map(LabeledModule,LabeledModule,LabeledModuleMap) -- creates a new LabeledModuleMap from a given LabeledModuleMap

Synopsis

Function: map
Usage:

map(F,G,f)
Inputs:
- F, a free module with labeled basis,
- G, a free module with labeled basis,
- f, a map of labeled modules,
Optional inputs:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- a map of labeled modules,

Description

This function produces has the same output map(F,G,matrix f). This function is most useful when the either source/target of $f$ is isomorphic to $F/G$ as a module with basis, but not as a labeled module.

i1 : S=QQ[x,y,z];

i2 : A=labeledModule(S^2)

      2
o2 = S

o2 : free S-module with labeled basis

i3 : F=(A**A)**A

      8
o3 = S

o3 : free S-module with labeled basis

i4 : G=A**(A**A)

      8
o4 = S

o4 : free S-module with labeled basis

i5 : f=map(F,G,id_(F))

o5 = | 1 0 0 0 0 0 0 0 |
     | 0 1 0 0 0 0 0 0 |
     | 0 0 1 0 0 0 0 0 |
     | 0 0 0 1 0 0 0 0 |
     | 0 0 0 0 1 0 0 0 |
     | 0 0 0 0 0 1 0 0 |
     | 0 0 0 0 0 0 1 0 |
     | 0 0 0 0 0 0 0 1 |

             8       8
o5 : Matrix S  <--- S

Ways to use this method: