# normalFormBergman -- Calls Bergman for a normal form calculation

## Synopsis

• Usage:
nfList = normalFormBergman(L,Igb)
• Inputs:
• Outputs:

## Description

This method takes a list of NCRingElements and calls Bergman to reduce each element to normal form relative to the given NCGroebnerBasis for the NCIdeal defining the NCRing to which the list elements belong.

 i1 : A = QQ{x,y,z} o1 = A o1 : NCPolynomialRing i2 : f = y*z + z*y - x^2 2 o2 = zy+yz-x o2 : A i3 : g = x*z + z*x - y^2 2 o3 = zx-y +xz o3 : A i4 : h = z^2 - x*y - y*x 2 o4 = z -yx-xy o4 : A i5 : I = ncIdeal {f,g,h} 2 2 2 o5 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy} o5 : NCIdeal i6 : Igb = ncGroebnerBasis I --Calling Bergman for NCGB calculation. Complete! 2 2 2 o6 = y x-xy ; Lead Term = (y x, 1) 2 2 2 yx -x y; Lead Term = (yx , 1) 2 zx-y +xz; Lead Term = (zx, 1) 2 zy+yz-x ; Lead Term = (zy, 1) 2 2 z -yx-xy; Lead Term = (z , 1) o6 : NCGroebnerBasis i7 : normalFormBergman(z^17,Igb) --Calling Bergman for NF calculation for 1 elements. Complete! Writing bergman input file. Writing bergman init file. 2 2 3 3 4 4 5 5 6 6 7 7 8 8 o7 = yxyxyxyxyxyxyxyxz+xyxyxyxyxyxyxyxyz+8x yxyxyxyxyxyxy z+8x yxyxyxyxyxy z+28x yxyxyxyxy z+28x yxyxyxy z+56x yxyxy z+56x yxy z+70x y z o7 : A

## Ways to use normalFormBergman :

• "normalFormBergman(List,NCGroebnerBasis)"
• "normalFormBergman(NCRingElement,NCGroebnerBasis)"

## For the programmer

The object normalFormBergman is .