leadMonomial(VectorInWidth) -- get the lead monomial of an element of a free OI-module

Function: leadMonomial
Usage:

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

Description

Returns the lead monomial of an element of a free OI-module according to the specified OIMonomialOrder.

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 : leadMonomial f

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

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

Caveat

Asking for the lead monomial of a zero element will cause an error.

Ways to use this method:

leadMonomial(VectorInWidth) -- get the lead monomial of an element of a free OI-module

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OIGroebnerBases.m2:2247:0.