labeledModule -- makes a labeled module

Synopsis

Usage:

labeledModule M

labeledModule R
Inputs:
- M, a module, which is free
- R, a ring,
Outputs:
- a free module with labeled basis,

Description

This is the basic construction for a LabeledModule. Given a free module $M$ of rank $r$, this constructs a labeled module with basis labeled by $\{0,..,r-1\}$ and no underlying modules.

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

i2 : E = labeledModule S^3

      3
o2 = S

o2 : free S-module with labeled basis

i3 : basisList E

o3 = {0, 1, 2}

o3 : List

i4 : underlyingModules E

o4 = {}

o4 : List

i5 : module E

      3
o5 = S

o5 : S-module, free

i6 : rank E

o6 = 3

For technical reasons, it is often convenient to construct a rank $1$ free module whose generator is labeled by the empty set. This is constructed by labeledModule S.

i7 : S = ZZ/101[a,b,c];

i8 : F = labeledModule S

      1
o8 = S

o8 : free S-module with labeled basis

i9 : basisList F

o9 = {{}}

o9 : List

i10 : underlyingModules F

o10 = {}

o10 : List

i11 : module F

       1
o11 = S

o11 : S-module, free

i12 : E = labeledModule S^1

       1
o12 = S

o12 : free S-module with labeled basis

i13 : basisList E

o13 = {0}

o13 : List

i14 : underlyingModules E

o14 = {}

o14 : List

Ways to use labeledModule :

labeledModule(Module)
labeledModule(Ring)

For the programmer

The object labeledModule is a method function.