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