normalForm -- Represent a bracket polynomial in a normal form with respect to a Groebner basis

Description

The relations between brackets generate an ideal, which are the classic Plücker relations. A Groebner basis for this ideal allows one to represent a polynomial in brackets in a unique normal form.

i1 : B = bracketRing(4,2)

o1 = B
      4,2

o1 : BracketRing

i2 : f = [1 2]_B * [3 4]_B - [1 3]_B * [2 4]_B + [1 4]_B * [2 3]_B

o2 = [23]*[14]-[24]*[13]+[34]*[12]

o2 : GCExpression

i3 : normalForm(f)

o3 = 0

o3 : GCExpression

See also Bracket, toBracketPolynomial, and bracketRing

Ways to use normalForm:

normalForm(GCExpression)

For the programmer

The object normalForm is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Brackets.m2:564:0.