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

Synopsis

Usage:
bas = basis(n,B)
Function: basis
Inputs:
- n, an integer
- I, an object of class NCRing
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 graded 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 = ncIdeal{p,q,r}

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

o5 : NCIdeal

i6 : B = A/I
--Calling Bergman for NCGB calculation.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12160-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12160-0/3.ter ... Complete!

o6 = B

o6 : NCQuotientRing

i7 : bas = basis(4,B)

     |  4   2           3          2 2     2    3   4   3          2            2    3  |
o7 = | x   x yx  yxyx  x y  xyxy  x y   yxy   xy   y   x z  xyxz  x yz  yxyz  xy z  y z |

o7 : NCMatrix