installGeneratorsInWidth -- install the generators for a component of a free OI-module in a specified width

Synopsis

Usage:

installGeneratorsInWidth(F, n)
Inputs:
- F, an instance of the type FreeOIModule,
- n, an integer,

Description

This method assigns the generators of the width n component of F to the appropriate IndexedVariable corresponding to the basis symbol of F.

i1 : P = makePolynomialOIAlgebra(2, x, QQ);

i2 : F = makeFreeOIModule(e, {1,1}, P);

i3 : installGeneratorsInWidth(F, 2);

i4 : e_(2,{1},1)

o4 = 1e
       2,{1},1

                                 4
o4 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

i5 : e_(2,{1},2)

o5 = 1e
       2,{1},2

                                 4
o5 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

i6 : e_(2,{2},1)

o6 = 1e
       2,{2},1

                                 4
o6 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

i7 : e_(2,{2},2)

o7 = 1e
       2,{2},2

                                 4
o7 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

i8 : x_(1,1)*e_(2,{1},1)+x_(2,1)*e_(2,{1},2)-x_(1,2)*e_(2,{2},1)-x_(2,2)*e_(2,{2},2)

o8 = -x   e        + x   e        - x   e        + x   e
       1,2 2,{2},1    1,1 2,{1},1    2,2 2,{2},2    2,1 2,{1},2

                                 4
o8 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

Ways to use installGeneratorsInWidth:

installGeneratorsInWidth(FreeOIModule,ZZ)

For the programmer

The object installGeneratorsInWidth is a method function.