VectorInWidth - VectorInWidth -- subtract an element of a free OI-module from another

Operator: -
Usage:

f - g
Inputs:
- f, an instance of the type VectorInWidth,
- g, an instance of the type VectorInWidth,
Outputs:
- an instance of the type VectorInWidth,

Description

Subtracts g from f.

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

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

i3 : installGeneratorsInWidth(F, 3);

i4 : f = x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2)

o4 = x   x   e        + x   x   e
      1,2 1,1 3,{2},1    2,2 2,1 3,{1, 3},2

                                             6
o4 : (QQ[x   , x   , x   , x   , x   , x   ])  in width 3
          2,3   2,2   2,1   1,3   1,2   1,1

i5 : g = x_(2,2)*x_(2,1)*e_(3,{1,3},2)+x_(2,1)*e_(3,{1,2},2)

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

                                             6
o5 : (QQ[x   , x   , x   , x   , x   , x   ])  in width 3
          2,3   2,2   2,1   1,3   1,2   1,1

i6 : f - g

o6 = x   x   e        - x   e
      1,2 1,1 3,{2},1    2,1 3,{1, 2},2

                                             6
o6 : (QQ[x   , x   , x   , x   , x   , x   ])  in width 3
          2,3   2,2   2,1   1,3   1,2   1,1

Ways to use this method:

VectorInWidth - VectorInWidth -- subtract an element of a free OI-module from another

The source of this document is in OIGroebnerBases.m2:2385:0.