           32a-36b-30c 0           0           |
                {2} | 0           0           32a-36b-30c 0           |
                {2} | 0           0           0           32a-36b-30c |
                {3} | 0           0           0           0           |

           15                                                                                                                                      10
      2 : S   <---------------------------------------------------------------------------------------------------------------------------------- S   : 2
                 {0} | 32a-36b-30c 0           0           0           0           0           0           0           0          0           |
                 {2} | 0           32a-36b-30c 0           0           0           0           0           0           0          0           |
                 {2} | 0           0           32a-36b-30c 0           0           0           0           0           0          0           |
                 {2} | 0           0           0           32a-36b-30c 0           0           0           0           0          0           |
                 {3} | 0           0           0           0           0           0           0           0           0          0           |
                 {2} | 0           0           0           0           32a-36b-30c 0           0           0           0          0           |
                 {2} | 0           0           0           0           0           32a-36b-30c 0           0           0          0           |
                 {2} | 0           0           0           0           0           0           32a-36b-30c 0           0          0           |
                 {3} | 0           0           0           0           0           0           0           0           0          0           |
                 {4} | 0           0           0           0           0           0           0           32a-36b+42c -19c       19c         |
                 {4} | 0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    |
                 {4} | 0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      |
                 {4} | 0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        |
                 {4} | 0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     |
                 {4} | 0           0           0           0           0           0           0           -29a        24a        24a-36b-30c |

           34                                                                                                                                                                                                                                                                         20
      3 : S   <--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- S   : 3
                 {0} | 32a-36b-30c 0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           32a-36b-30c 0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           32a-36b-30c 0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           0           32a-36b-30c 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                        |
                 {2} | 0           0           0           0           32a-36b-30c 0           0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           0           0           0           32a-36b-30c 0           0           0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           0           0           0           0           32a-36b-30c 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                        |
                 {2} | 0           0           0           0           0           0           0           32a-36b-30c 0           0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           0           0           0           0           0           0           32a-36b-30c 0           0           0          0           0           0          0           0           0          0           0                        |
                 {2} | 0           0           0           0           0           0           0           0           0           32a-36b-30c 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                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           32a-36b+42c -19c       19c         0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           29b+10c     19b-29c    -19b+22c    0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a+29c    -19a-24c   19a+8c      0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -10b        32a-7b-30c -22b        0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -10a-29b    29a+24b    -22a-8b     0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           -29a        24a        24a-36b-30c 0           0          0           0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           32a-36b+42c -19c       19c         0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           29b+10c     19b-29c    -19b+22c    0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a+29c    -19a-24c   19a+8c      0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10b        32a-7b-30c -22b        0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -10a-29b    29a+24b    -22a-8b     0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           -29a        24a        24a-36b-30c 0           0          0           0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           32a-36b+42c -19c       19c         0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           29b+10c     19b-29c    -19b+22c    0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a+29c    -19a-24c   19a+8c      0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10b        32a-7b-30c -22b        0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -10a-29b    29a+24b    -22a-8b     0                        |
                 {4} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           -29a        24a        24a-36b-30c 0                        |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           19a2+19b2+32ac-36bc+42c2 |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           -22a2-32ab+7b2+30bc-10c2 |
                 {5} | 0           0           0           0           0           0           0           0           0           0           0           0          0           0           0          0           0           0          0           24a2-36ab-24b2-30ac-29c2 |

o28 : SimplicialModuleMap

i29 : assert(source h === prune source f)

i30 : assert(target h === prune target f)

Ways to use this method:

minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module
minimalPresentation(SimplicialModuleMap)

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SimplicialModules/SimplicialModuleDOC.m2:1255:0.

minimalPresentation(SimplicialModule) -- minimal presentation of all terms in a simplicial module

Description

See also

Ways to use this method: