basis(ZZ,NCIdeal) -- Returns a basis of an NCIdeal in a particular degree.

Synopsis

• Function: basis

• Usage:

  bas = basis(n,I)

• Inputs:
  • n, an integer,
  • I, an instance of the type NCIdeal,
• Optional inputs:
  • Degree => ..., default value null,
  • Limit => ..., default value infinity,
  • SourceRing => ..., default value null,
  • Strategy => ..., default value null,
  • Truncate => ..., default value false,
  • Variables => ..., default value null,
• Outputs:
  • bas, an instance of the type NCMatrix,

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 : bas = basis(3,I)

o6 = | z*x^2-y^2*x+x*z*x z*y*x+y*z*x-x^3 z^2*x-y*x^2-x*y*x -y*x^2+x^2*y -y^2*x+x*y^2 z*x*y-y^3+x*z*y z*y^2+y*z*y-y*x^2 z^2*y-y^2*x-y*x*y -z*x^2+x^2*z -z*y*x-y^3+y*x*z+x^3 -z*y^2+z*x*z+y*x^2+x*y*x -z*x*y+y^3+x*y*z-x^3 -z*y^2+y^2*z z*y*z-z*x^2+y^2*x+y*x*y -y*x^2+x*z^2-x*y*x y*z^2-y^2*x-y*x*y z^3-z*y*x-z*x*y |

o6 : NCMatrix