ncLeftIdeal -- Define a left ideal in a noncommutative ring

Synopsis

Usage:

I = ncLeftIdeal fs
Inputs:
- fs, an instance of the type NCRingElement, or a List of NCRingElements
Outputs:
- I, an instance of the type NCLeftIdeal,

Description

This defines a left ideal in a noncommutative ring. Not much can be done with these objects at this point (as one can tell by the dearth of operations that take an NCLeftIdeal as input), but eventually it will be a 'fully featured' object.

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

Ways to use ncLeftIdeal :

ncLeftIdeal(List)
ncLeftIdeal(NCRingElement)

For the programmer

The object ncLeftIdeal is a method function.