map(LabeledModule,LabeledModule,ZZ) -- creates scalar multiplication by an integer as a LabeledModuleMap

Synopsis

Function: map
Usage:

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

Description

This function produces essentially the same output as map(Module,Module,ZZ), except that the output map belongs to the class LabeledModuleMap, and thus remembers the labeled module structure of the source and target. If $m=0$ then the output is the zero map. If $m\ne 0$, then $F$ and $G$ must have the same rank.

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

i2 : F=labeledModule(S^3);

o2 : free S-module with labeled basis

i3 : G=labeledModule(S^2);

o3 : free S-module with labeled basis

i4 : g=map(F,G,0)

o4 = 0

             3       2
o4 : Matrix S  <--- S

i5 : h=map(F,F,1)

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

             3       3
o5 : Matrix S  <--- S

Ways to use this method: