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

Synopsis

• Function: basis

• Usage:

  bas = basis(n,B)

• Inputs:
  • n, an integer,
  • I, an instance of the type NCRing,
• 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 : B = A/I
--Calling Bergman for NCGB calculation.
Complete!

o6 = B

o6 : NCQuotientRing

i7 : bas = basis(4,B)

o7 = | x^4 x^2*y*x y*x*y*x x^3*y x*y*x*y x^2*y^2 y*x*y^2 x*y^3 y^4 x^3*z x*y*x*z x^2*y*z y*x*y*z x*y^2*z y^3*z |

o7 : NCMatrix