RingElement * VectorInWidth -- multiply an element of a free OI-module by a ring element

Operator: *
Usage:

r * f
Inputs:
- r, a ring element,
- f, an instance of the type VectorInWidth,
Outputs:
- an instance of the type VectorInWidth,

Description

Multiplies f by r provided that r belongs to the underlying polynomial ring of the component in which f lives.

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

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

i3 : installGeneratorsInWidth(F, 2);

i4 : f=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)

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

i5 : (x_(1,2)+x_(2,2)^2)*f

       2                  2              2                                     3                                 2
o5 = -x   x   e        - x   e        + x   x   e        + x   x   e        - x   e        - x   x   e        + x   x   e        + x   x   e
       2,2 1,2 2,{2},1    1,2 2,{2},1    2,2 1,1 2,{1},1    1,2 1,1 2,{1},1    2,2 2,{2},2    2,2 1,2 2,{2},2    2,2 2,1 2,{1},2    2,1 1,2 2,{1},2

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

Ways to use this method:

RingElement * VectorInWidth -- multiply an element of a free OI-module by a ring element

The source of this document is in OIGroebnerBases.m2:2339:0.