normalFormBergman -- Calls Bergman for a normal form calculation

Synopsis

Usage:

nfList = normalFormBergman(L,Igb)
Inputs:
- L, an instance of the type NCRingElement, or a List of NCRingElements
- Igb, an instance of the type NCGroebnerBasis,
Outputs:
- nfList, a list,

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 a method function with options.