use(ModuleInWidth) -- use a component of a free OI-module

Function: use
Usage:

use M
Inputs:
- M, an instance of the type ModuleInWidth,

Description

This method invokes use on the underlying polynomial ring of M. This is useful since distinct components of a free OI-module need not be modules over the same polynomial ring.

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

i2 : F = makeFreeOIModule(e, {1,1,2}, P);

i3 : installGeneratorsInWidth(F, 1);

i4 : installGeneratorsInWidth(F, 2);

i5 : use F_1; b1 = x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2)

o6 = x   e        + x   e
      1,1 1,{1},1    2,1 1,{1},2

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

i7 : use F_2; b2 = x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3)

o8 = x   x   e        + x   x   e
      1,2 1,1 2,{2},2    2,2 2,1 2,{1, 2},3

                                 5
o8 : (QQ[x   , x   , x   , x   ])  in width 2
          2,2   2,1   1,2   1,1

Ways to use this method:

use(ModuleInWidth) -- use a component of a free OI-module

The source of this document is in OIGroebnerBases.m2:2177:0.