Macaulay2 » Documentation
Packages » OIGroebnerBases > leadTerm(VectorInWidth)
next | previous | forward | backward | up | index | toc

leadTerm(VectorInWidth) -- get the lead term of an element of a free OI-module

Synopsis

Description

Returns the lead term 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 : leadTerm 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

Ways to use this method: