twoSidedNCGroebnerBasisBergman -- Calls Bergman to compute a two sided noncommutative Groebner Basis.

Synopsis

• Usage:

  twoSidedNCGroebnerBasisBergman I

• Inputs:
  • I, an instance of the type NCIdeal, or a List of NCRingElements
• Optional inputs:
  • DegreeLimit => an integer, default value 10, specifies the maximum degree for the Groebner basis calculation
  • NumModuleVars => an integer, default value 0, specifies the number of module variables in the ring of the Groebner basis
  • MakeMonic => a Boolean value, default value true, specifies whether the Bergman output should be made monic
  • CacheBergmanGB => a Boolean value, default value true, specifies whether or not to cache the Groebner basis for later use
• Outputs:
  • an instance of the type NCGroebnerBasis,

Description

i1 : A = QQ{x,y,z}

o1 = A

o1 : NCPolynomialRing

i2 : p = y*z + z*y - x^2

            2
o2 = zy+yz-x

o2 : A

i3 : q = x*z + z*x - y^2

         2
o3 = zx-y +xz

o3 : A

i4 : r = z^2 - x*y - y*x

      2
o4 = z -yx-xy

o4 : A

i5 : I = ncIdeal {p,q,r}

                             2      2      2
o5 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy}

o5 : NCIdeal

i6 : Igb = twoSidedNCGroebnerBasisBergman 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