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

Synopsis

Usage:
bas = basis(n,I)
Function: basis
Inputs:
- n, an integer
- I, an object of class NCRightIdeal
Optional inputs:
- Degree => ...,
- Limit => ...,
- SourceRing => ...,
- Truncate => ...,
- Variables => ...,
Outputs:
- bas, an object of class NCMatrix

Description

This command returns a basis (or minimal generating set, if the ground ring is not a field), of a homogeneous right ideal in a noncommutative ring.

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 = ncRightIdeal{p,q,r}

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

o5 : NCRightIdeal

i6 : bas = basis(3,I)

     |   2  2                3   2    2           3        2      2    2        2       2    2        2  2    3         |
o6 = | zx -y x+xzx  zyx+yzx-x   z x-yx -xyx  zxy-y +xzy  zy +yzy-x y  z y-yxy-xy   zxz-y z+xz   zyz+yz -x z  z -yxz-xyz |

o6 : NCMatrix