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

Synopsis

• Function: basis

• Usage:

  bas = basis(n,I)

• Inputs:
  • n, an integer,
  • I, an instance of the type NCLeftIdeal,
• 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 = ncLeftIdeal{p,q,r}

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

o5 : NCLeftIdeal

i6 : bas = basis(3,I)

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

o6 : NCMatrix